Tesi sul tema "Modality (Logic)"

There’s a venerable tradition in philosophy to look to our concepts when it comes to appreciating facts about absolute real modality, i.e. how things can and must be in an absolute sense. Given the absence of a modal sensorium, the traditional model stated that modal facts have something to do with conceptual relations. Squares must be four-­‐sided, for example, because the concept having four sides is part of the concept square. If this example could be generalised, it would not only provide a model for the epistemology of modality, it would also explain why much of our modal knowledge is a priori. The fact that we plausibly don’t need any empirical information in order to understand our concepts would explain why their analysis, and the subsequent appreciation of the corresponding modal facts, can be had from the armchair. In the wake of an externalist and scientistic trend in philosophy in the latter half of the 20th century, this model has come under severe attack. Orthodoxy has it now that concepts were the wrong place to look. Not only are there substantial modal facts whose recognition requires empirical investigation, even the application conditions, i.e. meanings, of many concepts are essentially a posteriori. This thesis rehearses the main arguments for rejecting the tradition, defends its central tenets and urges that, while the externalist arguments provide important insights, they do nothing to overturn the traditional model, but rather point to where it needs qualification. It spells out how we must understand its key notions—meaning, apriority, modality—in order to retain what is plausible about the traditional model. It is argued that an appeal to concepts in modal epistemology is inevitable, and that this is a tradition to foster.

Thesis (Ph. D.)--University of California, San Diego, 2008.
Title from first page of PDF file (viewed December 5, 2008). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 160-164).

ModaI logic is concerned with the logic of necessity and possibility. The central problem of modal ontology is summed up in the following question, "What are the ontological commitments of the user of modal terminology? " This thesis is primarily about the ontological commitments that Aristotle made when he employed modal terms. Aristotle’s modal ontology is h e r e analysed in conjunction with four modal problems. My primary objective, is to clarify some of the discussions of Aristotle's modal ontology that have been advanced by certain twentieth century philosophers. The first problem to be considered is the famous ' sea battle’ argument of De Interpretatione 9 . Here is a summary of the problem: If it is currently true that there will be a sea battle tomorrow, then in some sense it is inevitable that there will in fact be a sea battle; if predictions are true, is not a form of determinism being supported? One analysis in particular is studied at length, namely that of Jaakko Hintikka. Hintikka holds that the sea battle argument is best Interpreted if the metaphysical principle of plenitude is attributed to Aristotle. The principle of plenitude effectively merges modality with temporality; what is necessarily the case is always true, and vice versa. Hintikka also interprets Aristotle's stand on the ‘Master Argument’ of Diodorus in light of the attribution of the principle of plenitude to Aristotle. Diodorus' argument is the second of the four problems that this essay considers,. Unlike Aristotle, Diodorus appears to have favored a strong version of determinism. According to Hintikka, Diodorus actually strove to prove the principle of plenitude (as opposed to assuming it, as Aristotle presumably did). I am very sceptical regarding Hintikka's interpretations of these two problems. The sea battle argument is not adequately answered by the solution which Hintikka sees Aristotle adopting. Alternative answers are relatively easy to come by. The evidence cited by Hintikka for ascribing the principle of plenitude is, it is shown, somewhat inconclusive. As for the Master Argument, there is a great deal of paucity in regards to textual evidence. Hinikka himself virtually concedes this point. (Thus, whereas I feel it to be incumbent to offer an alternative interpretation of the sea battle argument, I do not share this attitude towards the Master Argument.) The third and fourth problems play a key role in twentieth century analytic philosophy. Both were first formulated by W.V. Quine in the forties. These problems are somewhat subtle and will not be explained further. Suffice it to say that an analysis of Aristotle's works by Alan Code reveals that the Stagirite had an answer to Quine's criticisms of modal logic.
Arts, Faculty of
Philosophy, Department of
Graduate

Orientador: Marcelo Esteban Coniglio
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas
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Resumo: Esse é um estudo sobre a viabilidade de matrizes finitas como semântica para lógica modal. Separamos nossa análise em dois casos: matrizes determinísticas e não-determinísticas. No primeiro caso, generalizamos o Teorema de Incompletude de Dugundji, garantindo que uma vasta família de lógicas modais não pode ser caracterizada por matrizes determinísticas finitas. No segundo caso, ampliamos a semântica de matrizes não- determinísticas para lógica modal proposta independentemente por Kearns e Ivlev. Essa ampliação engloba sistemas modais que, de acordo com nossa generalização, não podem ser caracterizados por matrizes determinísticas finitas
Abstract: This is a study on the feasibility of finite matrices as semantics for modal logics. We separate our analysis into two cases: deterministic and non-deterministic matrices. In the first case, we generalize Dugundji's Incompleteness Theorem, ensuring that a wide family of modal logic cannot be characterized by deterministic finite matrices. In the second, we extend the non-deterministic matrices semantics to modal logics proposed independently by Kearns and Ivlev. This extension embraces modal systems that, according to our generalization, cannot be characterized by finite deterministic matrices
Doutorado
Filosofia
Doutor em Filosofia

In the last 30 years there has been growing interest in and a greater appreciation of the unique contributions that medieval authors have made to the history of logic. In this thesis, we compare and contrast the modal logics of Robert Kilwardby and John Buridan and explore how their two conceptions of modality relate to and differ from modern notions of modal logic. We develop formal reconstructions of both authors' logics, making use of a number of different formal techniques. In the case of Robert Kilwardby we show that using his distinction between per se and per accidens modalities, he is able to provide a consistent interpretation of the apodictic fragment of Aristotle's modal syllogism and that, by generalising this distinction to hypothetical construction, he can develop an account of connexive logic. In the case of John Buridan we show that his modal logic is a natural extension of the usual Kripke-style possible worlds semantics, and that this modal logic can be shown to be sound and complete relative to a proof-theoretic formalisation of Buridan's treatment of the expository syllogism.

Modal logics have found applications in many diferent contexts. For example, epistemic modal logics can be used to reason about security protocols, temporal modal logics can be used to reason about the correctness of distributed systems and propositional dynamic logic can reason about the correctness of programs. However, pure modal logic is expressively weak and cannot represent many interesting secondorder properties that are expressible, for example, in the μ-calculus. Here we investigate the extension of modal logics with propositional quantification modulo bisimulation (bisimulation quantification). We extend existing work on bisimulation quantified modal logic by considering the variety of logics that result by restricting the structures over which they are interpreted. We show this can be a natural extension of modal logic preserving the intuitions of both modal logic and propositional quantification. However, we also find cases where such intuitions are not preserved. We examine cases where the axioms of pure modal logic and propositional quantification are preserved and where bisimulation quantifiers preserve the decidability of modal logic. We translate a number of recent decidability results for monadic second-order logics into the context of bisimulation quantified modal logics, and show how these results can be used to generate a number of interesting bisimulation quantified modal logics.

In this paper, I begin to develop a theory called Paradise on the Cheap - in so doing, I intend to provide a rival to David Lewis' modal realism. Paradise on the Cheap grounds possibilia in the features of the actual world; and so, it does not require realist commitments to the existence of non-actual worlds and individuals. I explain modality, conterfactuals, content, and properties in terms of recombinations of actual-world features, second-order mathematical schemata, and the similarity relations which hold between these things and parts of the actual world. Because the ontology of Paradise on the Cheap promotes unity and economy of theory to a greater extent than does model realism's ontology, I argue that we should accept the former theory instead of the latter. Moreover, I address the question of whether inference to the best explanation is an argumentative strategy that is even available to modal realists.
vii, 141 leaves : ill. ; 28 cm.

This dissertation is devoted to developing modal logical tools that can be used in the field of proof theory and ordinal analysis. More precisely, we focus on the relation between strictly positive modal logics and both Turing progressions and ordinal notation systems. With respect to the former one, we introduce the system TSC that is tailored to generate exactly all relations that hold between different Turing progressions given a particular set of natural consistency notions. We also present an arithmetical interpretation for this modal system, named the Formalized Turing progressions interpretation. The logic is proven to be arithmetically sound and complete with respect to this interpretation. After exploring the arithmetical semantics of TSC, we investigate the relational semantics of this system. For this purpose, we make use of the universal model of the closed fragment of Go¨del-Lo¨b’s Polymodal Logic (GLP), namely Ignatiev’s universal frame. By slightly modifying the relations defined in this model, we obtain a new frame which is proven to be a universal model for TSC. Moreover, we show how the domain of this frame can be reduced to sequences with finite support while keeping the completeness of the system. As for ordinal notations systems, we present the logic BC (for Bracket Calculus). Unlike other provability logics, BC is based on a purely modal signature that gives rise to an ordinal notation system instead of modalities indexed by some ordinal given a priori. Moreover, since the order between these notations can be established in terms of derivability within the calculus, the inferences in this system can be carried out without using any external property of ordinals. The presented logic is proven to be equivalent to Reflection Calculus (RCΓ0 ), that is, to the strictly positive fragment of GLPΓ0 .
El objetivo de esta tesis es desarrollar herramientas de lógica modal que puedan ser utilizadas en el campo de la teoría de la demostración y el análisis ordinal. Más precisamente, nos centramos en la relación entre las lógicas modales estrictamente positivas y las progresiones de Turing, y entre dichas lógicas y los sistemas de notación ordinal que surgen de ellas. Con respecto a la primera parte, hemos introducido el sistema TSC, diseñado para generar exactamente todas las relaciones válidas entre las diferentes progresiones de Turing, dado un conjunto particular de nociones de consistencia naturales. También presentamos una interpretación aritmética para este sistema modal, denominada interpretación de las Progresiones de Turing formalizadas. Demostramos que la lógica es aritméticamente correcta y completa con respecto a esta interpretación. Tras de estudiar la semántica aritmética de TSC, investigamos la semántica relacional de este sistema. Para este propósito, hacemos uso del modelo universal para el fragmento cerrado de Gödel-Löb’s Polymodal Logic (GLP), a saber, el marco universal de Ignatiev. Modificando ligeramente las relaciones definidas en este modelo, obtenemos un nuevo marco. Demostramos que éste es un modelo universal para TSC. Asimismo, mostramos cómo el dominio de este marco puede reducirse a secuencias con soporte finito manteniendo la completud del sistema. Respecto a los sistemas de notación ordinal, presentamos la lógica BC (por Bracket Calculus). A diferencia de otras lógicas de la demostrabilidad, BC se basa en un lenguaje puramente modal que da lugar a un sistema de notación ordinal, en lugar de estar construido mediante modalidades indexadas por algún ordinal dado a priori. Además, ya que el orden entre estas notaciones puede establecerse en términos de derivabilidad dentro del cálculo, las inferencias en este sistema pueden llevarse a cabo sin usar ninguna propiedad externa de los ordinales. Demostramos que la lógica presentada es equivalente al Reflection Calculus (RCΓ0 ), es decir, al fragmento estrictamente positivo de GLPΓ0 .

