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Articoli di riviste sul tema "Modality (Logic)"

Autore: Grafiati

Pubblicato: 4 giugno 2021

Ultima modifica: 28 luglio 2024

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1

Avron, Arnon, e Anna Zamansky. "Paraconsistency, self-extensionality, modality". Logic Journal of the IGPL 28, n. 5 (27 novembre 2018): 851–80. http://dx.doi.org/10.1093/jigpal/jzy064.

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Abstract Paraconsistent logics are logics that, in contrast to classical and intuitionistic logic, do not trivialize inconsistent theories. In this paper we take a paraconsistent view on two famous modal logics: B and S5. We use for this a well-known general method for turning modal logics to paraconsistent logics by defining a new (paraconsistent) negation as $\neg \varphi =_{Def} \sim \Box \varphi$ (where $\sim$ is the classical negation). We show that while that makes both B and S5 members of the well-studied family of paraconsistent C-systems, they differ from most other C-systems in having the important replacement property (which means that equivalence of formulas implies their congruence). We further show that B is a very robust C-system in the sense that almost any axiom which has been considered in the context of C-systems is either already a theorem of B or its addition to B leads to a logic that is no longer paraconsistent. There is exactly one notable exception, and the result of adding this exception to B leads to the other logic studied here, S5.

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Birštunas, Adomas. "Efficient decision procedure for Belief modality". Lietuvos matematikos rinkinys 45 (18 dicembre 2005): 321–25. http://dx.doi.org/10.15388/lmr.2005.26673.

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This paper defines decision algorithm for subclass of BKD45DKDIKD logic which is based on known algorithm for temporal BKD45DKDIKD logic [2]. BDI logics are widely used in agent based systems. Such usage of BDI logic can be found in [1]. The original decision algorithm uses loop-check technique for BEL and temporal operators. Applied loop-check technique is not optimized and therefore loop-check takes most of the time used in decision algorithm. Some examples of efficient loop-check applications for logic KT, S4 and some subclasses of intuitionistic logic can be found in [4]. Another efficient loop-check can be found in work [3]. We concentrate on our attitude on loop-check optimization for BEL operator. This paper defines decision algorithm modification, which uses efficient loop-check for BEL operator, but do not effect performance of other parts of algorithm. We define optimization only for BEL operator and therefore we omit temporal operators in this paper.

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3

Speranski, Stanislav O. "Negation as a modality in a quantified setting". Journal of Logic and Computation 31, n. 5 (5 aprile 2021): 1330–55. http://dx.doi.org/10.1093/logcom/exab025.

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Abstract The idea of treating negation as a modality manifests itself in various logical systems, especially in Došen’s propositional logic $\textsf {N}$, whose negation is weaker than that of Johansson’s minimal logic. Among the interesting extensions of $\textsf {N}$ are the propositional logics $\textsf {N}^{\ast }$ and $\textsf {Hype}$; the former was proposed in Cabalar et al. (2006, Proceedings of the 10th International Conference on Principles of Knowledge Representation and Reasoning, 25–36), while the latter has recently been advocated in Leitgeb (2019, J. Philos. Logic, 48, 305–405), but was first introduced in Moisil (1942, Disquisitiones Math. et Phys., 2, 3–98). I shall develop predicate versions of $\textsf {N}$ and $\textsf {N}^{\ast }$ and provide a simple Routley-style semantics for the predicate version of $\textsf {Hype}$. The corresponding strong completeness results will be proved by means of a useful general technique. It should be remarked that this work can also be seen as a starting point for the investigation of intuitionistic predicate modal logics.

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4

Petik, Ja O. "Modality and folk psychology". Studies in history and philosophy of science and technology 28, n. 1 (5 maggio 2019): 19–27. http://dx.doi.org/10.15421/271903.

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The connection of the modern psychology and formal systems remains an important direction of research. This paper is centered on philosophical problems surrounding relations between mental and logic. Main attention is given to philosophy of logic but certain ideas are introduced that can be incorporated into the practical philosophical logic. The definition and properties of basic modal logic and descending ones which are used in study of mental activity are in view. The defining role of philosophical interpretation of modality for the particular formal system used for research in the field of psychological states of agents is postulated. Different semantics of modal logic are studied. The hypothesis about the connection of research in cognitive psychology (semantics of brain activity) and formal systems connected to research of psychological states is stated.

