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1
Wansing, Heinrich. "Displaying modal logic /." Dordrecht [u.a.] : Kluwer, 1998. http://www.gbv.de/dms/ilmenau/toc/24662969X.PDF.
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Papacchini, Fabio. "Minimal model reasoning for modal logic." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/minimal-model-reasoning-for-modal-logic(dbfeb158-f719-4640-9cc9-92abd26bd83e).html.
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Model generation and minimal model generation are useful for tasks such as model checking, query answering and for debugging of logical specifications. Due to this variety of applications, several minimality criteria and model generation methods for classical logics have been studied. Minimal model generation for modal logics how ever did not receive the same attention from the research community. This thesis aims to fill this gap by investigating minimality criteria and designing minimal model generation procedures for all the sublogics of the multi-modal logic S5(m) and their extensions with universal modalities. All the procedures are minimal model sound and complete, in the sense that they generate all and only minimal models. The starting point of the investigation is the definition of a Herbrand semantics for modal logics on which a syntactic minimality criterion is devised. The syntactic nature of the minimality criterion allows for an efficient minimal model generation procedure, but, on the other hand, the resulting minimal models can be redundant or semantically non minimal with respect to each other. To overcome the syntactic limitations of the first minimality criterion, the thesis moves from minimal modal Herbrand models to semantic minimality criteria based on subset-simulation. At first, theoretical procedures for the generation of models minimal modulo subset-simulation are presented. These procedures for the generation of models minimal modulo subset-simulation are minimal model sound and complete, but they might not terminate. The minimality criterion and the procedures are then refined in such a way that termination can be ensured while preserving minimal model soundness and completeness.
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Batchelor, Roderick. "Investigations in modal logic." Thesis, King's College London (University of London), 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.409258.
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Wilkinson, Toby. "Enriched coalgebraic modal logic." Thesis, University of Southampton, 2013. https://eprints.soton.ac.uk/354112/.
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We formalise the notion of enriched coalgebraic modal logic, and determine conditions on the category V (over which we enrich), that allow an enriched logical connection to be extended to a framework for enriched coalgebraic modal logic. Our framework uses V-functors L: A → A and T: X → X, where L determines the modalities of the resulting modal logics, and T determines the coalgebras that provide the semantics. We introduce the V-category Mod(A, α) of models for an L-algebra (A, α), and show that the forgetful V-functor from Mod(A, α) to X creates conical colimits. The concepts of bisimulation, simulation, and behavioural metrics (behavioural approximations),are generalised to a notion of behavioural questions that can be asked of pairs of states in a model. These behavioural questions are shown to arise through choosing the category V to be constructed through enrichment over a commutative unital quantale (Q, Ⓧ, I) in the style of Lawvere (1973). Corresponding generalisations of logical equivalence and expressivity are also introduced,and expressivity of an L-algebra (A, α) is shown to have an abstract category theoretic characterisation in terms of the existence of a so-called behavioural skeleton in the category Mod(A, α). In the resulting framework every model carries the means to compare the behaviour of its states, and we argue that this implies a class of systems is not fully defined until it is specified how states are to be compared or related.
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Murakami, Yuko. "Modal logic of partitions." [Bloomington, Ind.] : Indiana University, 2005. http://wwwlib.umi.com/dissertations/fullcit/3162977.
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Thesis (Ph.D.)--Indiana University, Dept. of Philosophy, 2005.Title from PDF t.p. (viewed Dec. 2, 2008). Source: Dissertation Abstracts International, Volume: 66-02, Section: A, page: 0620. Chairs: Lawrence Moss; Michael Dunn.
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Zanichelli, Riccardo <1993>. "Aristotle’s modal syllogistic and first-order modal logic." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2022. http://amsdottorato.unibo.it/10396/1/rzamsafml.pdf.
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In Prior Analytics 1.1–22, Aristotle develops his proof system of non-modal and modal propositions. This system is given in the language of propositions, and Aristotle is concerned with establishing some properties and relations that the expressions of this language enjoy. However, modern scholarship has found some
of his results inconsistent with positions defended elsewhere. The set of rules of inference of this system has also caused perplexity: there does not seem to be a single interpretation that validates all the rules which Aristotle is explicitly committed to using in his proofs. Some commentators have argued that these and other problems cannot be successfully addressed from the viewpoint of the traditional, ‘first-order’ interpretation of Aristotle’s syllogistic, whereby propositions are taken to involve quantification over individuals only. Accordingly, this interpretation not only is inadequate for formal analysis, but also stems from a misunderstanding of Aristotle’s ideas about quantification. On the contrary, in this study I purport to vindicate the adequacy and plausibility of the first-order interpretation. Together with some assumptions about the language of propositions and an appropriate regimentation, the first-order interpretation yields promising solutions to many of the problems raised by the modal syllogistic. Thus, I present a reconstruction of the language of propositions and a formal interpretation thereof which will prove respectful and responsive to most of the views endorsed by Aristotle in the ‘modal’ chapters of the Analytics.
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Thalmann, Lars. "Term-modal logic and quantifier-free dynamic assignment logic." Doctoral thesis, Uppsala : Institutionen för informationsteknologi, Univ. [distributör], 2000. http://publications.uu.se/theses/91-506-1443-6/.
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Chou, Soi Ngan. "Normal systems of modal logic." Thesis, University of Macau, 2000. http://umaclib3.umac.mo/record=b1446655.
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Martin, Alan J. "Modal and fixpoint linear logic." Thesis, University of Ottawa (Canada), 2002. http://hdl.handle.net/10393/6074.
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This thesis provides adaptations of the algebraic and relational semantics of modal logic to model J.-Y. Girard's linear logic extended with general modalities. This work extends the work of M. D'Agostino, D. Gabbay, and A. Russo on modalities in implication systems, which include a fragment of linear logic, and the work of J.-Y. Girard on phase semantics for linear logic. We develop deductive systems based on the Gentzen-style sequent calculi of Ohnishi and Matsumoto and the indexed sequents of Mints, and prove cut-elimination properties. We show that semantics and deductive systems that are equivalent for classical modal logic become nonequivalent when adapted to linear logic. We also provide a semantics based on Girard's phase semantics for the fixpoint operators of the modal mu-calculus, developed by D. Kozen, E. A. Emerson, E. Clarke, and others, in linear logic, and consider the translation of Y. Lafont's exponentials with the Free Storage rule into linear logic with fixpoint operators.
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Costa, Marcos Mota do Carmo. "Characterization of modal (action) logic." Thesis, Imperial College London, 1990. http://hdl.handle.net/10044/1/47821.
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Frittella, Sabine. "Monotone Modal Logic and Friends." Thesis, Aix-Marseille, 2014. http://www.theses.fr/2014AIXM4751/document.
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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 pasThe 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
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Rößiger, Martin. "Coalgebras, clone theory, and modal logic." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2000. http://nbn-resolving.de/urn:nbn:de:swb:14-993474604234-75966.