O presente trabalho tem como objetivo proporcionar aos estudantes que precisem da lógica modal como ferramenta um texto conciso mas suficientemente completo. Embora seja um texto de cunho matemático, procura-se manter o equilíbrio entre os conceitos matemáticos e suas motivações filosóficas, pela crença de que tal equilíbrio é essencial para situar o pensamento em um texto introdutório. O primeiro capítulo começa com um breve histórico filosófico e trabalha os conceitos fundamentais de um ponto de vista sintático. O segundo capítulo retoma os conceitos do primeiro capítulo de um ponto de vista semântico e faz a conexão entre sintaxe e semântica. O terceiro capítulo trabalha o conceito de bissimulação e apresenta ferrametas que abrirão caminho para aplicações.
The goal of this work is to provide the studens who need to deal with modal logic as a tool with a text which might be concise but complete enough at the same time. Although this is a rather mathematical text, an effort is made in order to maintain the equilibrium between mathematical concepts and their philosophical origins for believing this equilibium is of great importance for clarifing the ideas in a work for beginners. The first chapter starts with a brief historical approach of logic and then discusses some fundamental concepts from a syntactical point of view. The second chapter discusses the same concepts from a semantical point of view and links syntact and semantics. The third chapter presents the concept of bisimulation and paves the way for working with applications.

In this thesis we extend BDI logics, which are normal multimodal logics with an arbitrary set of normal modal operators, from three different perspectives. Firstly, based on some recent developments in modal logic, we examine BDI logics from a combining logic perspective and apply combination techniques like fibring/dovetailing for explaining them. The second perspective is to extend the underlying logics so as to include action constructs in an explicit way based on some recent action-related theories. The third perspective is to adopt a non-monotonic logic like defeasible logic to reason about intentions in BDI. As such, the research captured in this thesis is theoretical in nature and situated at the crossroads of various disciplines relevant to Artificial Intelligence (AI). More specifically this thesis makes the following contributions: 1. Combining BDI Logics through fibring/dovetailing: BDI systems modeling rational agents have a combined system of logics of belief, time and intention which in turn are basically combinations of well understood modal logics. The idea behind combining logics is to develop general techniques that allow to produce combinations of existing and well understood logics. To this end we adopt Gabbay's fibring/dovetailing technique to provide a general framework for the combinations of BDI logics. We show that the existing BDI framework is a dovetailed system. Further we give conditions on the fibring function to accommodate interaction axioms of the type G [superscript k,l,m,n] ([diamond][superscript k] [superscript l] [phi] [implies] [superscript m] [diamond][superscript n] [phi]) based on Catach's multimodal semantics. This is a major result when compared with other combining techniques like fusion which fails to accommodate axioms of the above type. 2. Extending the BDI framework to accommodate Composite Actions: Taking motivation from a recent work on BDI theory, we incorporate the notion of composite actions, [pi]-1; [pi]-2 (interpreted as [pi]-1 followed by [pi]-2), to the existing BDI framework. To this end we introduce two new constructs Result and Opportunity which helps in reasoning about the actual execution of such actions. We give a set of axioms that can accommodate the new constructs and analyse the set of commitment axioms as given in the original work in the background of the new framework. 3. Intention reasoning as Defeasible reasoning: We argue for a non-monotonic logic of intention in BDI as opposed to the usual normal modal logic one. Our argument is based on Bratman's policy-based intention. We show that policy-based intention has a defeasible/non-monotonic nature and hence the traditional normal modal logic approach to reason about such intentions fails. We give a formalisation of policy-based intention in the background of defeasible logic. The problem of logical omniscience which usually accompanies normal modal logics is avoided to a great extend through such an approach.

Orientador: Itala Maria Loffredo D'Ottaviano
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas
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Resumo: Esta dissertação tem como objetivo a análise de um resultado em lógica aléticoepistêmica, divulgado por Frederic Fitch em 1963, conhecido como Paradoxo da Cognoscibilidade. Segundo este resultado, se todas verdades podem ser conhecidas, então todas verdades são conhecidas. Isto sugere que há alguma verdade impossível de ser conhecida. Descrevemos, nesta dissertação, a lógica modal alética e a epistêmica, que consistem em recursos formais requeridos para a análise do Paradoxo. Também esclarecemos o papel deste no debate filosófico entre as correntes de pensamento realistas e antirealistas. Apontamos e analisamos duas propostas de solução do Paradoxo mais discutidas na literatura. Como principal ojetivo desta dissertação, investigamos o Paradoxo da Cognoscibilidade em sistemas multiagentes. Demonstramos que, apesar de em tais sistemas o Paradoxo ser minimizado, ele ainda não é completamente resolvido. Por fim, também apresentamos várias formas de obter a contraparte doxástica do Resultado, conhecida como Paradoxo da Credibilidade
Abstract: This text studies a result in epistemic-alethic logic, published by Frederic Fitch in 1963, known as Knowability Paradox. According to this result, if all truths are knowable, then all truths are known. This suggests there are unknowable truths. We describe alethic and epistemic modal logics, which are formal resources required in order to study the paradox. Also, we examine its role in the philosophical debate between realists and anti-realists. We point out and analize two attempts to solve the Paradox. The main aim of this text is to explore the Knowability Paradox in multi-agents systems. We shoe that, although in these systems the Paradox is weaker, it's not entirely solved. We also show many ways to derive the doxastic counterpart of the result, known as Belivability Paradox
Mestrado
Filosofia
Mestre em Filosofia

This thesis is devoted to fragmentalism, a non-standard tense realism introduced by Kit Fine (Modality and Tense: Philosophical Papers. Oxford: OUP, pp. 261-320, 2005). In the first three chapters, I will show how to develop a fragmentalist version of presentism – which I will call fragmentalist presentism – in order to face some of the problems usually ascribed to standard presentism. In particular, the goal of the fist chapter is to search for a way to reconcile the correspondence theory of truth (CTT), i.e., the thesis that truth supervenes on facts, with a presentist metaphysics. According to what we might call unrestricted CTT, the truth of past- and future-tensed sentences supervenes – respectively – on past and future facts. Since the standard presentist denies the existence of past and future entities (and facts concerning them that do not obtain in the present), she seems to lack the resources to accept both past- and future-tensed true sentences and unrestricted CTT. I will argue that by endorsing fragmentalist presentism one can uphold past- and future-tensed truths together with unrestricted CTT. In the second chapter, I argue that the adoption of an unrestricted principle of bivalence is compatible with a metaphysics that (i) denies that the future is real, (ii) adopts nomological indeterminism, and (iii) exploits a branching structure to provide a semantics for future contingent claims. To this end, I will show how to reconcile – within Fine’s non-standard tense realism – a genuinely A-theoretic branching-time model with the idea that there is a branch corresponding to the thin red line, that is, the branch that will turn out to be the actual future history of the world. Many four-dimensionalists think of continuants as mereological sums of stages from different times. These sums would perdure, that is, they would persist by having different stages. This view is generally taken to be incompatible with presentism: if there is no time except the present, then nothing can be a sum of such stages. The aim of the third chapter is to show that fragmentalist presentism provides us with the tools to embrace both a presentist metaphysics and (a non-standard version of) perdurantism. In the last chapter, I will extend the fragmentalist approach to modality, by analysing the modal analogue of fragmentalist presentism. The simplest quantified modal logic is generally regarded as incompatible with actualism, the view that everything there is is actual. It is usually held that whoever wants to preserve the former while embracing the latter is somehow bound to enrich the inventory of the world with entities able to play the role traditionally ascribed to possibilia: abstract individualities or contingently non-concrete entities. I will hold that there is another way to reconcile actualism and the simplest quantified modal logic (a way that commits us to accept neither abstract individualities nor contingently non-concrete entities), by exploiting what we might call fragmentalist actualism.