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5

Spies, Simon, Lennard Gäher, Joseph Tassarotti, Ralf Jung, Robbert Krebbers, Lars Birkedal e Derek Dreyer. "Later credits: resourceful reasoning for the later modality". Proceedings of the ACM on Programming Languages 6, ICFP (29 agosto 2022): 283–311. http://dx.doi.org/10.1145/3547631.

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In the past two decades, step-indexed logical relations and separation logics have both come to play a major role in semantics and verification research. More recently, they have been married together in the form of step-indexed separation logics like VST, iCAP, and Iris, which provide powerful tools for (among other things) building semantic models of richly typed languages like Rust. In these logics, propositions are given semantics using a step-indexed model, and step-indexed reasoning is reflected into the logic through the so-called “later” modality. On the one hand, this modality provides an elegant, high-level account of step-indexed reasoning; on the other hand, when used in sufficiently sophisticated ways, it can become a nuisance, turning perfectly natural proof strategies into dead ends. In this work, we introduce later credits , a new technique for escaping later-modality quagmires. By leveraging the second ancestor of these logics—separation logic—later credits turn “the right to eliminate a later” into an ownable resource, which is subject to all the traditional modular reasoning principles of separation logic. We develop the theory of later credits in the context of Iris, and present several challenging examples of proofs and proof patterns which were previously not possible in Iris but are now possible due to later credits.

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6

THIELECKE, HAYO. "Control effects as a modality". Journal of Functional Programming 19, n. 1 (gennaio 2009): 17–26. http://dx.doi.org/10.1017/s0956796808006734.

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AbstractWe combine ideas from types for continuations, effect systems and monads in a very simple setting by defining a version of classical propositional logic in which double-negation elimination is combined with a modality. The modality corresponds to control effects, and it includes a form of effect masking. Erasing the modality from formulas gives classical logic. On the other hand, the logic is conservative over intuitionistic logic.

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7

Wilson, Alastair. "Modality: Metaphysics, Logic and Epistemology". Australasian Journal of Philosophy 89, n. 4 (dicembre 2011): 755–56. http://dx.doi.org/10.1080/00048402.2011.592541.

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8

KACHI, Daisuke. "Partial Logic as a Logic of Extensional Alethic Modality". Journal of the Japan Association for Philosophy of Science 34, n. 2 (2007): 61–70. http://dx.doi.org/10.4288/kisoron1954.34.61.

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9

White, Graham. "Causality, Modality, and Explanation". Notre Dame Journal of Formal Logic 49, n. 3 (luglio 2008): 313–43. http://dx.doi.org/10.1215/00294527-2008-015.

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10

Kurokawa, Hidenori, e Hirohiko Kushida. "Resource sharing linear logic". Journal of Logic and Computation 30, n. 1 (gennaio 2020): 295–319. http://dx.doi.org/10.1093/logcom/exaa013.

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Abstract In this paper, we introduce a new logic that we call ‘resource sharing linear logic (RSLL)’. In linear logic (LL), formulas without modality express some resource-conscious situation (a formula can be used only once); formulas with modality express a situation with unlimited resources. We introduce the logic RSLL in which we have a strengthened modality (S5-modality) that can be understood as expressing not only unlimited resources but also resources shared by different agents. Observing that merely strengthening the modality allows weakening axiom to be derivable in a Hilbert-style formulation of this logic, we reformulate RSLL as a logic similar to affine logic by a hypersequent calculus that has weakening as a primitive rule. We prove the completeness of the hypersequent calculus with respect to phase semantics and the cut-elimination theorem for the system by a syntactical method. We also prove the decidability of RSLL via a computational interpretation of RSLL, which is a parallel version of Kopylov’s computational model for LL. We then introduce an explicit counterpart of RSLL in the style of Artemov’s justication logic (JRSLL). We prove a realization theorem for RSLL via its explicit counterpart.

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11

SANO, KATSUHIKO, e YASUO NAKAYAMA. "Bimodal Logic with the Irreflxive Modality". Journal of the Japan Association for Philosophy of Science 34, n. 1 (2007): 1–10. http://dx.doi.org/10.4288/kisoron1954.34.1.

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12

Odland. "Peirce's Triadic Logic: Modality and Continuity". Transactions of the Charles S. Peirce Society 57, n. 2 (2021): 149. http://dx.doi.org/10.2979/trancharpeirsoc.57.2.01.