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gekürzte Fassung: Coalgebren wurden sowohl in der Mathematik (seit den 70er Jahren) als auch in der theoretischen Informatik (seit den 90er Jahren) untersucht. In der Mathematik sind Coalgebren dual zu universellen Algebren definiert. Sie bestehen aus einer Trägermenge A zusammen mit Cofunktionen ? : A ? , die A in die n-fache disjunkte Vereinigung von sich selbst abbilden. Das Ziel der Forschung ist hier vor allem, duale Versionen von Definitionen und Resultaten aus der universellen Algebra für die Welt der Coalgebren zu finden. Die theoretische Informatik betrachtet Coalgebren von kategorieller Seite aus. Für einen gegebenen Funktor F : C ? C sind Coalgebren als Paare (S,"alpha") definiert, wobei S ein Objekt von C und "alpha" : S ? F(S) ein Morphismus in C ist. Somit stellt der obige Ansatz mit Cofunktionen einen Spezialfall dar. Begriffe wie Homomorphismus oder Bisimularität lassen sich auf einfache Weise ausdrücken und handhaben. Solche Coalgebren modellieren eine große Anzahl von dynamischen Systemen. Das liefert eine kanonische und vereinheitlichende Sicht auf diese Systeme. Die vorliegende Dissertation führt beide genannten Forschungsrichtungen der Coalgebren weiter: Teil I beschäftigt sich mit "klassischen" Coalgebren, also solchen, wie sie in der universellen Algebra untersucht werden. Insbesondere wird das Verhältnis zur Klontheorie erforscht. Teil II der Arbeit widmet sich dem kategoriellen Ansatz aus der theoretischen Informatik. Von speziellem Interesse ist hier die Anwendung von Coalgebren zur Spezifikation von Systemen. Coalgebren und Klontheorie In der universellen Algebra spielen Systeme von Funktionen eine bedeutende Rolle, u.a. in der Klontheorie. Dort betrachtet man Funktionen auf einer festen gegebenen Grundmenge. Klone von Funktionen sind Mengen von Funktionen, die alle Projektionen enthalten und die gegen Superposition (d.h. Einsetzen) abgeschlossen sind. Extern lassen sich diese Klone als Galois-abgeschlossene Mengengzgl. der Galois-Verbindung zwischen Funktionen und Relationen darstellen. Diese Galois-Verbindung wird durch die Eigenschaft einer Funktion induziert, eine Relation zu bewahren. Dual zu Klonen von Funktionen wurde von B. Csákány auch Klone von Cofunktionen untersucht. Folglich stellt sich die Frage, ob solche Klone ebenfalls mittels einer geeigneten Galois-Verbindung charakterisiert werden können. Die vorliegende Arbeit führt zunächst den Begriff von Corelationen ein. Es wird auf kanonische Weise definiert, was es heißt, daß eine Cofunktion eine Corelation bewahrt. Dies mündet in einer Galois-Theorie, deren Galois-abgeschlossene Mengen von Cofunktionen tatsächlich genau die Klone von Cofunktionen sind. Überdies entsprechen die Galois-abgeschlossenen Mengen von Corelationen genau den Klonen von Corelationen. Die Galois-Theorien von Funktionen und Relationen einerseits und Cofunktionen und Corelationen anderseits sind sich sehr ähnlich. Das wirft die Frage auf, welche Voraussetzungen allgemein nötig sind, um solche und ähnliche Galois-Theorien aufzustellen und die entsprechenden Galois-abgeschlossenen Mengen zu charakterisieren. Das Ergebnis ist eine Metatheorie, bei der die Gemeinsamkeiten in den Charakterisierungen der Galois-abgeschlossenen Mengen herausgearbeitet sind. Bereits bekannte Galois-Theorien erweisen sich als Spezialfälle dieser Metatheorie, und zwar die Galois-Theorien von partiellen Funktionen und Relationen, von mehrwertigen Funktionen und Relationen und von einstelligen Funktionen und Relationen....
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McPartlin, Michael P. "Non-classical modal logic for belief." Thesis, University of Edinburgh, 1991. http://hdl.handle.net/1842/11150.
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The standard model of knowledge and belief attributes to agents the ability to reason perfectly in classical logic. This is known as the problem of logical omniscience and, in accordance with the requirements of their contexts of use, has led to the development of a number of alternative epistemic logics. Some of these alternatives can, like the standard model, be regarded as presenting for discussion and analysis in a base language a system of reasoning, or consequence relation: the relation under which beliefs are closed. Adopting this perspective with regard to a useful four-valued logic, the resulting extension of the standard model is described and many technical points of comparison with the original model are given.
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Gaudou, Benoît. "Formalizing social attitudes in modal logic." Toulouse 3, 2008. http://thesesups.ups-tlse.fr/315/.
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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 langagesOne 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
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French, Timothy Noel. "Bisimulation quantifiers for modal logics." University of Western Australia. School of Computer Science and Software Engineering, 2006. http://theses.library.uwa.edu.au/adt-WU2007.0013.
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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.
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Dickson, Mark William. "Aristotle's modal ontology." Thesis, University of British Columbia, 1989. http://hdl.handle.net/2429/42125.
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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
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Reddy, Pamoori Venkateswara. "Tableau systems for tense logics : a constraint approach." Thesis, Imperial College London, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.283438.
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Jungteerapanich, Natthapong. "Tableau systems for the modal μ-calculus." Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/4208.
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The main content of this thesis concerns a tableau method for solving the satisfiability problem for the modal μ-calculus. A sound and complete tableau system for the modal μ-calculus is given. Since every tableau in such tableau system is finite and bounded by the length of the formula, the tableau system may be used as a decision procedure for determining the satisfiability of the formula. An alternative proof of the small model property is obtained: every satisfiable formula has a model of size singleexponential in the length of the formula. Contrary to known proofs in literature, the results presented here do not rely on automata theory. Two simplifications of the tableau system are given. One is for the class of aconjunctive formulae. The resulting tableau system has been used to prove the completeness of Kozen’s axiomatisation with respect to the aconjunctive fragment of the modal μ- calculus. Another is for the formulae in the class Πμ 2 . In addition to the tableau method, the thesis explores some model-surgery techniques with the aim that such techniques may be used to directly prove the small model theorem. The techniques obtained so far have been used to show the small model property for Πμ 2 -formulae and for formulae with linear models.
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Girard, Patrick. "Modal logic for belief and preference change /." May be available electronically:, 2008. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.
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Su, Ezgi Iraz. "Extensions of equilibrium logic by modal concepts." Thesis, Toulouse 3, 2015. http://www.theses.fr/2015TOU30056/document.
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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 ASPHere-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
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Oliver, Martin John. "Visualisation and manipulation tools for Modal logic." Thesis, Open University, 1998. http://oro.open.ac.uk/56464/.