In the central part of this thesis we study for different interpretability logics the following aspects: completeness for modal semantics, decidability and algorithmic complexity. In particular, we will study two basic types of relational semantics for interpretability logics. One is the Veltman semantics, which we shall refer to as the regular or ordinary semantics; the other is called generalised Veltman semantics. In the recent years and especially during the writing of this thesis, generalised Veltman semantics was shown to be particularly well-suited as a relational semantics for interpretability logics. In particular, modal completeness results are easier to obtain in some cases; and decidability can be proven via filtration in all known cases. We prove various new and reprove some old completeness results with respect to the generalised semantics. We use the method of filtration to obtain the finite model property for various logics. Apart from results concerning semantics in its own right, we also apply methods from semantics to determine decidability (implied by the finite model property) and complexity of provability (and consistency) problems for certain interpretability logics. From the arithmetical standpoint, we explore three different series of interpretability principles. For two of them, for which arithmetical and modal soundness was already known, we give a new proof of arithmetical soundness. The third series results from our modal considerations. We prove it arithmetically sound and also characterise frame conditions w.r.t. ordinary Veltman semantics. We also prove results concerning the new series and generalised Veltman semantics.
El tema d’aquesta tesis són les lògiques d’interpretabilitat les quals descriuen el comportament del predicat d’interpretabilitat. Per tal de discutir la interpretabilitat entre teories matemàtiques, permeteu que primer diguem unes paraules sobre interpretacions. Hi ha diferents nocions d’una interpretació en ús, però una cosa que tenen en comú és que totes involucren una traducció que preserva l’estructura; aquesta traducció transforma formules de la teoria interpretada a formules de la teoria interpretadora. Aquest mapa cal que preservi la demostrabilitat fins a un cert punt, i.e. si A és un teorema de la teoria interpretada, llavors la imatge de A ha de ser demostrable en la teoria interpretadora. Que aquest mapa preservi l’estructura significa que almenys commuta amb les connectives lògiques. Les fórmules quantificades poden ser modificades lleugerament quan són interpretades; específicament hom pot fitar el domini de (totes) les fórmules quantificades fent servir un predicat fixat anomenat domini especificador (i.e. estem interessats en interpretabilitat relativitzada). Això ens permet construir una interpretació de, per exemple, una teoria de nombres en una teoria de conjunts, on (per la construcció habitual) només alguns conjunts es fan servir per representar nombres. Podem requerir els axiomes de la teoria interpretada de ser demostrables en la teoria interpretadora, però també podem requerir que això també es compleixi per tots els teoremes de la teoria interpretada (aquesta diferència és rellevant només quan hom treballa en una metateoria dèbil). Les lògiques d’interpretabilitat descriuen el comportament d’un tipus específic d’interpretabilitat. Per començar, limitem el nostre interès en teories de primer ordre. En segon lloc, només ens concentrem en interpretabilitat entre extensions finites d’una teoria fixada T. En tercer lloc, estem interessats en interpretabilitat formalitzada, i.e, no estudiem el problema de si T + A interpreta T + B, sinó el problema de si T pot demostrar que T + A interpreta T + B. En quart lloc, no estem interessats per quines A i B tenim que T + A interpreta T + B, sinó que estem interessats en aquelles propietats que són estructurals en el sentit que es compleixen per qualsevol tria de A i B. Optem per teoremes d’interpretabilitat en aquesta tesi; i.e. per tal que T + A interpreti T + B hem requerit que la traducció de qualsevol teorema de T + B sigui demostrable en T + A. La teoria T hauria de ser suficientment forta; i.e. seqüencial. Si tal teoria és axiomatitzable, té un predicat IntT(·, ·), definit d’una manera natural, expressant el fet que el primer argument del predicat interpreta el segon argument. La lògica d’interpretabilitat de T és definida d’una manera molt semblant a la lògica de demostrabilitat de T, però amb un operador binari: _; la interpretació corresponent d’aquest operador és IntT. Així, la lògica d’interpretabilitat d’una teoria T és el conjunt de totes les fórmules lògiques modals en el llenguatge de lògiques d’interpretabilitat que són demostrables per qualsevol lectura aritmètica que es doni a les variables proposicionals i prenent els operadors modals a les seves aritmetitzacions corresponents. A diferència del que pot ser el cas en lògiques de demostrabilitat, la lògica d’interpretabilitat de T realment depèn de T. Per exemple, la lògica d’interpretabilitat de la teoria de conjunts de Gödel-Bernays (que és la lògica denominada ILP), i la lògica d’interpretabilitat de l’Aritmètica de Peano (que és la lògica denominada ILM), difereixen. Donada una teoria seqüencial T, hi ha una certa quantitat de contingut, normalment denominat IL(All), que la lògica d’interpretabilitat de T inevitablement ha de tenir. Els continguts exactes de IL(All) no són coneguts; de fet, millorar la fita inferior és la pregunta que motiva la major part de les investigació en aquest camp. Una simple fita és la lògica d’interpretabilitat bàsica, denominada IL. Aquesta és una extensió de la lògica de demostrabilitat i conté cinc esquemes d’axioma addicionals que en la literatura són coneguts com J1-J5. Tornant a la qüestió de IL(All), hi ha una manera interessant i sorprenent de millorar les millors fites inferiors conegudes, i.e. de trobar nous principis d’interpretabilitat aritmèticament vàlids. L’enfocament és estudiar semàntiques relacionals modals (semblant a Kripke). Nous principis aritmèticament vàlids han sorgit prenent les condicions de marc de principis ja coneguts, modificant-les, i llavors obtenint la fórmula modal que caracteritza la condició de marc modificada. Això, efectivament, no garanteix la validesa aritmètica de la fórmula modal obtinguda de tal forma, però noves fórmules aritmèticament vàlides s’han descobert talment. Un altre enfocament relacionat és intentar establir completesa d’una certa extensió de IL. Si la demostració de completesa modal falla per a alguna extensió concreta, estendre l’extensió més enllà, fins que sigui modalment completa, pot produir noves fórmules aritmèticament vàlides (aquest intent serà seguit en el capítol final de la tesi). Hi ha dos tipus de semàntiques modals per lògiques d’interpretabilitat. Una és coneguda com semàntica regular Veltman (o semàntica ordinària Veltman, o només Veltman semantics quan no hi ha risc d’ambigüitat). L’altra és coneguda com semàntica generalitzada Veltman, introduïda per Verbrugge, que combina una semàntica en l’estil de Kripke amb una semàntica de veïnat. La semàntica regular Veltman pot ser usada per demostrar completesa per moltes lògiques d’interpretabilitat. Tanmateix, per lògiques més complexes, la semàntica generalitzada Veltman es poden emprar per donar demostracions de completesa més simples i fàcils d’entendre. En els darrers anys i especialment durant la redacció d’aquesta tesi, la semàntica generalitzada Veltman ha sigut provada de ser particularment ben adequada com a semàntica relacional per lògiques d’interpretabilitat. En particular, resultats sobre completesa modal són més fàcils d’obtenir en alguns casos; i decidibilitat pot ser demostrada via filtració en tots els casos coneguts. Demostrem diversos nous i redemostrem alguns resultats coneguts respecte la semàntica generalitzada.En alguns casos, només sabem que una lògica és completa respecte la semàntica generalitzada Veltman. També hi ha exemples de lògiques completes respecte semàntica generalitzada Veltman però incompletes respecte semàntica regular Veltman. Tots els resultats de complexitat (la majoria dels quals són establerts en aquesta tesi) estan basats en semàntica regular Veltman. Pel que fa a decidibilitat, sembla que la semàntica generalitzada Veltman és una eina més apropiada, ja que permet un mètode uniforme per obtenir la propietat de model finit. En aquesta tesi estudiarem diverses propietats d’interpretabilitat relativitzada formalitzada. En la part central d’aquesta tesi estudiem per diferents lògiques d’interpretabilitat els següents aspectes: completesa per semàntiques modal, decidibilitat i complexitat algorísmica. A banda de resultats al voltant de les semàntiques en el seu si, també apliquem mètodes de semàntiques per determinar la complexitat de problemes de demostrabilitat (i de consistència) per certes lògiques d’interpretabilitat. Des del punt de vista aritmètic, explorem tres sèries diferents de principis d’interpretabilitat. Per dos d’ells, pels quals la solidesa aritmètica i modal ja era coneguda, donem una nova demostració de solidesa aritmètica. La tercera sèrie resulta de les nostres consideracions modals. Demostrem que és sòlida aritmèticament i que també caracteritza condicions de marc respecte semàntica regular Veltman. A més, donem una demostració de completesa per certes lògiques relacionades amb la tercera sèrie (les lògiques ILWR i ILW!). Permeteu que descrivim l’estructura de la tesi. En el Capítol 1 donem una introducció informal del tema general de la tesi. En el Capítol 2 donem una introducció més formal, definicions bàsiques i presentem alguns resultats senzills. En els dos capítols subseqüents explorem completesa modal. Primer introduïm l’eina clau: etiquetes asseguradores. Aquí presentem la teoria general d’etiquetes asseguradores, incloent la noció d’etiquetes asseguradores Γ-completes. Desenvolupem la teoria usada posteriorment en la tesi, però també demostrem resultats interessants per si sols (com la caracterització de Γ-completesa). En el Capítol 4 fem servir etiquetes asseguradores per tal d’obtenir diversos resultats de completes respecte la semàntica generalitzada Veltman. Definim ILX-estructures per X _{M, P,M0, P0, R} i X _ {W,W_} i demostrem que la les lògiques ILX corresponents són completes respecte la seva classe de marcs característica. En particular obtenim que ILP0 i ILR són completes, els quals són resultats nous. També definim el problema d’iteració d’etiqueta i introduïm un tipus especial d’estructures, ILWP-estructures, que poden ser usades per solucionar aquest problema en el cas simple de la lògica ILP. La motivació d’això és que el problema d’iteració d’etiqueta reapareix en lògiques més complexes com ILWR, on la solució encara és desconeguda. Sospitem que la mateixa solució pot ser aplicable fins i tot en lògiques més complexes, però hi ha altres problemes que encara no s’han solucionat en aquest cas. Tornem al tema de completesa en el capítol final de la tesi on entre altres resultats donem una demostració condicional de la completesa de ILWR. En el Capítol 5 apliquem resultats de completesa i obtenim resultats de decidibilitat. Aquest és una aplicació, i potser la més útil, de la semàntica generalitzada: l’habilitat de definir filtracions amb bon comportament. El Capítol 6 tracta la complexitat; demostrem que IL, ILW i ILP són PSPACE-completes. En el Capítol 7 treballem amb l’aspecte aritmètic de les lògiques d’interpretabilitat. Concretament, donem una nova demostració de solidesa per dues sèries de principis recentment descobertes. En el capítol final, Capítol 8, introduïm una altra sèrie de principis, demostrem que és aritmèticament sòlida i la hi donem semàntica ordinària Veltman. Com ja hem mencionat abans, també donem demostracions condicionals de completesa per lògiques relacionades amb aquesta sèrie nova.

The writer has attempted to discuss the distinction between the necessary and the contingent. It begins with a criticism against the possibility for a so-called ‘a possible worlds realism’ to give a “philosophical explanation” of this distinction. The writer argues that this is impossible, since it requires that a notion of this distinction be already accepted (more precisely that the necessity of such a theory is already accepted). After this specific criticism, the writer intends to show that this is a more general problem that follows any explanation of the contingent/necessary distinction. The writer then discusses the counter-argument that the requirements placed on these explanations are set to high, therefore the writer shows in theory the problem can be solved and sketches a more specific way how to explain and show the basis for this distinction.
Författaren har avsett att diskutera distinktionen mellan det nödvändiga och det kontingent. Det börjar med en kritik mot möjligheten för en så kallad ’möjliga världars realism’ att ge en ”filosofisk förklaring” av denna distinktion. Författaren argumenterar för att detta är omöjligt, eftersom det kräver att en sådan distinktion redan är accepterad (mer specifikt att nödvändigheten av en sådan teori redan är accepterad). Efter denna specifika kriticism, så avser författaren visa att detta problem är generellt och att det följer alla försök att förklara den kontingenta/nödvändiga distinktionen. Författaren diskuterar sedan motargumentet att de krav som ställts på dessa förklaringar är för högt ställda, därför visar författaren hur problemet kan lösas i teorin och visar också en förenklad modell av en lösningsmetod.

Orientador: Lucas Angioni
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas
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Resumo: Nesta tese discuto aspectos da logica de Aristóteles que sao ressaltados por abordagens contemporâneas dos Primeiros Analíticos e que mostram uma teoria mais rica e sutil do que tradicionalmente se entende como sendo a lógica aristotelica. Em especial, abordo teses sobre como devem ser compreendidas as proposições categóricas, o que sao precisamente silogismos, o que sao silogismos perfeitos e quais problemas enfrenta a parte da lógica de Aristoteles que lida com proposicoes modais. Nessa direcao, abordo evidencias textuais para duas concepcoes de proposicao categorica e as dificuldades para coaduna-las com as proposicoes singulares. Alem disso, argumento que silogismos devem ser compreendidos como cadeias de predicacoes e que Aristoteles concebe um sistema logico quando procura justificar quais arranjos entre termos formam de fato tais cadeias. Argumento, tambem, que os silogismos perfeitos sao evidentes nesse sistema nao porque considerados indemonstraveis, mas porque podem ser deduzidos a partir de definicoes das proposicoes categoricas e de certas regras gerais, isto e, de regras aplicaveis nao apenas a um tipo de proposicao categorica. Por fim, apresento as caracteristicas gerais e as dificuldades de uma parte da logica de Aristoteles muito pouco associada a logica aristotelica como tradicionalmente entendida: a silogistica modal
Abstract: The present dissertation discusses aspects of Aristotle's Logic which are enhanced by contemporary approaches to Prior Analytics and display a logical theory richer and subtler than what traditionally is comprehended as being the Aristotelian Logic. My main claims concern how categorical propositions must be understood, what is the exact nature of syllogisms, what is a perfect syllogism, as well as some questions in the part of Aristotelian Logic which deals with modal propositions. From an examination of texts that support two different conceptions of categorical proposition, I discuss the difficulties in adjusting each of them to singular propositions. I also argue that syllogisms must be comprehended as chains of predications and that Aristotle conceives a logical system when he proceeds to justify which terms arrangement does produce chains of the required kind. I also argue that in this system perfect syllogisms must be understood as evident not because they are unproved, but because they are deduced from definitions for categorical propositions and from general rules, i.e. rules not applied just to some categorical propositions. Finally, I discuss general features and problems concerning a part of Aristotle's Logic rarely attached to the Aristotelian Logic as traditionally comprehended: the modal syllogistic
Doutorado
Filosofia
Doutor em Filosofia