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13

Blee, Jeff, David Billington, Guido Governatori e Abdul Sattar. "Levels of modality for BDI Logic". Journal of Applied Logic 9, n. 4 (dicembre 2011): 250–73. http://dx.doi.org/10.1016/j.jal.2011.08.002.

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14

Esakia, Leo. "Intuitionistic logic and modality via topology". Annals of Pure and Applied Logic 127, n. 1-3 (giugno 2004): 155–70. http://dx.doi.org/10.1016/j.apal.2003.11.013.

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15

Shope, Robert K. "Powers, causation, and modality". Erkenntnis 28, n. 3 (maggio 1988): 321–62. http://dx.doi.org/10.1007/bf00184900.

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16

Healey, Richard. "Substance, modality and spacetime". Erkenntnis 42, n. 3 (maggio 1995): 287–316. http://dx.doi.org/10.1007/bf01129007.

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17

Stojnić, Una. "One's Modus Ponens : Modality, Coherence and Logic". Philosophy and Phenomenological Research 95, n. 1 (21 settembre 2016): 167–214. http://dx.doi.org/10.1111/phpr.12307.

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18

van Benthem, Johan. "Modality, bisimulation and interpolation in infinitary logic". Annals of Pure and Applied Logic 96, n. 1-3 (marzo 1999): 29–41. http://dx.doi.org/10.1016/s0168-0072(98)00029-3.

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19

Braüner, Torben. "Modal Logic, Truth, and the Master Modality". Journal of Philosophical Logic 31, n. 4 (agosto 2002): 359–86. http://dx.doi.org/10.1023/a:1019992820056.

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20

Fattorosi-Barnaba, Maurizio, e Uliano Paolozzi Balestrini. "The Modality of Finite (Graded Modalities VII)". Mathematical Logic Quarterly 45, n. 4 (1999): 471–80. http://dx.doi.org/10.1002/malq.19990450406.

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21

van der Hoeck, Wiebe. "Some considerations on the logics PFD A logic combining modality and probability". Journal of Applied Non-Classical Logics 7, n. 3 (gennaio 1997): 287–307. http://dx.doi.org/10.1080/11663081.1997.10510916.

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22

Kracht, Marcus, e Frank Wolter. "Properties of independently axiomatizable bimodal logics". Journal of Symbolic Logic 56, n. 4 (dicembre 1991): 1469–85. http://dx.doi.org/10.2307/2275487.

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In monomodal logic there are a fair number of high-powered results on completeness covering large classes of modal systems; witness for example Fine [74], [85] and Sahlqvist [75]. Monomodal logic is therefore a well-understood subject in contrast to polymodal logic, where even the most elementary questions concerning completeness, decidability, etc. have been left unanswered. Given that in many applications of modal logic one modality is not sufficient, the lack of general results is acutely felt by the “users” of modal logics, contrary to logicians who might entertain the view that a deep understanding of one modality alone provides enough insight to be able to generalize the results to logics with several modalities. Although this view has its justification, the main results we are going to prove are certainly not of this type, for they require a fundamentally new technique. The results obtained are called transfer theorems in Fine and Schurz [91] and are of the following type. Let L ∌ ⊥ be an independently axiomatizable bimodal logic and L⎕ and L∎ its monomodal fragments. Then L has a property P iff L⎕ and L∎ have P. Properties which will be discussed are completeness, the finite model property, compactness, persistence, interpolation and Halldén-completeness. In our discussion we will prove transfer theorems for the simplest case when there are just two modal operators, but it will be clear that the proof works in the general case as well.

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23

van Ditmarsch, H., e P. Iliev. "The succinctness of the cover modality". Journal of Applied Non-Classical Logics 25, n. 4 (2 ottobre 2015): 373–405. http://dx.doi.org/10.1080/11663081.2016.1144016.

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24

Reyes, Gonzalo E. "A topos-theoretic approach to reference and modality." Notre Dame Journal of Formal Logic 32, n. 3 (giugno 1991): 359–91. http://dx.doi.org/10.1305/ndjfl/1093635834.

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25

Font, Josep M. "Modality and possibility in some intuitionistic modal logics." Notre Dame Journal of Formal Logic 27, n. 4 (ottobre 1986): 533–46. http://dx.doi.org/10.1305/ndjfl/1093636766.