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In this thesis, an investigation into how visualisation and manipulation tools can provide better support for learners of Modal logic is described. Problems associated with learning Modal logic are also researched. Seven areas topics in Modal logic are investigated, as is the influence of domain independent factors (e. g. motivation) on learning. Studies show that students find concepts such as Modal proofs and systems difficult to learn, whilst possible worlds and Modes are fairly straightforward. Areas such as reference, belief and accessibility relations fall between these extremes. Two roles for representations in reasoning are identified: providing a concrete domain for students to reason about, and supporting the process of reasoning. Systems which make use of these complementary representations were found to be more effective for learners than either the syntactic or the diagrammatic representations traditionally used to teach Modal logic. A review of software used to support students learning logic highlights two important features: the use of examples, and automation of routine tasks. A learning environment for Modal logic was designed which incorporated these. The environment was developed using an adapted version of Smalltalk's Model-View-Controller mechanism, and incorporates complementary representations, enhance by direct manipulation. A further study investigates the added benefits of using this tool, as opposed to using the same representation but working with pen and paper. This confirms the importance of using 'concrete' content representations and minimising learners' cognitive load. Performance measures show that software users learnt more, had a deeper style of learning, and found the topics less abstract than their counterparts working with pen & paper. This research shows that complementary representations are an effective way of supporting students studying Modal logic, and that visualisation and manipulation tools which incorporate these systems will provide additional benefits for learners.
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Salvatore, Felipe de Souza. "Topics in modal quantification theory." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/8/8133/tde-14122015-122734/.
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The modal logic S5 gives us a simple technical tool to analyze some main notions from philosophy (e.g. metaphysical necessity and epistemological concepts such as knowledge and belief). Although S5 can be axiomatized by some simple rules, this logic shows some puzzling properties. For example, an interpolation result holds for the propositional version, but this same result fails when we add first-order quantifiers to this logic. In this dissertation, we study the failure of the Definability and Interpolation Theorems for first-order S5. At the same time, we combine the results of justification logic and we investigate the quantified justification counterpart of S5 (first-order JT45). In this way we explore the relationship between justification logic and modal logic to see if justification logic can contribute to the literature concerning the restoration of the Interpolation Theorem.A lógica modal S5 nos oferece um ferramental técnico para analizar algumas noções filosóficas centrais (por exemplo, necessidade metafísica e certos conceitos epistemológicos como conhecimento e crença). Apesar de ser axiomatizada por princípios simples, esta lógica apresenta algumas propriedades peculiares. Uma das mais notórias é a seguinte: podemos provar o Teorema da Interpolação para a versão proposicional, mas esse mesmo teorema não pode ser provado quando adicionamos quantificadores de primeira ordem a essa lógica. Nesta dissertação vamos estudar a falha dos Teoremas da Definibilidade e da Interpolação para a versão quantificada de S5. Ao mesmo tempo, vamos combinar os resultados da lógica da justificação e investigar a contraparte da versão quantificada de S5 na lógica da justificação (a lógica chamada JT45 de primeira ordem). Desse modo, vamos explorar a relação entre lógica modal e lógica da justificação para ver se a lógica da justificação pode contribuir para a restauração do Teorema da Interpolação.
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VASCONCELOS, DAVI ROMERO DE. "FIRST-ORDER MODAL LOGIC FOR REASONING ABOUT GAMES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2007. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=10082@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
O termo jogo tem sido utilizado como uma metáfora, em várias áreas do conhecimento, para modelar e analisar situações onde agentes(jogadores) interagem em ambientes compartilhados para a realização de seus objetivos sejam eles individuais ou coletivos. Existem diversos modelos propostos para jogos por diferentes áreas do conhecimento, tais como matemática, ciência da computação, ciência política e social, entre outras. Dentre as diversas formas de modelar jogos examinamos a Teoria dos Jogos e as lógicas para jogos. Neste trabalho apresentamos uma lógica modal de primeira-ordem baseada na lógica CTL, chamada de Game Analysis nalysis Logic, para raciocinar sobre jogos. Relacionamos os principais modelos da Teoria dos Jogos (jogo estratégico, extensivo, e de coalizão) e seus principais conceitos de soluções(equilíbrio de Nash, equilíbrio de subjogo perfeito,e core) aos modelos de GAL e às fórmulas de GAL, respectivamente. Além disso, estudamos as alternativas de quantificação De Re e De Dicto no contexto dos jogos extensivos, caracterizando o conceito de equilíbrio de Nash e equilíbrio de subjogo perfeito de acordo com as alternativas de quantificação. Relacionamos as lógicas Alternating-time lternating-Tempomporal Logic (A ATL) TL) e Coalitional Game Logic (CGL) com a lógica GAL, demonstrando que ambas as lógicas são fragmentos da lógica GAL. Outro resultado deste trabalho é caracterizar uma classe de sistemas multi- agentes,que é baseada na arquitetura de agentes Belief-Desir Desire- Intention(BDI), para a qual existem jogos extensivos e vice-v versa. Como conseqüência, os critérios de racionalidade da Teoria dos Jogos podem ser aplicados diretamente para agentes BDI e vice-versa. Assim, a abordagem deste trabalho pode ser utilizada para analisar sistemas multi-agentes. Do ponto de vista prático, apresentamos um verificador de modelos para a lógica GAL. Diversos estudos de casos são realizados utilizando o verificador de modelos.
Games are abstract models of decision-making in which decision-makers(players)interact in a shared environment to accomplish their goals. Several models have been proposed to analyze a wide variety of applications in many disciplines such as mathematics, computer science and even political and social sciences among others. In this work, we focus on Game Theory and Game Logics. We present a first-order modal logic based on CTL, namely Game Analysis Logic (GAL), to model and reason about out games. The standard models of Game Theory (strategic games, extensiv games and coalition games) as well as their solution concepts (Nash equilibrium, subgame perfect equilibrium and co re),respectively, are express as models dels of GAL and formulas of GAL. Moreover, we study the alternatives of De Re and De Dicto quantification in the context of extensive games. We also show that two of the most representative game logics, namely Alternating-time lternating-Temp empor oral Logic (A ATL) TL) and Coalitional Game Logic (CGL), are fragments of GAL. We also characterize haracterize a class of multi-agent systems, which is based on the architecture Belief-Desire- Intention (BDI), for which there is a somehow equivalent class of games and vice-versa. As a consequence, criteria of rationality for agents can be directly applied to players and vice-versa. Game analysis formal tools can be applied to MAS as well. From a practical poin of view, we provide and develop a model-checker for GAL. In addition, we perform case studies using our prototype.
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Schwarzentruber, François. "Seeing, Knowing, doing : case studies in modal logic." Toulouse 3, 2010. http://thesesups.ups-tlse.fr/1264/.
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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 ouverteAgents 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
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Pemmaraju, Sriram V. "Modal logics of provability." Thesis, Virginia Tech, 1989. http://hdl.handle.net/10919/44652.