S’inscrivant dans la philosophie de la connaissance et des sciences, notre étude traite des objets théoriques, selon une perspective modale inédite. Les connaissances théoriques ont pour finalité de porter sur des vérités factuelles,et traditionnellement, on considère par conséquent que ces connaissances peuvent être formulées dans un cadre extensionnel : en termes d’adéquation ou tout au moins de relations avec des objets de notre monde actuel. Mais nous appuyant sur les avancées récentes de la philosophie de la logique modale,nous soutenons que l’entreprise scientifique conçoit des modèles théoriques qui portent sur tout un ensemble de situations, car ils postulent des objets qui sont à considérer dans une perspective modale : les objets théoriques sont intrinsèquement modaux, existant ou pouvant être reconnus dans une pluralité de situations actuelles ou possibles. Cet aspect modal des modèles scientifiques nécessite donc d’examiner l’identification des objets théoriques à travers diverses circonstances alternatives éventuelles. En effet, la question de l’application d’un modèle scientifique, liée au débat fondamental entre réalisme et instrumentalisme, prend selon nous racine dans le problème modal de la reconnaissance d’un objet théorique idéal en un objet actuel ou possible. La notion de modalité nous sera donc utile dans l’analyse fondamentale de l’argumentation scientifique
In the field of the philosophy of knowledge and science, my study deals with theoretical objects in a new modal perspective. Theoretical knowledge is intended to cover factual truths and therefore one traditionally considers that this knowledge can be formulated in an extensional framework: in terms of adequacy, or, at least, of relationships with objects of our actual world. But basing my work on recent advances in the philosophy of modal logic, I will argue that scientific enterprise develops theoretical models about a variety of situations because they postulate objects that have to be considered in a modal perspective: theoretical objects are intrinsically modal, existing or recognizable in a plurality of actual or possible situations. Therefore, this modal aspect of scientific models requires that the identification of theoretical objects across various possible alternative circumstances should be examined. Indeed, the issue of the application of a scientific model, linked to the fundamental debate between realism and instrumentalism, lies with recognizing an ideal theoretical object in an actual or possible object. The concept of modality will also be useful in the fundamental analysis of scientific argumentation

According to Zadeh, the term “fuzzy logic” has two different meanings: wide and narrow. In a narrow sense it is a logical system which aims a formalization of approximate reasoning, and so it can be considered an extension of many-valued logic. However, Zadeh also says that the agenda of fuzzy logic is quite different from that of traditional many-valued logic, as it addresses concepts like linguistic variable, fuzzy if-then rule, linguistic quantifiers etc. Hájek, in the preface of his foundational book Metamathematics of Fuzzy Logic, agrees with Zadeh’s distinction, but stressing that formal calculi of many-valued logics are the kernel of the so-called Basic Fuzzy logic (BL), having continuous triangular norms (t-norm) and their residua as semantics for the conjunction and implication respectively, and of its most prominent extensions, namely Lukasiewicz, Gödel and Product fuzzy logics. Taking advantage of the fact that a t-norm has residuum if, and only if, it is left-continuous, the logic of the left-continuous t-norms, called MTL, was soon after introduced. On the other hand, classical modal logic is an active field of mathematical logic, originally introduced at the beginning of the XXth century for philosophical purposes, that more recently has shown to be very successful in many other areas, specially in computer science. That are the most well-known semantics for classical modal logics. Modal expansions of non-classical logics, in particular of many-valued logics, have also been studied in the literature. In this thesis we focus on the study of some modal logics over MTL, using natural generalizations of the classical Kripke relational structures where propositions at possible words can be many-valued, but keeping classical accessibility relations. In more detail, the main goal of this thesis has been to study modal expansions of the logic of a left-continuous t-norm, defined over the language of MTL expanded with rational truth-constants and the Monteiro-Baaz Delta-operator, whose intended (standard) semantics is given by Kripke models with crisp accessibility relations and taking the unit real interval [0, 1] as set of truth-values. To get complete axiomatizations, already known techniques based on the canonical model construction are uses, but this requires to ensure that the underlying (propositional) fuzzy logic is strongly standard complete. This constraint leads us to consider axiomatic systems with infinitary inference rules, already at the propositional level. A second goal of the thesis has been to also develop and automated reasoning software tool to solve satisfiability and logical consequence problems for some of the fuzzy logic modal logics considered. This dissertation is structured in four parts. After a gentle introduction, Part I contains the needed preliminaries for the thesis be as self-contained as possible. Most of the theoretical results are developed in Parts II and III. Part II focuses on solving some problems concerning the strong standard completeness of underlying non-modal expansions. We first present and axiomatic system for the non-nodal propositional logic of a left-continuous t-norm who makes use of a unique infinitary inference rule, the “density rule”, that solves several problems pointed out in the literature. We further expand this axiomatic system in order to also characterize arbitrary operations over [0, 1] satisfying certain regularity conditions. However, since this axiomatic system turn out to be not well-behaved for the modal expansion, we search for alternative axiomatizations with some particular kind of inference rules (that will be called conjunctive). Unfortunately, this kind of axiomatization does not necessarily exist for all left-continuous t-norms (in particular, it does not exist for the Gödel logic case), but we identify a wide class of t-norms for which it works. This “well-behaved” t-norms include all ordinal sums of Lukasiewiczand Product t-norms. Part III focuses on the modal expansion of the logics presented before. We propose axiomatic systems (which are, as expected, modal expansions of the ones given in the previous part) respectively strongly complete with respect to local and global Kripke semantics defined over frames with crisp accessibility relations and worlds evaluated over a “well-behaved” left-continuous t-norm. We also study some properties and extensions of these logics and also show how to use it for axiomatizing the possibilistic logic over the very same t-norm. Later on, we characterize the algebraic companion of these modal logics, provide some algebraic completeness results and study the relation between their Kripke and algebraic semantics. Finally, Part IV of the thesis is devoted to a software application, mNiB-LoS, who uses Satisfability Modulo Theories in order to build an automated reasoning system to reason over modal logics evaluated over BL algebras. The acronym of this applications stands for a modal Nice BL-logics Solver. The use of BL logics along this part is motivated by the fact that continuous t-norms can be represented as ordinal sums of three particular t-norms: Gödel, Lukasiewicz and Product ones. It is then possible to show that these t-norms have alternative characterizations that, although equivalent from the point of view of the logic, have strong differences for what concerns the design, implementation and efficiency of the application. For practical reasons, the modal structures included in the solver are limited to the finite ones (with no bound on the cardinality).

Orientador: Itala M. Loffredo D'Ottaviano
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas
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Resumo: O presente trabalho tem por objetivo examinar, sob a perspectiva lógico- filosófica da paraconsistência e da modalidade, as relações entre os conceitos lógico-filosófico-formais de negação paraconsistente e o conceito de modalidade. Nosso objetivo central consiste no exame de um operador modal de negação paraconsistente. Examinamos conhecidos resultados envolvendo os operadores modais e paraconsistentes, como as lógicas modais normais K, T, S4, S5 e outras lógicas modais; algumas lógicas paraconsistentes, incluindo a lógica modal paraconsistente Z. Além disso, realizamos uma análise crítica concernente às relações entre o conhecido Quadrado de Oposições Aristotélico e a negação paraconsistente, contribuindo para o tema com alguns argumentos. Finalmente, investigamos a questão de como a generalização do Quadrado de Oposições Aristotélico, dita Teoria de n-Oposições, se relaciona com o tema da modalidade, da paraconsistência e da geometrização lógica, propondo idéias para este último.
Abstract: The present work aims to investigate, under the logical-philosophical perspective of paraconsistency and modality, relations between the logical-philosophical-formal concept of paraconsistent negation and the concept of modality. Our main task is the analysis of a modal operator of paraconsistent negation. We have examined some known results involving modal and paraconsistent operators, such as the modal normal logics K, T, S4, S5 and other modal logics; some paraconsistent logics, including modal paraconsistent logic Z. We also have proceeded a critical analysis concerning relations between the well known Aristotle's Square of Oppositions and paraconsistent negation, contributing to the theme with some arguments. Finally, we have investigated the question of how the generalization of the Square of Oppositions, through the n-Oppositions Theory, may be related to the themes of modality, paraconsistency and logic geometrization, proposing some ideas.
Mestrado
Mestre em Filosofia

This research examines how cross-modal and within-modal matching differ. Three broad classes of difference are considered, that crossmodal matching requires (a) "translation" between modality-specific stores or (b) "transformation" of information when different information is available through each modality or (c) transformation, whatever the information available through each modality, owing to differences in encoding strategy. Visual-kinaesthetic matching of the end-point of lever movements has been investigated. It is argued that adult cross-modal performance depends on information and strategy, not directly on modality. Results with children have been less clear, experiments were therefore undertaken, with subjects aged 6-9 years. The hypothesis was that childrens' performance also would be determined by available information, and strategy. With information differences eliminated, modality conditions did not differ in within-subject variability, with up to 20 second unfilled retention intervals. With visual information enhanced by background cues and emphasis of the body midline, visual matching was superior to kinaesthetic, and within-modal was superior to cross-modal matching. These differences disappeared with practice, together with coding relative to the midline in the cross-modal conditions. Midline-relative coding was the norm with the midline emphasised, and without background cues. With or without variability differences, VV did not differ from KK in bias, but KV resulted in greater overshooting, VK greater undershooting. The most likely explanation is resistance to movement when perception is kinaesthetic, causing overestimation of distance moved. Consideration of the information normally available to subjects, generated the hypothesis that temporal and spatial parameters should interact more with kinaesthetic than with visual perception. This was supported, since movement velocity biased only kinaesthetic judgements. It is concluded that matching performance depends on the information encoded and used as the basis of matching, which depends on strategy; strategy depends on information (a) available during stimulus presentation, (b) normally available in each modality, (c) which it is anticipated will be available during response.

The current study examined the impact of self-presentation and self-esteem concerns on goal choice. Subjects who were high or low in self-esteem worked on a series of analogies and were presented with noncontingent or contingent success feedback. They were then told that their performance on an upcoming puzzle task would be either public or private. Subjects were then allowed to choose a goal level for the upcoming task. Subsequent performance on a standard test was measured. In general, males chose more difficult goals than did females and high esteem subjects chose more difficult goals than did low esteem subjects. Analyses indicated that when low esteem male subjects were given noncontingent success feedback and were led to believe that their choice of goal was public, they reported lower performance expectations and showed a tendency to choose more difficult goals than did comparison groups. No performance differences emerged across any of the experimental conditions. The results are discussed within goal setting theory and in light of previous research on self-handicapping. The implications of this investigation for future research are also considered.
M.S.

Orientador: Itala Maria Loffredo D'Ottaviano
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas
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Resumo: O presente trabalho tem por objetivo investigar o papel da negação no âmbito das modalidades, de forma a poder esclarecer até que ponto a negação pode ser atenuada, controlada ou mesmo totalmente eliminada em favor da melhor expressabilidade lógica de certas teorias, asserções ou raciocínios que sofrem os efeitos da negação. Contudo, atenuar ou eliminar a negação tem um alto preço: métodos tradicionais em lógica podem deixar de ser válidos e certos resultados, como teoremas de completude para sistemas lógicos, podem ser derrogados. Do ponto de vista formal, a questão central que investigamos aqui e até que ponto tais métodos podem ser restabelecidos. Com tal finalidade, iniciamos nosso estudo a partir do que denominamos sistemas anódicos" (sem negação) e, a posteriori, introduzimos gradativamente o elemento catódico" (negações, com diversas gradações e diferentes características) nos sistemas modais por meio de combinações com certas lógicas paraconsistentes, as chamadas lógicas da inconsistência formal (LFIs). Todos os sistemas tratados são semanticamente caracterizados por semânticas de mundos possíveis; resultados de incompletude são também obtidos e discutidos. Obtemos ainda semânticas modais de traduções possíveis para diversos desses sistemas. Avançamos na direção das multimodalidades, investigando os assim chamados sistemas multimodais anódicos e catódicos. Finalmente, procuramos avaliar criticamente o alcance e o interesse dos resultados obtidos na direção da racionalidade sensível à negação.
Abstract: The present work aims to investigate the role of negations in the scope of modalities and in the reasoning expressed by modalities. The investigation starts from what we call anodic" systems (without any form of negation) and gradually reaches the cathodic" elements, where negations are introduced by means of combining modal logics with certain paraconsistent logics known as logics of formal inconsistency (LFIs). We obtain completeness results for all treated systems, and also show that certain incompleteness results can be obtained. The class of the investigated systems includes all normal modal logics that are extended by means of the schema Gk;l;m;n due to E. J. Lemmon and D. Scott combined with LFIs. We also tackle the question of obtaining modal possible-translations semantics for these systems. Analogous results are analyzed in the scope of multimodalities, where anodic as much as cathodic logics are studied. Finally, we advance a critical evaluation of the reach and scope of all the results obtained to what concerns expressibility of reasoning considered to be sensible to negation. We also critically assess the obtained results in contrast with problems of rationality that are sensible to negation.
Doutorado
Doutor em Filosofia