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26

Dal Lago, Ugo, e Claudia Faggian. "On Multiplicative Linear Logic, Modality and Quantum Circuits". Electronic Proceedings in Theoretical Computer Science 95 (1 ottobre 2012): 55–66. http://dx.doi.org/10.4204/eptcs.95.6.

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27

Yashin, A. D., e A. G. Makarov. "Irreflexive Modality, the Dummett Logic, and Continual Chains". Siberian Mathematical Journal 59, n. 2 (marzo 2018): 368–74. http://dx.doi.org/10.1134/s0037446618020209.

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28

Wölfl, Stefan. "Combinations of Tense and Modality for Predicate Logic". Journal of Philosophical Logic 28, n. 4 (agosto 1999): 371–98. http://dx.doi.org/10.1023/a:1004359325754.

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29

Martin, John N. "Lukasiewicz's Many-valued Logic and Neoplatonic Scalar Modality". History and Philosophy of Logic 23, n. 2 (giugno 2002): 95–120. http://dx.doi.org/10.1080/01445340210154330.

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30

Chellas, Brian F. "Time and modality in the logic of agency". Studia Logica 51, n. 3-4 (1992): 485–517. http://dx.doi.org/10.1007/bf01028972.

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31

Demri, Stéphane, e Raul Fervari. "The power of modal separation logics". Journal of Logic and Computation 29, n. 8 (dicembre 2019): 1139–84. http://dx.doi.org/10.1093/logcom/exz019.

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Abstract We introduce a modal separation logic MSL whose models are memory states from separation logic and the logical connectives include modal operators as well as separating conjunction and implication from separation logic. With such a combination of operators, some fragments of MSL can be seen as genuine modal logics whereas some others capture standard separation logics, leading to an original language to speak about memory states. We analyse the decidability status and the computational complexity of several fragments of MSL, obtaining surprising results by design of proof methods that take into account the modal and separation features of MSL. For example, the satisfiability problem for the fragment of MSL with $\Diamond $, the difference modality $\langle \neq \rangle $ and separating conjunction $\ast $ is shown Tower-complete whereas the restriction either to $\Diamond $ and $\ast $ or to $\langle \neq \rangle $ and $\ast $ is only NP-complete. We establish that the full logic MSL admits an undecidable satisfiability problem. Furthermore, we investigate variants of MSL with alternative semantics and we build bridges with interval temporal logics and with logics equipped with sabotage operators.

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32

Fatic, Aleksandar. "Modal logic in integrative philosophical practice". Filozofija i drustvo 34, n. 3 (2023): 424–37. http://dx.doi.org/10.2298/fid2303424f.

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The paper discusses the differences between a practical emphasis on binary logic on the one hand, and modal logic, on the other, specifically in the fields of philosophical practice and psychotherapy. Although studies of practical applications of modal logic in the helping professions are recent, the discussion largely revolves around the controversial application of modality in psychotherapy by C.G. Jung and Lacan?s psychoanalysis. The present argument touches on some of the conceptual dilemmas associated with the relationship between logical modality, intuition and scientificity in psychotherapy, all of which are a part of the philosophical foundation of psychotherapy.

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Sagüillo Fernández-Vega, José Miguel. "Hilary Putnam on the philosophy of logic and mathematics". THEORIA. An International Journal for Theory, History and Foundations of Science 33, n. 2 (20 giugno 2018): 183. http://dx.doi.org/10.1387/theoria.17626.

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I discuss Putnam’s conception of logical truth as grounded in his picture of mathematical practice and ontology. i begin by comparing Putnam’s 1971 Philosophy of Logic with Quine’s homonymous book. Next, Putnam’s changing views on modality are surveyed, moving from the modal pre-formal to the de-modalized formal characterization of logical validity. Section three suggests a complementary view of Platonism and modalism underlying different stages of a dynamic mathematical practice. The final section argues for the pervasive platonistic conception of the working mathematician.

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34

Thom, Paul. "De Re Modality and the New Essentialism: A Dilemma". Notre Dame Journal of Formal Logic 44, n. 4 (ottobre 2003): 189–99. http://dx.doi.org/10.1305/ndjfl/1091122497.

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35

Kubinjec, Janko. "Modality of judgments on justice". Glasnik Advokatske komore Vojvodine 79, n. 9 (2007): 287–94. http://dx.doi.org/10.5937/gakv0709287k.