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Gödel proved his Incompleteness theorems for any theory 'strong' enough to represent recursive functions. In the process he showed that the provability predicate can be represented in such theories. Modal logics of provability are modal logics which attempt to express the concept of 'provability' and 'consistency' using the modal operators '[]' and '<>' respectively. This is achieved by forcing '[]' to behave like the provability predicate. GL is a modal logic which has been shown to be complete and sound with respect to arithmetic theories (theories which can represent all recursive functions), hence results about concepts such as 'consistency,' 'provability' and 'decidability' in arithmetic theories can be stated and proved in GL. It has also been proved that GL is complete with respect to the class of finite, transitive, reversely well-founded models. This essentially means that the set of theorems of GL is recursive and hence there exists an effective procedure to determine whether a given wff is a theorem of GL or not. We investigate a weaker version of GL called GH and show that GH is not complete with respect to arithmetic theories. We show this by first showing that GH is a proper subset of GL and then showing that the theorems missing from GH are properties of the provability predicate. We finally, show that GH is not complete with respect to the class of transitive, reversely well-founded models and hence not sound and complete with respect to any frame.
Master of Science
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Motoura, Shota. "A General Framework for Dynamic Epistemic Logic." 京都大学 (Kyoto University), 2017. http://hdl.handle.net/2433/225384.
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Coscarelli, Bruno Costa. "Introdução à Lógica Modal." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-17062009-161423/.
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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.
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Simpson, Alex K. "The proof theory and semantics of intuitionistic modal logic." Thesis, University of Edinburgh, 1994. http://hdl.handle.net/1842/407.
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Possible world semantics underlies many of the applications of modal logic in computer science and philosophy. The standard theory arises from interpreting the semantic definitions in the ordinary meta-theory of informal classical mathematics. If, however, the same semantic definitions are interpreted in an intuitionistic meta-theory then the induced modal logics no longer satisfy certain intuitionistically invalid principles. This thesis investigates the intuitionistic modal logics that arise in this way. Natural deduction systems for various intuitionistic modal logics are presented. From one point of view, these systems are self-justifying in that a possible world interpretation of the modalities can be read off directly from the inference rules. A technical justification is given by the faithfulness of translations into intuitionistic first-order logic. It is also established that, in many cases, the natural deduction systems induce well-known intuitionistic modal logics, previously given by Hilbert-style axiomatizations. The main benefit of the natural deduction systems over axiomatizations is their susceptibility to proof-theoretic techniques. Strong normalization (and confluence) results are proved for all of the systems. Normalization is then used to establish the completeness of cut-free sequent calculi for all of the systems, and decidability for some of the systems. Lastly, techniques developed throughout the thesis are used to establish that those intuitionistic modal logics proved decidable also satisfy the finite model property. For the logics considered, decidability and the finite model property presented open problems.
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Chen, Liang-Ting. "On a purely categorical framework for coalgebraic modal logic." Thesis, University of Birmingham, 2014. http://etheses.bham.ac.uk//id/eprint/4882/.
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A category CoLog of distributive laws is introduced to unify different approaches to modal logic for coalgebras, based merely on the presence of a contravariant functor P that maps a state space to its collection of predicates. We show that categorical constructions, including colimits, limits, and compositions of distributive laws as a tensor product, in CoLog generalise and extend existing constructions given for Set coalgebraic logics and that the framework does not depend on any particular propositional logic or state space. In the case that P establishes a dual adjunction with its dual functor S, we show that a canonically defined coalgebraic logic exists for any type of coalgebras. We further restrict our discussion to finitary algebraic logics and study equational coalgebraic logics. Objects of predicate liftings are used to characterise equational coalgebraic logics. The expressiveness problem is studied via the mate correspondence, which gives an isomorphism between CoLog and the comma category from the pre-composition to the post-composition with S. Then, the modularity of the expressiveness is studied in the comma category via the notion of factorisation system.
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Cloete, Walter (Walter Theophilus Woldemar). "A many-dimensional approach to simulations in modal logic." Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/20152.
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Thesis (MSc)--Stellenbosch University, 2012.ENGLISH ABSTRACT: Truth preservation is an important topic in model theory. However a brief examination of the models for a logic often show that isomorphism is needlessly restrictive as a truth preserving construction. In the case of modal logics with Kripke semantics the notions of simulation and bisimulation prove far more practical and interesting than isomorphism. We present and study these various notions, followed by a discussion of Shehtman’s frame product as semantics for certain many-dimensional modal logics. We show how simulations and bisimulations can be interpreted inside models over frame products. This is followed by a discussion on a category-theoretic setting for frame products, where the arrows may run between frames with different types.
AFRIKAANSE OPSOMMING: Die behou van waarheid is ’n prominente onderwerp in modelteorie. ’n Vlugtige ondersoek van die modelle vir ’n besondere logika wys egter dat isomorfisme onnodig beperkend as waarheid-behoudende konstruksie is. In die geval van modale logika met Kripke se semantiek is simulasie en bisimulasie heelwat meer prakties en interessant as isomorfisme. Na die bekendstel en studie van hierdie onderskeie begrippe bespreek ons Shehtman se raamproduk as semantiek vir sekere meer-dimensionele modale logikas. Ons wys ons hoe simulasies en bisimulasies binne modelle oor sulke raamprodukte geïnterpreteer kan word. Daarna bespreek ons ’n kategorie-teoretiese konteks vir raamprodukte, waar die pyle tussen rame met verskillende tipes mag loop.
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Paxton, Alan. "Using modal logic proofs to test implementation-specification relations." Thesis, University of Edinburgh, 2000. http://hdl.handle.net/1842/15603.
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This thesis shows how to make use of the intensional information relating specifications to implementations. It views the proofs of properties of specifications as identifying the intensional parts of implementations relevant to the property. It provides a concrete instance of such proofs by adopting labelled transition systems, modal-mu calculus and the tableau methods of Stirling and Bradfield as a framework for generating intensional information. The intensional information generated from proofs about models of systems can be used to verify behaviours of implementations of systems. By annotating implementations of systems with the atomic actions of their models we can apply oracle technique to verifying implementation behaviour. The extra richness of intensional information allows oracles derived from proofs, rather than just from properties, to be much more discriminating of failures in the implementation. The emphasis of oracle-based testing and verification is on practical improvements in the quality of distributed systems. Therefore the intensional idea is developed into a framework for a practical system. Case study systems are examined to identify where system developers can be helped by computerised systems to integrate auditioning into the software development process.
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Kretz, Mathis. "Proof-theoretic aspects of modal logic with fixed points /." Bern : [s.n.], 2006. http://www.zb.unibe.ch/download/eldiss/06kretz_m.pdf.
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Bruse, Florian [Verfasser]. "Extremal fixpoints for higher-order modal logic / Florian Bruse." Kassel : Universitätsbibliothek Kassel, 2020. http://d-nb.info/1220854093/34.
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Peron, Newton Marques 1982. "(In)completude modal por (N)matrizes finitas." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/281196.
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Orientador: Marcelo Esteban ConiglioTese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas
Made available in DSpace on 2018-08-25T12:43:36Z (GMT). No. of bitstreams: 1 Peron_NewtonMarques_D.pdf: 1773917 bytes, checksum: da2d2a1b1ecf8da6e26e419dee4888c5 (MD5) Previous issue date: 2014
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
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Fajardo, Rogerio Augusto dos Santos. "\"Combinações de lógicas modais não-normais\"." Universidade de São Paulo, 2004. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-13122007-203348/.
