Relevant bibliographies by topics / Modality (Logic)

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Modality (Logic)'

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Published: 4 June 2021
Last updated: 28 July 2024

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Journal articles on the topic "Modality (Logic)"

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Avron, Arnon, and Anna Zamansky. "Paraconsistency, self-extensionality, modality." Logic Journal of the IGPL 28, no. 5 (November 27, 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 (December 18, 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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Speranski, Stanislav O. "Negation as a modality in a quantified setting." Journal of Logic and Computation 31, no. 5 (April 5, 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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Petik, Ja O. "Modality and folk psychology." Studies in history and philosophy of science and technology 28, no. 1 (May 5, 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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Spies, Simon, Lennard Gäher, Joseph Tassarotti, Ralf Jung, Robbert Krebbers, Lars Birkedal, and Derek Dreyer. "Later credits: resourceful reasoning for the later modality." Proceedings of the ACM on Programming Languages 6, ICFP (August 29, 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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THIELECKE, HAYO. "Control effects as a modality." Journal of Functional Programming 19, no. 1 (January 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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Wilson, Alastair. "Modality: Metaphysics, Logic and Epistemology." Australasian Journal of Philosophy 89, no. 4 (December 2011): 755–56. http://dx.doi.org/10.1080/00048402.2011.592541.

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KACHI, Daisuke. "Partial Logic as a Logic of Extensional Alethic Modality." Journal of the Japan Association for Philosophy of Science 34, no. 2 (2007): 61–70. http://dx.doi.org/10.4288/kisoron1954.34.61.

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White, Graham. "Causality, Modality, and Explanation." Notre Dame Journal of Formal Logic 49, no. 3 (July 2008): 313–43. http://dx.doi.org/10.1215/00294527-2008-015.

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Kurokawa, Hidenori, and Hirohiko Kushida. "Resource sharing linear logic." Journal of Logic and Computation 30, no. 1 (January 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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Dissertations / Theses on the topic "Modality (Logic)"

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Brodowski, Björn. "Concepts and modality." Thesis, University of Aberdeen, 2012. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=195807.

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There’s a venerable tradition in philosophy to look to our concepts when it comes to appreciating facts about absolute real modality, i.e. how things can and must be in an absolute sense. Given the absence of a modal sensorium, the traditional model stated that modal facts have something to do with conceptual relations. Squares must be four-­‐sided, for example, because the concept having four sides is part of the concept square. If this example could be generalised, it would not only provide a model for the epistemology of modality, it would also explain why much of our modal knowledge is a priori. The fact that we plausibly don’t need any empirical information in order to understand our concepts would explain why their analysis, and the subsequent appreciation of the corresponding modal facts, can be had from the armchair. In the wake of an externalist and scientistic trend in philosophy in the latter half of the 20th century, this model has come under severe attack. Orthodoxy has it now that concepts were the wrong place to look. Not only are there substantial modal facts whose recognition requires empirical investigation, even the application conditions, i.e. meanings, of many concepts are essentially a posteriori. This thesis rehearses the main arguments for rejecting the tradition, defends its central tenets and urges that, while the externalist arguments provide important insights, they do nothing to overturn the traditional model, but rather point to where it needs qualification. It spells out how we must understand its key notions—meaning, apriority, modality—in order to retain what is plausible about the traditional model. It is argued that an appeal to concepts in modal epistemology is inevitable, and that this is a tradition to foster.
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Cavanaugh, Daniel J. "The cellular logic of pain modality discrimination." Diss., Search in ProQuest Dissertations & Theses. UC Only, 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3390112.

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Peñafuerte, Araceli Sandil. "An actualist ontology for counterfactuals." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2008. http://wwwlib.umi.com/cr/ucsd/fullcit?p3330773.

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Thesis (Ph. D.)--University of California, San Diego, 2008.
Title from first page of PDF file (viewed December 5, 2008). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 160-164).
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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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Baysal, Onur Alizde Rarail. "Lower-top and upper-bottom points for any formula in temporal logic/." [s.l.]: [s.n.], 2006. http://library.iyte.edu.tr/tezler/master/matematik/T000549.pdf.