This thesis is concerned with the debate between absolutists and relativists about generality. Absolutists about quantification contend that we can quantify over absolutely everything; relativists deny this. The introduction motivates and elucidates the dispute. More familiar, restrictionist versions of relativism, according to which the range of quantifiers is always subject to restriction, are distinguished from the view defended in this thesis, an expansionist version of relativism, according to which the range of quantifiers is always open to expansion. The remainder of the thesis is split into three parts. Part I focuses on generality. Chapter 2 is concerned with the semantics of quantifiers. Unlike the restrictionist, the expansionist need not disagree with the absolutist about the semantics of quantifier domain restriction. It is argued that the threat of a certain form of semantic pessimism, used as an objection against restrictionism, also arises, in some cases, for absolutism, but is avoided by expansionism. Chapter 3 is primarily engaged in a defensive project, responding to a number of objections in the literature: the objection that the relativist is unable to coherently state her view, the objection that absolute generality is needed in logic and philosophy, and the objection that relativism is unable to accommodate ‘kind generalisations’. To meet these objections, suitable schematic and modal resources are introduced and relativism is given a precise formulation. Part II concerns issues in the philosophy of mathematics pertinent to the absolutism/relativism debate. Chapter 4 draws on the modal and schematic resources introduced in the previous chapter to regiment and generalise the key argument for relativism based on the set-theoretic paradoxes. Chapter 5 argues that relativism permits a natural motivation for Zermelo-Fraenkel set theory. A new, bi-modal axiomatisation of the iterative conception of set is presented. It is argued that such a theory improves on both its non-modal and modal rivals. Part III aims to meet a thus far unfulfilled explanatory burden facing expansionist relativism. The final chapter draws on principles from metasemantics to offer a positive account of how universes of discourse may be expanded, and assesses the prospects for a novel argument for relativism on this basis.

Two main questions are addressed in this dissertation, namely: 1. What is the correct higher-order modal theory; 2. What does it take for theories to be equivalent. The whole dissertation consists of an extended argument in defence of the joint truth of two higher-order modal theories, namely, Plantingan Moderate Contingentism, a higher-order necessitist theory advocated by Plantinga (1974) and committed to the contingent being of some individuals, and Williamsonian Thorough Necessitism, a higher-order necessitist theory advocated by Williamson (2013) and committed to the necessary being of every possible individual. The case for the truth of these two theories relies on defences of the following metaphysical theses: i) Thorough Serious Actualism, according to which no things could have been related and yet be nothing, ii) Higher-Order Necessitism, according to which necessarily, every higher-order entity is necessarily something. It is shown that Thorough Serious Actualism and Higher-Order Necessitism are both implicit commitments of very weak logical theories. Prima facie, Plantingan Moderate Contingentism and Williamsonian Thorough Necessitism are jointly inconsistent. The argument for their joint truth thus relies also on showing i) their equivalence, and ii) that the dispute between Plantingans and Williamsonians is merely verbal. The case for i) and ii) relies on the Synonymy Account, an account of theory equivalence developed and defended in the dissertation. According to the account, theories are equivalent just in case they have the same structure of entailments and commitments, and the occupiers of the places in that structure are the same propositions. An immediate consequence of the Synonymy Account is that proponents of synonymous theories are engaged in merely verbal disputes. The Synonymy Account is also applied to the debate between noneists and Quineans, revealing that what is in question in that debate is what are the expressive resources available to describe the world.

Les arguments de concevabilité sont des arguments philosophiques reposant sur le principe selon lequel tout ce qui est concevable est possible. Cette thèse se propose d'évaluer à un niveau général cette forme d'argumentation en s'appuyant sur des exemples historiques et contemporains. les arguments de concevabilité, quelle que soit la position philosophique qu'ils visent à défendre, soulèvent en effet des difficultés qui leur sont communes et ont trait principalement (i) à la définition de la notion de possibilitée, (ii) à la définition de la notion de concevabilité, et (iii) à la légitimité de l'inférence allant de l'une à l'autre. Le travail consiste d'abord (chapitres 1-3) à construire la catégorie que constituent les arguments de concevabilité en spécifiant notamment le genre de thèses philosophiques qu'ils peuvent chercher à établir. Une fois précisés les objectifs que les arguments de concevabilité peuvent viser, il s'engage (chapitres 4-8) dans l'examen de savoir si les ressources fournies par Ia concevabilité et l'inférence menant du concevable vers le possible suffisent à les atteindre. Pour ce faire, le travail propose une analyse détaillée des différentes formes de possibilité (chapitres 4-5) et de concevabilité (chapitres 6-8) impliquées dans ces arguments. II aboutit à une position dite sceptique modérée au sujet de la validité de cette forme d'argumentation, sur la base de la démonstration que, pour les thèses philosophiques qui nécessitent l'etablissement d'une possibilité métaphysique, la concevabilitée s'avère être un guide insuffisamment fiable, quelle que soit la manière dont on comprend la concevabilité. Mais il défend aussi l'idée que le fait que les arguments de concevabilité ne soient pas toujours concluants n'implique pas qu'ils sont depourvus d'utilité argumentative: car ils nous obligent à clarifier les implications modales de nos conceptions philosophiques et la manière dont nous pouvons raisonner au sujet de ces implications. Cette conception des arguments de concevabilité est appliquée pour finir à la clarification d'un chapitre essentiel de la philosophie de la cognition contemporaine relatif à la possibilité de fournir une explication naturaliste (physicaliste) de la conscience phénoménale, et ou un argument de concevabilité qui a fait couler beaucoup d'encre, dit argument des zombis, joue un rôle essentiel
Conceivability arguments are philosophical arguments which rely crucially on the principle according to which conceivability entails possibility. This dissertation provides an analysis and a critical assessment of this kind of argumentative strategy, on the basis of contemporary and historical examples. Various possible explanations of the notion of conceivability are considered and it is argued that the inference from conceivability to possibility does not enable conceivability arguments to reach all their intended conclusions, especially those pertaining to substantial metaphysical issues

Cette thèse prend ses racines dans la tradition sémantique montagovienne et dynamique standard. L’objet est les conditions dans lesquelles un syntagme nominal peut agir comme antécédent d'une expression anaphorique. Le travail porte sur l'accessibilité des référents de discours dans un système formel de la sémantique dynamique. Le cadre choisi est celui proposé par De Groote, type théorique Dynamic Logic (TTDL) car il fait appel à des outils mathématiques et logiques standards, qui permettent de conserver le principe de compositionnalité. Nous étendons la couverture de la gestion de l’accessibilité des référents dans TTDL à deux cas naturellement problématique pour les théories sémantiques dynamiques classiques, en particulier, l'anaphore sous la double négation et les modalités. Une adaptation est définie pour chaque cas et enfin, l'intégration des différentes solutions est proposée, ce qui montre la souplesse de TTDL
This thesis has its roots in the standard Montagovian and dynamic semantic tradition. The subject is conditions under which a noun phrase may act as antecedent of a particular anaphoric expression. The work thesis deals with the accessibility of discourse referents using a formal system of dynamic semantics. The framework used is the one proposed by De Groote, Type Theoretic Dynamic Logic (TTDL) because it follows the Montagovian tradition and only makes use of standard mathematical and logical tools which allows to maintain compositionnality. We extend the coverage of TTDL to cases which are naturally problematic for classical dynamic semantic theories. In particularly, this thesis aims to extend TTDL's coverage of the accessibility of referents to two exceptions of classical dynamic theories, namely anaphora under double negation and modality. An adaptation is defined for each case and finally, an integration of various solutions is proposed, which shows the flexibility of TTDL

Cette thèse prend ses racines dans la tradition sémantique montagovienne et dynamique standard. L’objet est les conditions dans lesquelles un syntagme nominal peut agir comme antécédent d'une expression anaphorique. Le travail porte sur l'accessibilité des référents de discours dans un système formel de la sémantique dynamique. Le cadre choisi est celui proposé par De Groote, type théorique Dynamic Logic (TTDL) car il fait appel à des outils mathématiques et logiques standards, qui permettent de conserver le principe de compositionnalité. Nous étendons la couverture de la gestion de l’accessibilité des référents dans TTDL à deux cas naturellement problématique pour les théories sémantiques dynamiques classiques, en particulier, l'anaphore sous la double négation et les modalités. Une adaptation est définie pour chaque cas et enfin, l'intégration des différentes solutions est proposée, ce qui montre la souplesse de TTDL
This thesis has its roots in the standard Montagovian and dynamic semantic tradition. The subject is conditions under which a noun phrase may act as antecedent of a particular anaphoric expression. The work thesis deals with the accessibility of discourse referents using a formal system of dynamic semantics. The framework used is the one proposed by De Groote, Type Theoretic Dynamic Logic (TTDL) because it follows the Montagovian tradition and only makes use of standard mathematical and logical tools which allows to maintain compositionnality. We extend the coverage of TTDL to cases which are naturally problematic for classical dynamic semantic theories. In particularly, this thesis aims to extend TTDL's coverage of the accessibility of referents to two exceptions of classical dynamic theories, namely anaphora under double negation and modality. An adaptation is defined for each case and finally, an integration of various solutions is proposed, which shows the flexibility of TTDL

Dans cette thèse, nous étudions la théorie de la preuve des logiques modales non-normales. Ces logiques ont été considérées dès les prémisses de la logique modale moderne, et ont été appliquées à de nombreux domaines, tels que le raisonnement déontique, le raisonnement épistémique, ainsi que le raisonnement dans les systèmes multi-agents. Nous définissons des systèmes de preuve pour des logiques modales non-normales ayant de bonnes propriétés calculatoires et sémantiques. Ces systèmes permettent de donner des procédures de décision et d'extraire des contre-modèles pour les formules non-valides qui sont en même temps adaptés à l'implémentation dans des démonstrateurs. Ils peuvent également être utilisés pour l'automatisation du raisonnement déontique et épistémique
This thesis provides a proof-theoretical investigation of non-normal modal logics. Non-normal modal logics are modal logics that do not satisfy some of the modal principles of the weakest normal modal logic K. They have been studied since the very beginning of modern modal logic, and have found an interest in many areas, such as deontic, epistemic, and multi-agent reasoning. Moreover, they have been also studied as modal extensions of intuitionistic, rather than classical, logic. Non-normal modal logics have been mainly investigated from the point of view of the semantics. In contrast, their proof theory is not equally developed. In this thesis we pursue two general aims: concerning non-normal modal logic with a classical base, we aim to define proof systems for them with “good” computational and semantic properties, such as providing decision procedures, allowing for countermodel extraction, and being suited for theorem-proving. Concerning non-normal modal logic with an intuitionistic base, we aim to lay down a general framework for defining intuitionistic counterparts of classical non-normal modal logics, that should also capture relevant systems already studied in the literature. The thesis consists of three main parts. The first part contains an introduction to the semantics and the proof systems of both classical and intuitionistic non-normal modal logics. The second part presents our original results about classical non-normal modal logics: we introduce a new semantics and propose two new kinds of sequent calculi. In the third part we define a family of intuitionistic non-normal modal logics and provide both sequent calculi and a semantic characterisation

Gli studi attuali portano a concludere che esiste un parallelismo tra la realizzazione di manufatti e la struttura e il ruolo delle narrazioni, a partire da quando il linguaggio non era ancora stato adottato (realizzazione di bifacciali) fino ai nostri giorni (applicazioni dell’intelligenza artificiale). Ruolo costante è la soluzione dei problemi che l’essere umano deve affrontare nella vita e il superamento delle situazioni di incertezza che normalmente si presentano. Le narrazioni giocano un ruolo fondamentale nel risolvere gli aspetti di ansia risultanti, anche quando non si arriva alla soluzione reale dei problemi. Le narrazioni rinforzano ciò che la vita insegna, aumentando le capacità di adattamento e di sopravvivenza. Si può considerare costante nell’ambito dell’evoluzione umana l’aspetto sistemico della narrazione e l’utilizzo dei modelli che questa realizza, esplicitamente o meno. L’opinione pubblica si concretizza nella costruzione e nell’uso di modelli rappresentativi della realtà. In questo ambito si inseriscono gli effetti del progresso tecnologico, in un contesto di globalizzazione, di aumento della complessità e di dinamiche di cambiamento sempre più rapide. È ipotizzabile che l’opinione pubblica deva orientarsi sempre di più verso la realizzazione di un benessere visto non come traguardo da raggiungere, ma come processo in cui ci si sente bene, si possono coltivare i propri talenti, creare relazioni significative e dare un senso alle proprie azioni.