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Neste trabalho, estudamos algumas formas de combinar sistemas de Lógica Modal, analisando quando a combinação preserva propriedades como correção, completude e decidibilidade. Estendemos um estudo já realizado sobre combinações de sistemas de Lógica Modal Normal para sistemas de Lógica Modal Não-normal. O principal resultado deste trabalho é a preservação de completude da aplicação externa de um sistema de Lógica Modal Não-normal M em um sistema lógico L. Outro resultado importante é um exemplo de interação forte na combinação independente, ou fusão, de dois sistemas de Lógica Modal Não-normal.In this work, we study a few ways of combining Modal Logic systems, analysing when the combination preserves properties like soundness, completeness and decidability. We extend a study of the combination of Normal Modal Logic systems to Non-normal Modal Logic systems. The main result of this work is the completeness preservation in the external application of a Non-normal Modal Logic system M to a logic system L. Another important result is an example of strong interations arising in the fusion of two Non-normal Modal Logic system.
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Creel, James Silas. "Intention is commitment with expectation." Texas A&M University, 2005. http://hdl.handle.net/1969.1/2313.
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Modal logics with possible worlds semantics can be used to represent mental
states such as belief, goal, and intention, allowing one to formally describe the
rational behavior of agents. Agent??s beliefs and goals are typically represented in
these logics by primitive modal operators. However, the representation of agent??s
intentions varies greatly between theories. Some logics characterize intention as a
primitive operator, while others define intention in terms of more primitive constructs.
Taking the latter approach is a theory due to Philip Cohen and Hector
Levesque, under which intentions are a special form of commitment or persistent
goal. The theory has motivated theories of speech acts and joint intention
and innovative applications in multiagent systems and industrial robotics. However,
Munindar Singh shows the theory to have certain logical inconsistencies
and permit certain absurd scenarios. This thesis presents a modification of the
theory that preserves the desirable aspects of the original while addressing the
criticism of Singh. This is achieved by the introduction of an additional operator
describing the achievement of expectations, refined assumptions, and new defi-
nitions of intention. The modified theory gives a cogent account of the rational
balance between agents?? action and deliberation, and suggests the use of meansends
reasoning in agent implementations. A rule-based reasoner in Jess facilitates
evaluation of the predictiveness and intuitiveness of the theory, and provides a
prototypical agent based on the theory.
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Guido, Nicola. "On the Static Analysis for SPARQL Queries using Modal Logic." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAM059/document.
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L’analyse statique est une tâche essentielle dans l’optimisation des requêtes et la vérification de la base de graphes RDF. Nous étudions des techniques d’analyse statique pour SPARQL, le langage standard pour l’interrogation des données du Web sémantique. Plus précisément, nous étudions le problème d’inclusion des requêtes et de l’analyse de l’indépendance entre les requêtes et la mise à jour de la base de graphes RDF.Nous sommes intéressés par le développement de techniques grâce à des réductions au problème de la satisfaisabilité de la logique.Nous nous traitons le problème d’inclusion des requêtes SPARQL en présence de l’opérateur OPTIONAL. L’optionalité est l’un des constructeurs les plus compliqués dans SPARQL et aussi celui qui rend ce langage plus expressif que les langages de requêtes classiques, comme SQL.Nous nous concentrons sur la classe de requêtes appelée "well-designed SPARQL", proposées dans la littérature comme un fragment du langage avec de bonnes propriétés en matière d’évaluation des requêtes incluent l’opération OPTIONAL. À ce jour, l’inclusion de requête a été testée à l’aide de différentes techniques: homomorphisme de graphes, bases de données canoniques, techniques de la théorie des automates et réduction au problème de la validité d’une logique. Dans cette thèse, nous utilisons la dernière technique pour tester l’inclusion des requêtes SPARQL avec OPTIONAL utilisant une logique expressive appelée «logique K». En utilisant cette technique, il est possible de régler le problème d’inclusion des requêtes pour plusieurs fragment de SPARQL, même en présence de schémas. Cette extensibilité n’est pas garantie par les autres méthodes.Nous montrons comment traduire a graphe RDF en un système de transitions, ainsi que une requête SPARQL en une formula K. Avec ces traductions, l’inclusion des requêtes dans SPARQL peut être réduite au test de la validité d’une formule logique. Un avantage de cette approche est d’ouvrir la voie pour des implémentations utilisant solveurs de satisfiabilité pour K.Nous présentons un banc d’essais de tests d’inclusion pour les requêtes SPARQL avec OPTIONAL. Nous avons effectué des expériences pour tester et comparer des solveurs d’inclusion de l’état de l’art.Nous présentons également un aperçu préliminaire du problème d’indépendance entre requête et mise à jour. Une requête est indépendante de la mise à jour lorsque l’exécution de la mise à jour ne modifie pas le résultat de la requête. Bien que ce problème ait été intensivement étudié pour des fragments de calcul relationnel, il n’existe pas de travaux pour le langage de requêtes standard pour le web sémantique. Nous proposons une définition de la notion de l’indépendance dans le contexte de SPARQL et nous établissons des premières pistes de analyse statique dans certains situations d’inclusion entre une requête et une mise à jourStatic analysis is a core task in query optimization and knowledge base verification. We study static analysis techniques for SPARQL, the standard language for querying Semantic Web data. Specifically, we investigate the query containment problem and the query-update independence analysis. We are interested in developing techniques through reductions to the validity problem in logic.We address SPARQL query containment with optional matching. We focus on the class of well-designed SPARQL queries, proposed in the literature as a fragment of the language with good properties regarding query evaluation. SPARQL is interpreted over graphs, hence we encode it in a graph logic, specifically the modal logic K interpreted over label transition systems. We show that this logic is powerful enough to deal with query containment for the well-designed fragment of SPARQL. We show how to translate RDF graphs into transition systems and SPARQL queries into K-formulae. Therefore, query containment in SPARQL can be reduced to unsatisfiability in K.We also report on a preliminary overview of the SPARQL query-update problem. A query is independent of an update when the execution of the update does not affect the result of the query. Determining independence is especially useful in the contest of huge RDF repositories, where it permits to avoid expensive yet useless re-evaluation of queries. While this problem has been intensively studied for fragments of relational calculus, no works exist for the standard query language for the semantic web. We report on our investigations on how a notion of independence can be defined in the SPARQL context
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Mio, Matteo. "Game semantics for probabilistic modal μ-calculi." Thesis, University of Edinburgh, 2012. http://hdl.handle.net/1842/6223.