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Comeau, Ryan J. "The World Is Not Enough: An Enquiry into Realism about Modality." Kent State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=kent1374608481.

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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 Coniglio
Tese (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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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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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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Stoddard, Eve Chute Douglas L. "Measuring learning modalities with neuropsychological memory measures in a college population /." Philadelphia, Pa. : Drexel University, 2007. http://hdl.handle.net/1860/1797.

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Books on the topic "Modality (Logic)"

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Girle, Rod. Modal logics and philosophy: Introduction to modal logic. Teddington: Acumen, 2000.

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de, Rijke Maarten, ed. Advances in intensional logic. Dordrecht: Kluwer Academic Publishers, 1997.

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Girle, Rod. Modal logics and philosophy. Teddington: Acumen, 2000.

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Chagrov, Alexander. Modal logic. Oxford: Clarendon Press, 1997.

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Wansing, H. Displaying modal logic. Dordrecht [Netherlands]: Kluwer Academic, 1998.

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Marx, Maarten. Multi-dimensional modal logic. Dordrecht: Kluwer Academic Publishers, 1997.

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Benthem, J. F. A. K. van. Modal logic for open minds. Stanford, Calif: Center for the Study of Language and Information, 2010.

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Popkorn, Sally. First steps in modal logic. Cambridge: Cambridge University Press, 1994.

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1959-, Blackburn Patrick, Benthem, J. F. A. K. van, 1949-, and Wolter Frank, eds. Handbook of modal logic. Amsterdam: Elsevier, 2007.

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de, Rijke Maarten, ed. Diamonds and defaults: Studies in pure and applied intensional logic. Dordrecht: Kluwer Academic Publishers, 1993.

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Book chapters on the topic "Modality (Logic)"

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Stern, Johannes. "Modality and Logic." In Trends in Logic, 23–67. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22557-9_2.

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Akama, Seiki. "On Constructive Modality." In Applied Logic Series, 143–58. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5638-7_7.

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Ghilardi, Silvio. "The Invariance Modality." In Outstanding Contributions to Logic, 165–75. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-06843-0_6.

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Smoryński, C. "Provability as Modality." In Self-Reference and Modal Logic, 63–86. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4613-8601-8_2.

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Ågotnes, Thomas, and Natasha Alechina. "Embedding Coalition Logic in the Minimal Normal Multimodal Logic with Intersection." In Modality, Semantics and Interpretations, 1–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-47197-5_1.

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Venema, Yde. "Meeting a Modality?" In Applied Logic: How, What and Why, 343–61. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8533-0_12.

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Ma, Minghui, and Shanxia Wang. "Finite-Chain Graded Modal Logic." In Modality, Semantics and Interpretations, 71–85. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-47197-5_4.

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Font, Josep M., and Ventura Verdú. "Two Levels of Modality: An Algebraic Approach." In Logic Counts, 53–61. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-0687-7_5.

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Smith, Robin. "Ancient Greek modal logic." In The Routledge Handbook of Modality, 331–43. Abingdon, Oxon ; New York, NY: Routledge, 2021. |Includes bibliographical references and index.: Routledge, 2020. http://dx.doi.org/10.4324/9781315742144-37.

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Stern, Johannes. "Modality and Axiomatic Theories of Truth." In Trends in Logic, 121–73. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22557-9_4.

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Conference papers on the topic "Modality (Logic)"

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Guatto, Adrien. "A Generalized Modality for Recursion." In LICS '18: 33rd Annual ACM/IEEE Symposium on Logic in Computer Science. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3209108.3209148.

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Naumov, Pavel, and Oliver Orejola. "Shhh! The Logic of Clandestine Operations." In Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}. California: International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/ijcai.2023/368.

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An operation is called covert if it conceals the identity of the actor; it is called clandestine if the very fact that the operation is conducted is concealed. The paper proposes a formal semantics of clandestine operations and introduces a sound and complete logical system that describes the interplay between the distributed knowledge modality and a modality capturing coalition power to conduct clandestine operations.
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Wild, Paul, and Lutz Schröder. "A Characterization Theorem for a Modal Description Logic." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/181.