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Definition of the concept of justice comes from apodictic judgments, while definition of its individual validity comes from assertoric judgments. Argumentation as an element of justice in a logical sense is an assertoric judgment. Its definition brings light to the search for the logical nature of assertoric judgment - it is a contribution the philosophy of law may offer to the logic. In the argumentation assertoric judgment does not transform to problematic judgment and for this reason the justice can never be arbitrary.

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Epstein, Sophia, e Pavel Naumov. "Epistemic Logic of Know-Who". Proceedings of the AAAI Conference on Artificial Intelligence 35, n. 13 (18 maggio 2021): 11479–86. http://dx.doi.org/10.1609/aaai.v35i13.17367.

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The paper suggests a definition of "know who" as a modality using Grove-Halpern semantics of names. It also introduces a logical system that describes the interplay between modalities "knows who", "knows", and "for all agents". The main technical result is a completeness theorem for the proposed system.

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Tuboly, Adam Tamas. "Necessity Lost. Modality and Logic in Early Analytic Philosophy". History and Philosophy of Logic 41, n. 1 (12 novembre 2019): 97–100. http://dx.doi.org/10.1080/01445340.2019.1683268.

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Durst-Andersen, Per. "Language, culture and society: Modality, face and societal logic". Globe: A Journal of Language, Culture and Communication 17 (18 dicembre 2023): 83–93. http://dx.doi.org/10.54337/ojs.globe.v17i.8201.

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It is common to distinguish between individualistic cultures typically associated with Western countries and collectivistic cultures normally linked to Asian countries. Some countries are not easily characterized, because they are placed right in the middle of the continuum. This concerns, for instance, Russia. In this paper, I will attempt to demonstrate on the basis of the theory of communicative supertypes that the notion of individualism is intimately connected to the notion of alethic modality – concerned with laws of nature, i.e. what is possible, impossible, necessary and unnecessary – whereas the notion of collectivism is tied up with the notion of deontic modality having to do with laws of society, i.e. permission, prohibition, obligation and non-obligation. Specifically, the British-English speaking speech community is based on the alethic notion of possibility and guided by the hearer's face, i.e. second person, in contrast to the Mandarin-Chinese-speaking community which is based on the deontic notion of obligation and guided by the speaker’s face, i.e. first person. Compared to this, the Russian-speaking community stands out as a third unnoticed variant that seems to differentiate nature and society by making a sharp distinction within their aspectually defined modality system, between alethic and deontic logic expressed by the perfective and the imperfective aspect, respectively. That Russian culture must be a third variant is confirmed by their understanding of face as being defined in relation to the situation itself, i.e. third person.

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MELLIÈS, PAUL-ANDRÉ, NICOLAS TABAREAU e CHRISTINE TASSON. "An explicit formula for the free exponential modality of linear logic". Mathematical Structures in Computer Science 28, n. 7 (21 aprile 2017): 1253–86. http://dx.doi.org/10.1017/s0960129516000426.

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The exponential modality of linear logic associates to every formula A a commutative comonoid !A which can be duplicated in the course of reasoning. Here, we explain how to compute the free commutative comonoid !A as a sequential limit of equalizers in any symmetric monoidal category where this sequential limit exists and commutes with the tensor product. We apply this general recipe to a series of models of linear logic, typically based on coherence spaces, Conway games and finiteness spaces. This algebraic description unifies for the first time a number of apparently different constructions of the exponential modality in spaces and games. It also sheds light on the duplication policy of linear logic, and its interaction with classical duality and double negation completion.

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Holm, Nicholas. "Conspiracy Theorizing Surveillance: considering modalities of paranoia and conspiracy in surveillance studies". Surveillance & Society 7, n. 1 (13 ottobre 2009): 36–48. http://dx.doi.org/10.24908/ss.v7i1.3306.

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In this paper I argue that the notion of paranoia can inform a post-panoptic theory of surveillance, without simply functioning as a pre-emptive dismissal of a critical engagement with technologies and regimes of surveillance as just paranoid. Rather, I seek to address how paranoia can be rearticulated to serve a productive, non-pathological function in an analysis of logics of surveillance. To this end, I consider the manner in which paranoia is characterised in popular cultural narratives and how the advent of cultural paranoia can be understood in the context of the expansion of state and corporate surveillance, especially in the UK and post-9/11 North America. Drawing on this notion of cultural paranoia, I then argue for three modalities of paranoia-as-surveillance theory. The first modality, the paranoia of the subject of surveillance, addresses the divergent panoptic subject who rejects the disciplinary logic of the panopticon; the second modality considers how the paranoid as the suspicious subject could be used to characterise the expansion of surveillance regimes through an ever-present need to observe; and the third modality of conspiracy theory proposes that a paranoid logic, akin to that of the conspiracy theory, sutures over epistemic gaps in the interpretation of information in instances of analytic deficit.