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The probabilistic (or quantitative) modal μ-calculus is a fixed-point logic designed for expressing properties of probabilistic labeled transition systems (PLTS’s). Two semantics have been studied for this logic, both assigning to every process state a value in the interval [0, 1] representing the probability that the property expressed by the formula holds at the state. One semantics is denotational and the other is a game semantics, specified in terms of two-player stochastic games. The two semantics have been proved to coincide on all finite PLTS’s. A first contribution of the thesis is to extend this coincidence result to arbitrary PLTS’s. A shortcoming of the probabilistic μ-calculus is the lack of expressiveness required to encode other important temporal logics for PLTS’s such as Probabilistic Computation Tree Logic (PCTL). To address this limitation, we extend the logic with a new pair of operators: independent product and coproduct, and we show that the resulting logic can encode the qualitative fragment of PCTL. Moreover, a further extension of the logic, with the operation of truncated sum and its dual, is expressive enough to encode full PCTL. A major contribution of the thesis is the definition of appropriate game semantics for these extended probabilistic μ-calculi. This relies on the definition of a new class of games, called tree games, which generalize standard 2-player stochastic games. In tree games, a play can be split into concurrent subplays which continue their evolution independently. Surprisingly, this simple device supports the encoding of the whole class of imperfect-information games known as Blackwell games. Moreover, interesting open problems in game theory, such as qualitative determinacy for 2-player stochastic parity games, can be reformulated as determinacy problems for suitable classes of tree games. Our main technical result about tree games is a proof of determinacy for 2-player stochastic metaparity games, which is the class of tree games that we use to give game semantics to the extended probabilistic μ-calculi. In order to cope with measure-theoretic technicalities, the proof is carried out in ZFC set theory extended with Martin’s Axiom at the first uncountable cardinal (MAℵ1). The final result of the thesis shows that the game semantics of the extended logics coincides with the denotational semantics, for arbitrary PLTS’s. However, in contrast to the earlier coincidence result, which is proved in ZFC, the proof of coincidence for the extended calculi is once again carried out in ZFC +MAℵ1.
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Kniazev, Roman. "On geometric models of epistemic logic." Electronic Thesis or Diss., Institut polytechnique de Paris, 2023. http://www.theses.fr/2023IPPAX132.
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Il y a environ 30 ans, deux approches majeures pour l'étude des systèmes distribués ont été développées. Une des approches a établi une perspective topologique sur le calcul distribué,exprimant la solvabilité des tâches distribuées à travers des notions standards de topologie algébrique, en modélisant les espaces d'états sous forme de complexes simpliciaux. En parallèle, une application importante de la logique épistémique, un type de logique modale, a apporté un point de vue alternatif sur la structure des systèmes distribués, en utilisant la notion de connaissance pour décrire le comportement des processus dans un système. On s'est récemment rendu compte que ces deux approches sont étroitement liées et que les modèles topologiques peuvent, en fait, servir de modèles de logique épistémique. Cette thèse poursuit un programme de recherche visant à unifier ces deux approches.Le premier objectif est de généraliser la sémantique actuelle de la logique épistémique basée sur les complexes simpliciaux au cas des ensembles simpliciaux. Nous montrons qu'avec ces modèles, on peut exprimer des connaissances de groupe non standard, c'est-à-dire des situations où la connaissance d'un groupe vu dans son ensemble est strictement supérieure à l'union des connaissances de ses membres.On considère ensuite une variante multi-sortes de la logique épistémique, dans laquelle les propriétés de l'environnement et les propriétés locales des agents sont exprimées séparément. Cette logique est interprétée dans les hypergraphes chromatiques, qui sont une généralisation supplémentaire des complexes simpliciaux, nous permettant de souligner le rôle des points de vue locaux des agents dans les systèmes distribués.On étudie la dynamique de la connaissance dans les systèmes distribués en introduisant une variante dynamique des hypergraphes chromatiques. Dans ces modèles, les points de vue locaux des agents sont dotés d'une structure temporelle, ce qui permet de modéliser l'évolution des connaissances dans le temps. De plus, on discute de la relation entre la connaissance et la concurrence dans ce contexte.Enfin, on présente une nouvelle direction de recherche qui se concentre sur l'utilisation de catégories supérieures dans l'étude des logiques modales multi-sortes. On montre que certaines logiques peuvent être représentées comme des catégories enrichies sur des ordres partiels, et qu'il y a une classe naturelle de modèles algébriques, par rapport à laquelle la logique est complèteOne approach established a topological perspective on distributed computing, expressing solvability of distributed tasks through standard notions of algebraic topology, by modelling spaces of states as simplicial complexes. In parallel, a prominent application of epistemic logic, a type of modal logic, provided an alternative point of view on the structure of distributed systems, by using the notion of knowledge to describe the behavior of processes in a system. It has recently been realized that these two approaches are closely related, and that the topological models can, in fact, serve as models of epistemic logic. This thesis continues a research program aimed at unification of these two approaches.Our first goal is to generalize the existing semantics of epistemic logic based on simplicial complexes to the case of simplicial sets. We show that with these models one can express non-standard group knowledge, that is situations when knowledge of a group seen as a whole is strictly greater than the union of knowledge of its members.We then proceed to study a many-sorted variant of epistemic logic, where properties of the environment and local properties of agents are expressed separately. This logic is interpreted in chromatic hypergraphs, which are a further generalization of simplicial complexes, allowing us to emphasize the role of local points of view of agents in distributed systems.We also investigate the dynamics of knowledge in distributed systems by introducing a dynamic variant of chromatic hypergraphs. In these models, local views of agents are supplemented with a temporal structure, which allows us to model the evolution of knowledge in time. Additionally, we discuss the relationship between knowledge and concurrency in this setting.Finally, we present a new direction of research that focuses on the use of higher categories in the study of many-sorted modal logics. We show that certain logics can be represented as categories enriched over partial orders, and that there is a naturally arising class of algebraic models, with respect to which the logic is complete
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Nair, Vineet. "On Extending BDI Logics." Thesis, Griffith University, 2003. http://hdl.handle.net/10072/365892.
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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.Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
School of Information Technology
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Gore, Rajeev. "Cut-free sequent and tableau systems for propositional normal modal logics." Thesis, University of Cambridge, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239668.
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Figueiredo, Daniel Oliveira. "Differential dynamic logic and applications." Master's thesis, Universidade de Aveiro, 2015. http://hdl.handle.net/10773/16841.
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Mestrado em Matemática e AplicaçõesNa área industrial e habitual usar ferramentas discretas em sistemas cuja evolução e contínua e regida pelas leis da mecânica. Estes sistemas que apresentam tanto comportamento contínuo como discreto são conhecidos como sistemas híbridos. A lógica diferencial dinâmica e uma lógica desenvolvida recentemente para trabalhar com estes sistemas. Neste trabalho, apresentamos a lógica diferencial dinâmica como uma generalização da lógica dinâmica (e, consequentemente, da lógica modal). Também são apresentadas algumas aplicações e discutida a utilidade destas lógicas nas áreas da mecânica e da biologia. Embora o uso de ferramentas computacionais seja comum e os resultados até agora obtidos sejam satisfatórios, os exemplos apresentados mostram que a lógica diferencial dinâmica pode ser usada como uma alternativa, assim como um complemento, na biologia sintética
In industry, it is often used discrete tools in system which behavior is continuous and modeled by the laws of mechanics. These systems which display both continuous and discrete dynamic behavior are known as hybrid systems. Di erential dynamic logic is a logic recently developed in order to reasoning about hybrid systems. In this work, we present the di erential dynamic logic as a generalization of dynamic logic (and consequently of modal logic). We also present some applications and we discuss about the utility of using these logics in the areas of mechanics and molecular biology. Although computational tools have been applied to reasoning about biological regulatory networks with satisfactory results, our examples show that di erential dynamic logic can be used as an alternative, or even as a complement, in synthetic biology.