Décrire un agent à l'aide de ses états mentaux, comme ses croyances ou ses intentions, est un des moyens les plus puissants pour expliquer ou prédire son comportement. En intelligence artificielle, de nombreuses recherches ont été mené pour décrire en logique (notamment en logique modale) ces attitudes mentales individuelles dans le but de les intégrer dans des agents artificiels. De nombreux exemples, comme : " Le gouvernement pense qu'une guerre est inévitable ", illustrent le fait que des attitudes mentales, en particulier des croyances, peuvent être attribuées à un groupe d'agent. Il est intéressant de constater que même si le groupe appelé " gouvernement ", formé de ministres, croit que la guerre est inévitable, certains ministres peuvent avoir un avis privé différent. Le but de cette thèse est donc de donner une représentation en logique modale de la croyance de groupe, d'en décrire les propriétés logiques et les liens qu'elle entretient avec les attitudes individuelles. Il apparait que la croyance de groupe dans ce sens émane souvent d'une discussion entre les différents membres du groupe pour arriver à un compromis. Nous montrerons donc les liens étroits qu'elle entretient avec le dialogue et les actes de langages
One of the most powerful tools to explain and predict an agent's behavior is to describe him thanks to his mental states, such as his beliefs or his intentions. In Artificial Intelligence, many researchers have focused on the formalization in modal logic of these individual mental attitudes, in order to use them in artificial agents. Lots of examples, such as: " The government believes that war will begin soon. ", highlight the fact that attitudes, and beliefs in particular, can be ascribed to a group of agents. Besides it is interesting to notice that, even if the government as a whole believes that war will begin soon, some government members can disagree privately. The first aim of this dissertation is to provide a logical framework to represent the concept of group belief and to describe its features and its links with individual mental attitudes. It also appears that group belief in this sense results from a debate between group members. The second aim of this dissertation is thus to highlight the close link existing between group belief, dialog and speech acts

Dans le domaine des jeux vidéos par exemple, surtout des jeux de rôles, les personnages virtuels perçoivent un environnement, en tirent des connaissances puis effectuent des actions selon leur besoin. De même en robotique, un robot perçoit son environnement à l'aide de capteurs/caméras, établit une base de connaissances et effectuent des mouvements etc. La description des comportements de ces agents virtuels et leurs raisonnements peut s'effectuer à l'aide d'un langage logique. Dans cette thèse, on se propose de modéliser les trois aspects "voir", "savoir" et "faire" et leurs interactions à l'aide de la logique modale. Dans une première partie, on modélise des agents dans un espace géométrique puis on définit une relation épistémique qui tient compte des positions et du regard des agents. Dans une seconde partie, on revisite la logique des actions "STIT" (see-to-it-that ou "faire en sorte que") qui permet de faire la différence entre les principes "de re" et "de dicto", contrairement à d'autres logiques modales des actions. Dans une troisième partie, on s'intéresse à modéliser quelques aspects de la théorie des jeux dans une variante de la logique "STIT" ainsi que des émotions contre-factuelles comme le regret. Tout au long de cette thèse, on s'efforcera de s'intéresser aux aspects logiques comme les complétudes des axiomatisations et la complexité du problème de satisfiabilité d'une formule logique. L'intégration des trois concepts "voir", "savoir" et "faire" dans une et une seule logique est évoquée en conclusion et reste une question ouverte
Agents are entities who perceive their environment and who perform actions. For instance in role playing video games, ennemies are agents who perceive some part of the virtual world and who can attack or launch a sortilege. Another example may concern robot assistance for disabled people: the robot perceives obstacles of the world and can alert humans or help them. Here, we try to give formal tools to model knowledge reasoning about the perception of their environment and about actions based, on modal logic. First, we give combine the standard epistemic modal logic with perception constructions of the form (agent a sees agent b). We give a semantics in terms of position and orientation of the agents in the space that can be a line (Lineland) or a plane (Flatland). Concerning Lineland, we provide a complete axiomatization and an optimal procedure for model-checking and satisfiability problem. Concerning Flatland, we show that both model-checking and satisfiability problem are decidable but the exact complexities and the axiomatization remain open problems. Thus, the logics of Lineland and Flatland are completely a new approach: their syntax is epistemic but their semantics concern spatial reasoning. Secondly, we study on the logic of agency ``see-to-it-that'' STIT made up of construction of the form [J]A standing for ``the coalition of agents J sees to it that A''. Our interest is motivated: STIT is strictly more expressive that standard modal logic for agency like Coalition Logic CL or Alternating-time Temporal Logic ATL. In CL or ATL the ``de re'' and ``de dicto'' problem is quite difficult and technical whereas if we combine STIT-operators with epistemic operators, we can solve it in a natural way. However this strong expressivity has a prize: the general version of STIT is undecidable. That is why we focus on some syntactic fragments of STIT: either we restrict the allowed coalitions J in constructions [J]A or we restrict the nesting of modal STIT-operators. We provide axiomatizations and complexity results. Finally, we give flavour to epistemic modal logic by adding STIT-operators. The logic STIT is suitable to express counterfactual statements like ``agent a could have choosen an action such that A have been true''. Thus we show how to model counterfactual emotions like regret, rejoicing, disappointment and elation in this framework. We also model epistemic games by adapting the logic STIT by giving explicitely names of actions in the language. In this framework, we can model the notion of rational agents but other kind of behaviour like altruism etc. , Nash equilibrium and iterated deletion of strictly dominated strategies

Les automates distribués sont des machines à états finis qui opèrent sur des graphes orientés finis. Fonctionnant comme des algorithmes distribués synchrones, ils utilisent leur graphe d'entrée comme un réseau dans lequel des processeurs identiques communiquent entre eux pendant un certain nombre (éventuellement infini) de rondes synchrones. Pour la variante locale de ces automates, où le nombre de rondes est borné par une constante, Hella et al. (2012, 2015) ont établi une caractérisation logique par des formules de la logique modale de base. Dans le cadre de cette thèse, nous présentons des caractérisations logiques similaires pour deux classes d'automates distribués plus expressives.La première classe étend les automates locaux avec une condition d'acceptation globale et la capacité d'alterner entre des modes de calcul non-déterministes et parallèles. Nous montrons qu'elle est équivalente à la logique monadique du second ordre sur les graphes.En nous restreignant à des transitions non-déterministes ou déterministes, nous obtenons également deux variantes d'automates strictement plus faibles pour lesquelles le problème du vide est décidable.Notre seconde classe adapte la notion standard d'algorithme asynchrone au cadre des automates distribués non-locaux. Les machines résultantes sont prouvées équivalentes à un petit fragment de la logique de point fixe, et plus précisément, à une variante restreinte du μ-calcul modal qui autorise les plus petits points fixes mais interdit les plus grands points fixes. Profitant du lien avec la logique, nous montrons aussi que la puissance expressive de ces automates asynchrones est indépendante du fait que des messages puissent être perdus ou non.Nous étudions ensuite la décidabilité du problème du vide pour plusieurs classes d'automates non-locaux. Nous montrons que le problème est indécidable en général, en simulant une machine de Turing par un automate distribué qui échange les rôles de l'espace et du temps. En revanche, le problème s'avère décidable en LOGSPACE pour une classe d'automates oublieux, où les nœuds voient les messages reçus de leurs voisins, mais ne se souviennent pas de leur propre état. Finalement, à titre de contribution mineure, nous donnons également de nouvelles preuves de séparation pour plusieurs hiérarchies d'alternance de quantificateurs basées sur la logique modale
Distributed automata are finite-state machines that operate on finitedirected graphs. Acting as synchronous distributed algorithms, they use their input graph as a network in which identical processors communicate for a possibly infinite number of synchronous rounds. For the local variant of those automata, where the number of rounds is bounded by a constant, Hella et al. (2012, 2015) have established a logical characterization in terms of basic modal logic. In this thesis, we provide similar logical characterizations for two more expressive classes of distributed automata.The first class extends local automata with a global acceptance condition and the ability to alternate between non deterministic and parallel computations. We show that it is equivalent to monadic second-order logic on graphs. By restricting transitions to be non deterministic or deterministic, we also obtain two strictly weaker variants for which the emptiness problem is decidable.Our second class transfers the standard notion of asynchronous algorithm to the setting of non local distributed automata. There sulting machines are shown to be equivalent to a small fragment of least fixpoint logic, and more specifically, to a restricted variantof the modal μ -calculus that allows least fixpoints but forbids greatest fixpoints. Exploiting the connection with logic, we additionally prove that the expressive power of those asynchronous automata is independent of whether or not messages can be lost.We then investigate the decidability of the emptiness problem forseveral classes of nonlocal automata. We show that the problem isundecidable in general, by simulating a Turing machine with adistributed automaton that exchanges the roles of space and time. Onthe other hand, the problem is found to be decidable in logspace for a class of forgetful automata, where the nodes see the messages received from their neighbors but cannot remember their own state. As a minor contribution, we also give new proofs of the strictness of several set quantifier alternation hierarchies that are based on modallogic