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Ewald, W. B. "Intuitionistic tense and modal logic". Journal of Symbolic Logic 51, n. 1 (marzo 1986): 166–79. http://dx.doi.org/10.2307/2273953.

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In this article we shall construct intuitionistic analogues to the main systems of classical tense logic. Since each classical modal logic can be gotten from some tense logic by one of the definitions(i) □ p ≡ p ∧ Gp ∧ Hp, ◇p ≡ p ∨ Fp ∨ Pp; or,(ii) □ p ≡ p ∧ Gp, ◇p = p ∨ Fp(see [5]), we shall find that our intuitionistic tense logics give us analogues to the classical modal logics as well.We shall not here discuss the philosophical issues raised by our logics. Readers interested in the intuitionistic view of time and modality should see [2] for a detailed discussion.In §2 we define the Kripke models for IKt, the intuitionistic analogue to Lemmon's system Kt. We then prove the completeness and decidability of this system (§§3–5). Finally, we extend our results to other sorts of tense logic and to modal logic.In the language of IKt, we have: sentence-letters p, q, r, etc.; the (intuitionistic) connectives ∧, ∨, →, ¬; and unary operators P (“it was the case”), F (it will be the case”), H (“it has always been the case”) and G (“it will always be the case”). Formulas are defined inductively: all sentence-letters are formulas; if X is a formula, so are ¬X, PX, FX, HX, and GX; if X and Y are formulas, so are X ∧ Y, X ∨ Y, and X → Y. We shall see that, in contrast to classical tense logic, F and P cannot be defined in terms of G and H.

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Vladimir, Rybakov. "Logics with the universal modality and admissible consecutions". Journal of Applied Non-Classical Logics 17, n. 3 (23 settembre 2007): 383–96. http://dx.doi.org/10.3166/jancl.17.383-396.

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Gluckman, John, e Margit Bowler. "The expression of modality in Logoori". Journal of African Languages and Linguistics 41, n. 2 (1 ottobre 2020): 195–238. http://dx.doi.org/10.1515/jall-2020-2010.

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Abstract This study presents a theoretically informed description of the expression of modality in Logoori (Luyia; Bantu). We document verbal and non-verbal modal expressions in Logoori, and show how these expressions fit into proposed typologies of modal systems (Kratzer, Angelika. 1981. The notional category of modality. In Hans-Jurgen Eikmeyer & Hannes Rieser (eds.), Words, worlds, and contexts: New approaches in word semantics, 38–74. Berlin: Mouton de Gruyter, Kratzer, Angelika. 1991. Modality. In Armin von Stechow & Dieter Wunderlich (eds.), Semantics: An international handbook of contemporary research, 639–650. Berlin: Mouton de Gruyter; van der Auwera, Johan & Vladimir Plungian. 1998. Modality’s semantic map. Linguistic Typology 2. 79–124. https://doi.org/10.1515/lity.1998.2.1.79; Nauze, Fabrice. 2008. Modality in typological perspective. Amsterdam: Institute for Logic, Language, and Computation PhD thesis). We show that Logoori’s modal system raises some interesting questions regarding the typology and theoretical analysis of modality and its relationship to other kinds of meaning. Our study contributes to the nascent but growing research on modal systems cross linguistically by adding data from an understudied Bantu language.

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Sano, Katsuhiko, e Jonni Virtema. "Characterising modal definability of team-based logics via the universal modality". Annals of Pure and Applied Logic 170, n. 9 (settembre 2019): 1100–1127. http://dx.doi.org/10.1016/j.apal.2019.04.009.

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SLAVNOV, SERGEY. "On Banach spaces of sequences and free linear logic exponential modality". Mathematical Structures in Computer Science 29, n. 2 (18 dicembre 2017): 215–42. http://dx.doi.org/10.1017/s0960129517000251.

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We introduce a category of vector spaces modelling full propositional linear logic, similar to probabilistic coherence spaces and to Koethe sequences spaces. Its objects are rigged sequence spaces, Banach spaces of sequences, with norms defined from pairing with finite sequences, and morphisms are bounded linear maps, continuous in a suitable topology. The main interest of the work is that our model gives a realization of the free linear logic exponentials construction.