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Mendler, M. "A modal logic for handling behavioural constraints in formal hardware verification." Thesis, University of Edinburgh, 1992. http://hdl.handle.net/1842/15374.
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The application of formal methods to the design of correct computer hardware depends crucially on the use of abstraction mechanisms to partition the synthesis and verification task into tractable pieces. Unfortunately however, behavioural abstractions are genuine mathematical abstractions only up to behavioural constraints, i.e. under certain restrictions imposed on the device's environment. Timing constraints on input signals form an important class of such restrictions. Hardware components that behave properly only under such constraints satisfy their abstract specifications only approximately. This is an impediment to the naive approach to formal verification since the question of how to apply a theorem prover when one only knows approximately what formula to prove has not as yet been dealt with. In this thesis we propose, as a solution, to interpret the notion of 'correctness up to constraint' as a modality of intuitionistic predicate logic so as to remove constraints from the specification and to make them part of its proof. This provides for an 'approximate' verification of abstract specifications and yet does not compromise the rigour of the argument since a realizability semantics can be used to extract the constraints. Also, the abstract verification is separated from constraint analysis which in turn may be delayed arbitrarily. In the proposed framework constraint analysis comes down to proof analysis and a computational semantics on proofs may be used to manipulate and simplify constraints.
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Kramdi, Seifeddine. "A modal approach to model computational trust." Thesis, Toulouse 3, 2015. http://www.theses.fr/2015TOU30146/document.
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Le concept de confiance est un concept sociocognitif qui adresse la question de l'interaction dans les systèmes concurrents. Quand la complexité d'un système informatique prohibe l'utilisation de solutions traditionnelles de sécurité informatique en amont du processus de développement (solutions dites de type dur), la confiance est un concept candidat, pour le développement de systèmes d'aide à l'interaction. Dans cette thèse, notre but majeur est de présenter une vue d'ensemble de la discipline de la modélisation de la confiance dans les systèmes informatiques, et de proposer quelques modèles logiques pour le développement de module de confiance. Nous adoptons comme contexte applicatif majeur, les applications basées sur les architectures orientées services, qui sont utilisées pour modéliser des systèmes ouverts telle que les applications web. Nous utiliserons pour cela une abstraction qui modélisera ce genre de systèmes comme des systèmes multi-agents. Notre travail est divisé en trois parties, la première propose une étude de la discipline, nous y présentons les pratiques utilisées par les chercheurs et les praticiens de la confiance pour modéliser et utiliser ce concept dans différents systèmes, cette analyse nous permet de définir un certain nombre de points critiques, que la discipline doit aborder pour se développer. La deuxième partie de notre travail présente notre premier modèle de confiance. Cette première solution basée sur un formalisme logique (logique dynamique épistémique), démarre d'une interprétation de la confiance comme une croyance sociocognitive, ce modèle présentera une première modélisation de la confiance. Apres avoir prouvé la décidabilité de notre formalisme. Nous proposons une méthodologie pour inférer la confiance en des actions complexes : à partir de notre confiance dans des actions atomiques, nous illustrons ensuite comment notre solution peut être mise en pratique dans un cas d'utilisation basée sur la combinaison de service dans les architectures orientées services. La dernière partie de notre travail consiste en un modèle de confiance, où cette notion sera perçue comme une spécialisation du raisonnement causal tel qu'implémenté dans le formalisme des règles de production. Après avoir adapté ce formalisme au cas épistémique, nous décrivons trois modèles basés sur l'idée d'associer la confiance au raisonnement non monotone. Ces trois modèles permettent respectivement d'étudier comment la confiance est générée, comment elle-même génère les croyances d'un agent et finalement, sa relation avec son contexte d'utilisationThe concept of trust is a socio-cognitive concept that plays an important role in representing interactions within concurrent systems. When the complexity of a computational system and its unpredictability makes standard security solutions (commonly called hard security solutions) inapplicable, computational trust is one of the most useful concepts to design protocols of interaction. In this work, our main objective is to present a prospective survey of the field of study of computational trust. We will also present two trust models, based on logical formalisms, and show how they can be studied and used. While trying to stay general in our study, we use service-oriented architecture paradigm as a context of study when examples are needed. Our work is subdivided into three chapters. The first chapter presents a general view of the computational trust studies. Our approach is to present trust studies in three main steps. Introducing trust theories as first attempts to grasp notions linked to the concept of trust, fields of application, that explicit the uses that are traditionally associated to computational trust, and finally trust models, as an instantiation of a trust theory, w.r.t. some formal framework. Our survey ends with a set of issues that we deem important to deal with in priority in order to help the advancement of the field. The next two chapters present two models of trust. Our first model is an instantiation of Castelfranchi & Falcone's socio-cognitive trust theory. Our model is implemented using a Dynamic Epistemic Logic that we propose. The main originality of our solution is the fact that our trust definition extends the original model to complex action (programs, composed services, etc.) and the use of authored assignment as a special kind of atomic actions. The use of our model is then illustrated in a case study related to service-oriented architecture. Our second model extends our socio-cognitive definition to an abductive framework that allows us to associate trust to explanations. Our framework is an adaptation of Bochman's production relations to the epistemic case. Since Bochman approach was initially proposed to study causality, our definition of trust in this second model presents trust as a special case of causal reasoning, applied to a social context. We end our manuscript with a conclusion that presents how we would like to extend our work
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Lehtinen, Maria Karoliina. "Syntactic complexity in the modal μ calculus." Thesis, University of Edinburgh, 2017. http://hdl.handle.net/1842/29520.