Les concepts d'action et de ressource sont omniprésents en informatique. La caractéristique principale d'une action est de changer l'état actuel du système modélisé. Une action peut ainsi être l'exécution d'une instruction dans un programme, l'apprentissage d'un fait nouveau, l'acte concret d'un agent autonome, l'énoncé d'un mot ou encore une tâche planifiée. La caractéristique principale d'une ressource est de pouvoir être divisée, par exemple pour être partagée. Il peut s'agir des cases de la mémoire d'un ordinateur, d'un ensemble d'agents, des différent sens d'une expression, d'intervalles de temps ou de droits d'accès. Actions et ressources correspondent souvent aux dimensions temporelles et spatiales du système modélisé. C'est le cas par exemple de l'exécution d'une instruction sur une case de la mémoire ou d'un groupe d'agents qui coopèrent. Dans ces cas, il est possible de modéliser les actions parallèles comme étant des actions opérant sur des parties disjointes des ressources disponibles. Les logiques modales permettent de modéliser les concepts d'action et de ressource. La sémantique relationnelle d'une modalité unaire est une relation binaire permettant d'accéder à un nouvel état depuis l'état courant. Ainsi une modalité unaire correspond à une action. De même, la sémantique d'une modalité binaire est une relation ternaire permettant d'accéder à deux états. En considérant ces deux états comme des sous-états de l'état courant, une modalité binaire modélise la séparation de ressources. Dans cette thèse, nous étudions des logiques modales utilisées pour raisonner sur les actions, les ressources et la concurrence. Précisément, nous analysons la décidabilité et la complexité du problème de satisfaisabilité de ces logiques. Ces problèmes consistent à savoir si une formule donnée peut être vraie. Pour obtenir ces résultats de décidabilité et de complexité, nous proposons des procédures de décision. Ainsi, nous étudions les logiques modales avec des modalités binaires, utilisées notamment pour raisonner sur les ressources. Nous nous intéressons particulièrement à l'associativité. Alors qu'il est généralement souhaitable que la modalité binaire soit associative, puisque la séparation de ressources l'est, cette propriété rend la plupart des logiques indécidables. Nous proposons de contraindre la valuation des variables propositionnelles afin d'obtenir des logiques décidables ayant une modalité binaire associative. Mais la majeure partie de cette thèse est consacrée à des variantes de la logique dynamique propositionnelle (PDL). Cette logiques possède une infinité de modalités unaires structurée par des opérateurs comme la composition séquentielle, l'itération et le choix non déterministe. Nous étudions tout d'abord des variantes de PDL comparables aux logiques temporelle avec branchement. Nous montrons que les problèmes de satisfaisabilité de ces variantes ont la même complexité que ceux des logiques temporelles correspondantes. Nous étudions ensuite en détails des variantes de PDL ayant un opérateur de composition parallèle de programmes inspiré des logiques de ressources. Cet opérateur permet d'exprimer la séparation de ressources et une notion intéressante d'actions parallèle est obtenue par la combinaison des notions d'actions et de séparation. En particulier, il est possible de décrire dans ces logiques des situations de coopération dans lesquelles une action ne peut être exécutée que simultanément avec une autre. Enfin, la contribution principale de cette thèse est de montrer que, dans certains cas intéressants en pratique, le problème de satisfaisabilité de ces logiques a la même complexité que PDL
The concepts of action and resource are ubiquitous in computer science. The main characteristic of an action is to change the current state of the modeled system. An action may be the execution of an instruction in a program, the learning of a new fact, a concrete act of an autonomous agent, a spoken word or a planned task. The main characteristic of resources is to be divisible, for instance in order to be shared. Resources may be memory cells in a computer, performing agents, different meanings of a phrase, time intervals or access rights. Together, actions and resources often constitute the temporal and spatial dimensions of a modeled system. Consider for instance the instructions of a computer executed at memory cells or a set of cooperating agents. We observe that in these cases, an interesting modeling of concurrency arises from the combination of actions and resources: concurrent actions are actions performed simultaneously on disjoint parts of the available resources. Modal logics have been successful in modeling both concepts of actions and resources. The relational semantics of a unary modality is a binary relation which allows to access another state from the current state. Hence, unary modalities are convenient to model actions. Similarly, the relational semantics of a binary modality is a ternary relation which allows to access two states from the current state. By interpreting these two states as substates of the current state, binary modalities allow to divide states. Hence, binary modalities are convenient to model resources. In this thesis, we study modal logics used to reason about actions, resources and concurrency. Specifically, we analyze the decidability and complexity of the satisfiability problem of these logics. These problems consist in deciding whether a given formula can be true in any model. We provide decision procedures to prove the decidability and state the complexity of these problems. Namely, we study modal logics with a binary modality used to reason about resources. We are particularly interested in the associativity property of the binary modality. This property is desirable since the separation of resources is usually associative too. But the associativity of a binary modality generally makes the logic undecidable. We propose in this thesis to constrain the valuation of propositional variables to make modal logics with an associative binary modality decidable. The main part of the thesis is devoted to the study of variants of the Propositional Dynamic Logic (PDL). These logics features an infinite set of unary modalities representing actions, structured by some operators like sequential composition, iteration and non-deterministic choice. We first study branching time variants of PDL and prove that the satisfiability problems of these logics have the same complexity as the corresponding branching-time temporal logics. Then we thoroughly study extensions of PDL with an operator for parallel composition of actions called separating parallel composition and based on the semantics of binary modalities. This operator allows to reason about resources, in addition to actions. Moreover, the combination of actions and resources provides a convenient expression of concurrency. In particular, these logics can express situations of cooperation where some actions can be executed only in parallel with some other actions. Finally, our main contribution is to prove that the complexity of the satisfiability problem of a practically useful variant of PDL with separating parallel composition is the same as the satisfiability problem of plain PDL

Lewisian Genuine Realism (GR) about possible worlds is often deemed unable to accommodate impossible worlds and reap the benefits that these bestow to rival theories. This thesis explores two alternative extensions of GR into the terrain of impossible worlds. It is divided in six chapters. Chapter I outlines Lewis’ theory, the motivations for impossible worlds, and the central problem that such worlds present for GR: How can GR even understand the notion of an impossible world, given Lewis’ reductive theoretical framework? Since the desideratum is to incorporate impossible worlds into GR without compromising Lewis’ reductive analysis of modality, Chapter II defends that analysis against (old and new) objections. The rest of the thesis is devoted to incorporating impossible worlds into GR. Chapter III explores GR-friendly impossible worlds in the form of set-theoretic constructions out of genuine possibilia. Then, Chapters IV-VI venture into concrete impossible worlds. Chapter IV addresses Lewis’ objection against such worlds, to the effect that contradictions true at impossible worlds amount to true contradictions tout court. I argue that even if so, the relevant contradictions are only ever about the non-actual, and that Lewis’ argument relies on a premise that cannot be nonquestion- beggingly upheld in the face of genuine impossible worlds in any case. Chapter V proposes that Lewis’ reductive analysis can be preserved, even in the face of genuine impossibilia, if we differentiate the impossible from the possible by means of accessibility relations, understood non-modally in terms of similarity. Finally, Chapter VI counters objections to the effect that there are certain impossibilities, formulated in Lewis’ theoretical language, which genuine impossibilia should, but cannot, represent. I conclude that Genuine Realism is still very much in the running when the discussion turns to impossible worlds.

Nous vivons dans un monde où l'information est constamment mise à jour. Les logiques dotées d'opérateurs dynamiques sont capables de raisonner sur les changements d'information multi-agents. La logique épistémique dynamique est la logique du changement de connaissances. Par exemple, dans la logique de l'annonce publique, une annonce restreint le domaine aux états où elle est vraie pour représenter les conséquences du changement de connaissances. Une généralisation de la logique épistémique dynamique est l'extension avec quantification. Elle comble un fossé intéressant entre la logique modale propositionnelle et la logique du premier ordre en termes d'expressivité et de décidabilité. La logique des annonces publiques arbitraires étend la logique des annonces publiques en ajoutant la quantification sur toutes les annonces. Elle est plus expressive que les logiques modales et la logique des annonces publiques, mais indécidable. Dans cette thèse, nous proposons de nouvelles versions de la logique d'annonce publique arbitraire. Tout d'abord, nous pouvons restreindre la quantification de toutes les annonces à des sous-ensembles de celles-ci. Plus précisément, les annonces concernées pourraient n'utiliser qu'un sous-ensemble de toutes les variables propositionnelles ou impliquer une formule donnée. Bien que ces variantes de la logique des annonces publiques arbitraires soient encore indécidables, nous montrons qu'il existe une hiérarchie intéressante de l'expressivité relative de ces variantes. Une autre approche est basée sur l'idée d'empaqueter des opérateurs ensemble. Les opérateurs groupés représentent des notions plus complexes et restreignent également l'expressivité des langages. La notion de "connaissabilité'' peut être interprétée comme "il existe un changement d'information possible après lequel l'agent sait quelque chose''. Il est naturel de la représenter par l'ensemble d'un opérateur dynamique quantifié et d'un opérateur épistémique. Dans cette thèse, nous proposons des logiques de connaissabilité utilisant de tels opérateurs. Nous montrons que s'il n'y a pas de restriction sur les annonces, alors la logique de connaissabilité est plus expressive que la logique d'annonce publique, mais indécidable. Si nous ne quantifions que les annonces booléennes, alors la logique a la même expressivité que la logique modale propositionnelle. En plus de l'extension avec la quantification, dans cette thèse, nous combinons également la logique épistémique dynamique avec un système normatif. La logique de mise à jour de flèches contient des modalités qui spécifient quelles relations doivent être préservées après la mise à jour par les conditions source et cible. Elle est conçue pour raisonner sur les changements de croyances multi-agents. Nous pouvons également l'utiliser pour représenter la notion de "norme'' qui régule les comportements des agents de manière conséquente. Nous proposons une logique normative de mise à jour des flèches qui combine la logique de mise à jour de flèches et la logique temporelle normative. Elle conclut également la combinaison additive, multiplicative et séquentielle des normes. La logique normative de mise à jour de flèches permet de distinguer les façons statiques et dynamiques de considérer les normes comme une logique épistémique dynamique. Nous montrons son expressivité relative par rapport à d'autres logiques apparentées, sa décidabilité et sa complexité
We live in a world where information is constantly being updated. Logics with dynamic operators are capable of reasoning about multi-agent information change. Dynamic epistemic logic is the logic of knowledge change. For example, in public announcement logic, an announcement restricts the domain to states where it is true to represent the consequences of knowledge change. A generalization of dynamic epistemic logic is the extension with quantification. It bridges an interesting gap between propositional modal logic and first-order logic in expressivity and decidability. Arbitrary public announcement logic extends public announcement logic by adding quantification over all announcements. It is more expressive than modal logics and public announcement logic, but undecidable. In this thesis, we propose some novel versions of arbitrary public announcement logic. Firstly, we can restrict the quantification from over all announcements to over subsets of them. To be specific, the announcements involved could use only a subset of all propositional variables or implied or implying a given formula. Even though these variants of arbitrary public announcement logic are still undecidable, we show there is an interesting hierarchy of relative expressivity of them. Another approach is based on the idea of packing operators together. Packed operators represent more complex notions and also restrict the expressivity of languages. The notion of "knowability'' can be interpreted as "there is a possible information change after which the agent knows something''. It is natural to represent by the package of a quantified dynamic operator and a epistemic operator. In this thesis, we propose logics of knowability using such packed operators. We show that if there is no restriction on announcements, then the logic of knowability is more expressive than public announcement logic, but undecidable; if we only quantify over boolean announcements, then the logic has the same expressivity as propositional modal logic. Besides the extension with quantification, in this thesis, we also combine dynamic epistemic logic with normative system. Arrow update logic contains modalities that specify which relations should be preserved after updating by source and target conditions. It is designed to reason about multi-agent belief change. We can also use it to represent the notion of "norm'' which regulates behaviors of agents in a consequential way. We propose normative arrow update logic which combines arrow update logic and normative temporal logic. It also concludes additive, multiplicative and sequential combination of norms. Normative arrow update logic can distinguish between static and dynamic ways to consider norms as dynamic epistemic logic. We show its relative expressivity with other related logics, its decidability, and complexity