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Cresswell, M. J. "Modality and Mellor's McTaggart". Studia Logica 49, n. 2 (giugno 1990): 163–70. http://dx.doi.org/10.1007/bf00935595.

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Badie, Farshad. "A. N. PRIOR’S SYSTEM Q: A REVIEW". Логико-философские штудии, n. 3 (15 novembre 2021): 161–74. http://dx.doi.org/10.52119/lphs.2021.61.96.001.

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In his “Time and Modality”, based on his own philosophical motivations, Arthur Norman Prior proposed the modal logic Q as a correct modal logic in 1957. Prior developed Q in order to offer a logic for contingent beings, in which one could rationally state that some beings are contingent and some are necessary. One may say that Q is an actualist modal logic with a natural semantics. This review article is a developed description/discussion of/on “The System Q” that is the fifth chapter of “Time and Modality”. I have attempted to analyse the logical structure of system Q in order to provide a more understandable description as well as logical analysis for today’s logicians, philosophers, and information-computer scientists. In the paper, the Polish notations are translated into modern notations in order to be more comprehensible and to support the developed formal descriptions and semantic analysis.

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Dobrovol’skij, Dmitrij. "On a special type of necessity modality: The German verb sollen viewed from parallel corpora". Voprosy Jazykoznanija, n. 6 (2021): 22. http://dx.doi.org/10.31857/0373-658x.2021.6.22-39.

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The article discusses the thesis that the German verb sollen expresses a special type of modality that occupies an intermediate position between necessity and possibility, i.e. the modality of weak ontological necessity. The modality expressed by the verb sollen can be characterized as follows: sollen points to the correlation of the state of aff airs P with a certain logic of development of events, not the only possible, but salient in some respect. This is the diff erence between this type of modality and “classical” necessity, which assumes that the state of aff airs P corresponds to the only possible logic of the world. The study was conducted on the material of the German-Russian parallel subcorpus of the Russian National Corpus, using the “monofocal” method of contrastive analysis, according to which the way of translating the analyzed linguistic unit into another language is used as a tool for its semantic analysis.

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Pavlova, Alexandra M. "Knowledge and its dynamics in intuitionistic logic". Philosophy Journal 15, n. 3 (29 agosto 2022): 113–24. http://dx.doi.org/10.21146/2072-0726-2022-15-3-113-124.

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Thе article examines the problem of superposition of deductive and cognitive attitudes in the context of intuitionistic logic. The prerequisites and methods of modelling the change in knowledge within the framework of epistemic logic are studied. The main emphasis is placed on the difference in the understanding of truth and knowledge in classical and intuitionistic logic. It is shown that an alternative understanding of truth in intuitionistic logic entails an understanding of the modality of knowledge that is different from the one used in classical logic.

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Petik, Jaroslav. "PHILOSOPHICAL PROBLEMS OF THE MENTALISTIC LOGIC". Sophia. Human and Religious Studies Bulletin 14, n. 2 (2019): 38–43. http://dx.doi.org/10.17721/sophia.2019.14.9.

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Paper deals with philosophical problems of mentalistic logic. Mentalistic logic is a formal system that concentrates on underpinning processes of mental life instead of certain elements of extrinsic rational behavior as most of existing logics (like BDI calculi) do. The project is compared to the existing logics of actions. Mentalistic logic is patually a formal system and partually phenomenological study of human mind. We presume formal signs such as propositions and modal operators refer to mental states and can describe the general structure of mental activity. That is purely the approach of classical phenomenology – the study of experience and its structures. On the other hand the usage of formal logic is a classic analytic philosophy of mind. So the things are getting more complicated when taking in consideration that the initial framework of a study is analytic philosophy and not continental phenomenology. Phenomenology is of different intellectual and methodological tradition than any type of analytic philosophy including analytic philosophy of mind. From that stanpoint it may be said that paper is also interesting as a purely methodological project – it tries to find bridges between phenomenology and philosophy of mind. As for the action logics, mentalistic logic also studies rational behavior but does it on the other lever and often with a different purpose. The main problem in this case is philosophical interpretation of modality. Minor problems include shared content, many leveled self-referential structures and vagueness. The paper also studies brain in a vatt thought experiment as a methodological concept. The research will have implications for philosophy of logic, artificial intelligence and theory of reference.

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