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This thesis studies how to eliminate syntactic complexity in Lμ, the modal μ calculus. Lμ is a verification logic in which a least fixpoint operator μ, and its dual v, add recursion to a simple modal logic. The number of alternations between μ and v is a measure of complexity called the formula’s index: the lower the index, the easier a formula is to model-check. The central question of this thesis is a long standing one, the Lμ index problem: given a formula, what is the least index of any equivalent formula, that is to say, its semantic index? I take a syntactic approach, focused on simplifying formulas. The core decidability results are (i) alternative, syntax-focused decidability proofs for ML and Pμ 1 , the low complexity classes of μ; and (ii) a proof that Ʃμ 2 , the fragment of Lμ with one alternation, is decidable for formulas in the dual class Pμ 2 . Beyond its algorithmic contributions, this thesis aims to deepen our understanding of the index problem and the tools at our disposal. I study disjunctive form and related syntactic restrictions, and how they affect the index problem. The main technical results are that the transformation into disjunctive form preserves Pμ 2 -indices but not μ 2 -indices, and that some properties of binary trees are expressible with a lower index using disjunctive formulas than non-deterministic automata. The latter is part of a thorough account of how the Lμ index problem and the Rabin–Mostowski index problem for parity automata are related. In the final part of the thesis, I revisit the relationship between the index problem and parity games. The syntactic index of a formula is an upper bound on the descriptive complexity of its model-checking parity games. I show that the semantic index of a formula Ψ is bounded above by the descriptive complexity of the model-checking games for Ψ. I then study whether this bound is strict: if a formula Ψ is equivalent to a formula in an alternation class C, does a formula of C suffice to describe the winning regions of the model-checking games of Ψ? I prove that this is the case for ML, Pμ 1 , Ʃμ 2 , and the disjunctive fragment of any alternation class. I discuss the practical implications of these results and propose a uniform approach to the index problem, which subsumes the previously described decision procedures for low alternation classes. In brief, this thesis can be read as a guide on how to approach a seemingly complex Lμ formula. Along the way it studies what makes this such a difficult problem and proposes novel approaches to both simplifying individual formulas and deciding further fragments of the alternation hierarchy.
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Johnston, Spencer C. "Essentialism, nominalism, and modality : the modal theories of Robert Kilwardby & John Buridan." Thesis, University of St Andrews, 2015. http://hdl.handle.net/10023/7820.
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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.
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Fritz, Peter. "Intensional type theory for higher-order contingentism." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:b9415266-ad21-494a-9a78-17d2395eb8dd.
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Things could have been different, but could it also have been different what things there are? It is natural to think so, since I could have failed to be born, and it is natural to think that I would then not have been anything. But what about entities like propositions, properties and relations? Had I not been anything, would there have been the property of being me? In this thesis, I formally develop and assess views according to which it is both contingent what individuals there are and contingent what propositions, properties and relations there are. I end up rejecting these views, and conclude that even if it is contingent what individuals there are, it is necessary what propositions, properties and relations there are. Call the view that it is contingent what individuals there are first-order contingentism, and the view that it is contingent what propositions, properties and relations there are higher-order contingentism. I bring together the three major contributions to the literature on higher-order contingentism, which have been developed largely independently of each other, by Kit Fine, Robert Stalnaker, and Timothy Williamson. I show that a version of Stalnaker's approach to higher-order contingentism was already explored in much more technical detail by Fine, and that it stands up well to the major challenges against higher-order contingentism posed by Williamson. I further show that once a mistake in Stalnaker's development is corrected, each of his models of contingently existing propositions corresponds to the propositional fragment of one of Fine's more general models of contingently existing propositions, properties and relations, and vice versa. I also show that Stalnaker's theory of contingently existing propositions is in tension with his own theory of counterfactuals, but not with one of the main competing theories, proposed by David Lewis. Finally, I connect higher-order contingentism to expressive power arguments against first-order contingentism. I argue that there are intelligible distinctions we draw with talk about "possible things", such as the claim that there are uncountably many possible stars. Since first-order contingentists hold that there are no possible stars apart from the actual stars, they face the challenge of paraphrasing such talk. I show that even in an infinitary higher-order modal logic, the claim that there are uncountably many possible stars can only be paraphrased if higher-order contingentism is false. I therefore conclude that even if first-order contingentism is true, higher-order contingentism is false.
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Zaverucha, Gerson. "A nonmonotonic multi-agent logic of belief : a Modal Defeasible Relevant approach." Thesis, Imperial College London, 1990. http://hdl.handle.net/10044/1/46629.
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Castellini, Claudio. "Automated reasoning in quantified modal and temporal logics." Thesis, University of Edinburgh, 2005. http://hdl.handle.net/1842/753.
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This thesis is about automated reasoning in quantified modal and temporal logics, with an application to formal methods. Quantified modal and temporal logics are extensions of classical first-order logic in which the notion of truth is extended to take into account its necessity or equivalently, in the temporal setting, its persistence through time. Due to their high complexity, these logics are less widely known and studied than their propositional counterparts. Moreover, little so far is known about their mechanisability and usefulness for formal methods. The relevant contributions of this thesis are threefold: firstly, we devise a sound and complete set of sequent calculi for quantified modal logics; secondly, we extend the approach to the quantified temporal logic of linear, discrete time and develop a framework for doing automated reasoning via Proof Planning in it; thirdly, we show a set of experimental results obtained by applying the framework to the problem of Feature Interactions in telecommunication systems. These results indicate that (a) the problem can be concisely and effectively modeled in the aforementioned logic, (b) proof planning actually captures common structures in the related proofs, and (c) the approach is viable also from the point of view of efficiency.
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Gutierrez, Julian. "On bisimulation and model-checking for concurrent systems with partial order semantics." Thesis, University of Edinburgh, 2011. http://hdl.handle.net/1842/5281.
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In concurrency theory—the branch of (theoretical) computer science that studies the logical and mathematical foundations of parallel computation—there are two main formal ways of modelling the behaviour of systems where multiple actions or events can happen independently and at the same time: either with interleaving or with partial order semantics. On the one hand, the interleaving semantics approach proposes to reduce concurrency to the nondeterministic, sequential computation of the events the system can perform independently. On the other hand, partial order semantics represent concurrency explicitly by means of an independence relation on the set of events that the system can execute in parallel; following this approach, the so-called ‘true concurrency’ approach, independence or concurrency is a primitive notion rather than a derived concept as in the interleaving framework. Using interleaving or partial order semantics is, however, more than a matter of taste. In fact, choosing one kind of semantics over the other can have important implications—both from theoretical and practical viewpoints—as making such a choice can raise different issues, some of which we investigate here. More specifically, this thesis studies concurrent systems with partial order semantics and focuses on their bisimulation and model-checking problems; the theories and techniques herein apply, in a uniform way, to different classes of Petri nets, event structures, and transition system with independence (TSI) models. Some results of this work are: a number of mu-calculi (in this case, fixpoint extensions of modal logic) that, in certain classes of systems, induce exactly the same identifications as some of the standard bisimulation equivalences used in concurrency. Secondly, the introduction of (infinite) higher-order logic games for bisimulation and for model-checking, where the players of the games are given (local) monadic second-order power on the sets of elements they are allowed to play. And, finally, the formalization of a new order-theoretic concurrent game model that provides a uniform approach to bisimulation and model-checking and bridges some mathematical concepts in order theory with the more operational world of games. In particular, we show that in all cases the logic games for bisimulation and model-checking developed in this thesis are sound and complete, and therefore, also determined—even when considering models of infinite state systems; moreover, these logic games are decidable in the finite case and underpin novel decision procedures for systems verification. Since the mu-calculi and (infinite) logic games studied here generalise well-known fixpoint modal logics as well as game-theoretic decision procedures for analysing concurrent systems with interleaving semantics, this thesis provides some of the groundwork for the design of a logic-based, game-theoretic framework for studying, in a uniform manner, several concurrent systems regardless of whether they have an interleaving or a partial order semantics.