Cette thèse étudie la théorie de la correspondance et la théorie des preuves pour la logique modale monotone et les logiques qui en sont proches.La première partie de la thèse établit une connexion formelle entre la théorie de la correspondance algorithmique et des résultats de caractérisation duale pour les treillis finis, similaire à la caractérisation par Nation d'une hiérarchie de variétés de treillis qui généralise les treillis distributifs. Cette connexion formelle est établie en utilisant la logique modale monotone. Nous adaptons l'algorithme ALBA pour la correspondance à l'environnement de la logique modale monotone, et nous utilisons un encodage, induit par une dualité, des treillis finis sous forme de 'neighbourhood frames' pour traduire les termes de la théorie des treillis en formules de la logic modal monotone.La deuxième partie de la thèse étend la théorie des 'display calculi' à la logique Baltag-Moss-Solecki pour les actions épistémiques et la connaissance (Epistemic Actions and Knowledge), à la logique modale monotone et à la logique propositionnelle dynamique (PDL). Nos résultats incluent plusieurs méta-théorèmes d'élimination de la coupure qui généralisent le théorème original de Belnap dans des dimensions différentes et indépendantes. Les deux principales généralisations des 'display calculi' traitées dans la thèse sont : la généralisation d'une théorie pour les langages ne contenant qu'un seul type à une théorie pour les langages contenant plusieurs types, et la généralisation d'une théorie pour les calculs satisfaisant la propriété de 'display' aux calculs ne la satisfaisant pas
The present thesis focuses on Monotone Modal Logic and closely related logics from the point of view of Correspondence Theory and Proof Theory.The first part of the thesis establishes a formal connection between algorithmic corre- spondence theory and certain dual characterization results for finite lattices, similar to Nation's characterization of a hierarchy of pseudovarieties of finite lattices progressively generalizing finite distributive lattices. This formal connection is established through monotone modal logic. Specifically, we adapt the correspondence algorithm ALBA to the setting of monotone modal logic, and we use a certain duality-induced encoding of finite lattices as monotone neighbourhood frames to translate lattice terms into formulas in monotone modal logic.The second part of the thesis extends the theory of display calculi to Baltag-Moss- Solecki's logic of Epistemic Actions and Knowledge (EAK), Monotone Modal Logic (MML), and Propositional Dynamic Logic (PDL). Our results include several cut-elimination metatheorems, which generalize the original metatheorem of Belnap in different and mutually independent dimensions. The two main generalizations of display calculi treated in the thesis are: the generalization from single type to multi-type languages, and from the full or relativized display property to no display property

La logique Here-and-there (HT) est une logique monotone à trois valeurs, intermédiaire entre les logiques intuitionniste et classique. La logique de l'équilibre est un formalisme non-monotone dont la sémantique est donnée par un critère de minimalisation sur les modèles de la logique HT. Ce formalisme est fortement lié à la programmation orientée ensemble réponse (ASP), un paradigme relativement nouveau de programmation déclarative. La logique de l'équilibre constitue la base logique de l'ASP: elle reproduit la sémantique par ensemble réponse des programmes logiques et étend la syntaxe de l'ASP à des théories propositionnelles plus générales, i.e., des ensembles finis de formules propositionnelles. Cette thèse traite aussi bien des logiques modales sous-jacentes à la logique de l'équilibre que de ses extensions modales. Ceci nous permet de produire un cadre complet pour l'ASP et d'examiner de nouveau la base logique de l'ASP. A cet égard, nous présentons d'abord une logique modale monotone appelée MEM et capable de caractériser aussi bien l'existence d'un modèle de la logique de l'équilibre que la relation de conséquence dans ces modèles. La logique MEM reproduit donc la propriété de minimalisation qui est essentielle dans la définition des modèles de la logique de l'équilibre. Nous définissons ensuite une extension dynamique de la logique de l'équilibre. Pour ce faire, nous étendons le langage de la logique HT par deux ensembles de programmes atomiques qui permettent de mettre à jour, si possible, les valeurs de vérité des variables propositionnelles. Ces programmes atomiques sont ensuite combinés au moyen des connecteurs habituels de la logique dynamique. Le formalisme résultant est appelé logique Here-and-there dynamique (D-HT) et permet la mise-à-jour des modèles de la logique de l'équilibre. Par ailleurs, nous établissons un lien entre la logique D-HT et la logique dynamique des affectations propositionnelles (DL-PA): les affectations propositionnelles mettent à vrai ou à faux les valeurs de vérité des variables propositionnelles et transforment le modèle courant comme en logique dynamique propositionnelle. En conséquence, DL-PA constitue également une logique modale sous-jacente à la logique de l'équilibre. Au début des années 1990, Gelfond avait défini les spécifications épistémiques (E-S) comme une extension de la programmation logique disjonctive par des notions épistémiques. L'idée de base des E-S est de raisonner correctement à propos d'une information incomplète au moyen de la notion de vue-monde dans des situations où la notion précédente d'ensemble réponse n'est pas assez précise pour traiter le raisonnement de sens commun et où il y a une multitude d'ensembles réponses. Nous ajoutons ici des opérateurs épistémiques au langage original de la logique HT et nous définissons une version épistémique de la logique de l'équilibre. Cette version épistémique constitue une nouvelle sémantique non seulement pour les spécifications épistémiques de Gelfond, mais aussi plus généralement pour les programmes logiques épistémiques étendus. Enfin, nous comparons notre approche avec les sémantiques existantes et nous proposons une équivalence forte pour les théories de l'E-HT. Ceci nous conduit naturellement des E-S aux ASP épistémiques et peut être considéré comme point de départ pour les nouvelles extensions du cadre ASP
Here-and-there (HT) logic is a three-valued monotonic logic which is intermediate between classical logic and intuitionistic logic. Equilibrium logic is a nonmonotonic formalism whose semantics is given through a minimisation criterion over HT models. It is closely aligned with answer set programming (ASP), which is a relatively new paradigm for declarative programming. To spell it out, equilibrium logic provides a logical foundation for ASP: it captures the answer set semantics of logic programs and extends the syntax of answer set programs to more general propositional theories, i.e., finite sets of propositional formulas. This dissertation addresses modal logics underlying equilibrium logic as well as its modal extensions. It allows us to provide a comprehensive framework for ASP and to reexamine its logical foundations. In this respect, we first introduce a monotonic modal logic called MEM that is powerful enough to characterise the existence of an equilibrium model as well as the consequence relation in equilibrium models. The logic MEM thus captures the minimisation attitude that is central in the definition of equilibrium models. Then we introduce a dynamic extension of equilibrium logic. We first extend the language of HT logic by two kinds of atomic programs, allowing to update the truth value of a propositional variable here or there, if possible. These atomic programs are then combined by the usual dynamic logic connectives. The resulting formalism is called dynamic here-and-there logic (D-HT), and it allows for atomic change of equilibrium models. Moreover, we relate D-HT to dynamic logic of propositional assignments (DL-PA): propositional assignments set the truth values of propositional variables to either true or false and update the current model in the style of dynamic epistemic logics. Eventually, DL-PA constitutes an alternative monotonic modal logic underlying equilibrium logic. In the beginning of the 90s, Gelfond has introduced epistemic specifications (E-S) as an extension of disjunctive logic programming by epistemic notions. The underlying idea of E-S is to correctly reason about incomplete information, especially in situations when there are multiple answer sets. Related to this aim, he has proposed the world view semantics because the previous answer set semantics was not powerful enough to deal with commonsense reasoning. We here add epistemic operators to the original language of HT logic and define an epistemic version of equilibrium logic. This provides a new semantics not only for Gelfond's epistemic specifications, but also for more general nested epistemic logic programs. Finally, we compare our approach with the already existing semantics, and also provide a strong equivalence result for EHT theories. This paves the way from E-S to epistemic ASP, and can be regarded as a nice starting point for further frameworks of extensions of ASP

De nombreuses situations font intervenir la notion de communication ainsi que des restrictions sur cette communication. C'est le cas lorsque l'on pense à des informations militaires, des communications médicales, des normes morales, des jeux, etc. Dans certaines des ces situations, il se peut qu'existent des structures pour penser et organiser le droit de communiquer. Dans l'armée par exemple une telle structure est assez simple et facile à comprendre: plus on est haut-placé dans la hiérarchie militaire, plus on a le droit de savoir et moins on a l'autorisation de dire. Le champ médical est un exemple où des restrictions plus subtiles empêchent un patron d'avoir accès à des données médicales d'un de ses travailleurs, alors qu'un docteur devrait pouvoir y avoir accès. Souvent, ces structures sont présentées sous la forme d'un ensemble de règles informelles, ensemble qui peut être incomplet et même contradictoire, laissant la justice décider ce qu'il convient de faire en cas de conflits. L'objectif de ce mémoire est d'apporter quelques éléments, dans le champ de la logique, pour une meilleure compréhension de la notion de `droit de savoir', éléments qui pourraient nous aider à comprendre et répondre aux problèmes pour lesquels cette notion rentre en jeu. On concentre notre réflexion sur la partie informative de la communication, ce qui amène notre sujet central à la notion de `droit de donner une information'
Many situations involve communication and some kind of restrictions on this communication. This is the case when we think about military information, medical communication, moral norms, games, etc. In some situations, we may have structures to think about and organize the right to communicate in such situations. In the army, for example, such a structure is quite simple and easy to understand: the higher you are in the hierarchy, the more you may know and the less you are allowed to say. Indeed, a general can know any secret information but have no right to reveal it to his soldiers, while a soldier can give any information he wants (and may have to give the information he has) without having the right to access most of the information. As another example, in the medical field, more subtle restrictions prevent a boss from getting one of his workers' medical information, while a doctor may have access to it. Often such structures are presented as an informal and incomplete set of rules, that may be contradictory (and let the justice decide what should be done in case of conflict). But we have no general framework to analyze such situations. The aim of this dissertation is to make some progress, in the field of logic, in the understanding of the notion of `right to say', progress that may help us understand and answer problems that involve such a notion. We focus on the informative part of communication (and not on its form) leading our topic to the notion of `right to give a piece of information'

La notion clé de la génération de conséquences est celle de l'impliqué premier, qui désigne une clause qui est impliquée par une formule et telle qu'il n'existe pas de clause logiquement plus forte impliquée par la formule. La notion d'impliqué premier s'est montrée très utile en intelligence artificielle, notamment pour la compilation de connaissances et le raisonnement abductif. Dans cette thèse nous étudions comment cette notion, jusqu'à présent étudiée en logique propositionnelle, peut être étendue à la logique modale Kn. Nous commençons par comparer plusieurs definitions plausibles d'impliqués premiers dans Kn, avant d'en selectionner une. Ensuite, nous proposons des algorithmes pour générer et reconnaître des impliqués premiers, et nous étudions la complexité de ces deux tâches. Puis, nous utilisons notre notion d'impliqué premier pour élaborer une forme normale pour Kn qui est dotée de propriétés intéressantes du point de vue de la compilation de connaissances
The key notion in consequence finding is that of prime implicates, which are defined to be the logically strongest clausal consequences of a formula. Prime implicates have proven useful in artificial intelligence, especially in knowledge compilation and abductive reasoning. In this thesis, we extend the investigation of prime implicates from propositional logic to the basic multi-modal logic Kn. We begin by comparing the properties of several plausible definitions of prime implicates in Kn in order to isolate the most suitable definition. We next study the computational aspects of the selected definition. Specifically, we provide algorithms for prime implicate generation and recognition, and we study the complexity of these tasks. Finally, we show how our notion of prime implicates can be used to define a normal form for Kn with interesting knowledge compilation properties