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Modal description logics feature modalities that capture dependence of knowledge on parameters such as time, place, or the information state of agents. E.g., the logic S5-ALC combines the standard description logic ALC with an S5-modality that can be understood as an epistemic operator or as representing (undirected) change. This logic embeds into a corresponding modal first-order logic S5-FOL. We prove a modal characterization theorem for this embedding, in analogy to results by van Benthem and Rosen relating ALC to standard first-order logic: We show that S5-ALC with only local roles is, both over finite and over unrestricted models, precisely the bisimulation-invariant fragment of S5-FOL, thus giving an exact description of the expressive power of S5-ALC with only local roles.
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Jiang, Junli, and Pavel Naumov. "In Data We Trust: The Logic of Trust-Based Beliefs." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/372.

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The paper proposes a data-centred approach to reasoning about the interplay between trust and beliefs. At its core, is the modality "under the assumption that one dataset is trustworthy, another dataset informs a belief in a statement". The main technical result is a sound and complete logical system capturing the properties of this modality.
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Ågotnes, Thomas, and Yì N. Wáng. "Somebody Knows." In 18th International Conference on Principles of Knowledge Representation and Reasoning {KR-2021}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/kr.2021/1.

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Several different notions of group knowledge have been extensively studied in the epistemic and doxastic logic literature, including common knowledge, general knowledge (everybody-knows) and distributed knowledge. In this paper we study a natural notion of group knowledge between general and distributed knowledge: somebody-knows. While something is general knowledge if and only if it is known by everyone, this notion holds if and only if it is known by someone. This is stronger than distributed knowledge, which is the knowledge that follows from the total knowledge in the group. We introduce a modality for somebody-knows in the style of standard group knowledge modalities, and study its properties. Unlike the other mentioned group knowledge modalities, somebody-knows is not a normal modality; in particular it lacks the conjunctive closure property. We provide an equivalent neighbourhood semantics for the language with a single somebody-knows modality, together with a completeness result: the somebody-knows modalities are completely characterised by the modal logic EMN extended with a particular weak conjunctive closure axiom. We also show that the satisfiability problem for this logic is PSPACE-complete. The neighbourhood semantics and the completeness and complexity results also carry over to logics for so-called local reasoning (Fagin et al. 1995) with bounded ``frames of mind'', correcting an existing completeness result in the literature (Allen 2005).
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FREYTES, HECTOR. "A LOGIC-ALGEBRAIC FRAMEWORK FOR CONTEXTUALITY AND MODALITY IN QUANTUM SYSTEMS." In Proceedings of the Young Quantum Meetings. WORLD SCIENTIFIC, 2014. http://dx.doi.org/10.1142/9789814596299_0014.

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Trindade, Rafael Gauna, Andrea Schwertner Charão, and Cassiano Andrei Dias da Silveira Schneider. "Logic in a Logic Way: um Aplicativo para Exercitar a Resolução de Problemas de Lógica da Olimpíada Brasileira de Informática." In XXV Workshop sobre Educação em Computação. Sociedade Brasileira de Computação - SBC, 2017. http://dx.doi.org/10.5753/wei.2017.3539.

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The Brazilian Olympiad of Informatics (OBI) mobilizes a large number of students in the country every year. In the competition named “Initiation”, the competitors solve logic problems without using the computer. In order to expand the alternatives for the preparation of the competitors in this modality, we developed ”Logic in a Logic Way”, a mobile application which supports the user in the use of a systematic method of solving textual problems of logic. In this article, we present the design, implementation and test of this application by tutors with experience in preparing students for OBI. The results indicate possible improvements to the application, which is available as an open source software.
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Naumov, Pavel, and Jia Tao. "Knowing-How under Uncertainty (Extended Abstract)." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/719.

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Logical systems containing knowledge and know-how modalities have been investigated in several recent works. Independently, epistemic modal logics in which every knowledge modality is labeled with a degree of uncertainty have been proposed. This article combines these two research lines by introducing a bimodal logic containing knowledge and know-how modalities, both labeled with a degree of uncertainty. The main technical results are soundness, completeness, and incompleteness of the proposed logical system with respect to two classes of semantics.
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Wild, Paul, Lutz Schröder, Dirk Pattinson, and Barbara König. "A Modal Characterization Theorem for a Probabilistic Fuzzy Description Logic." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/263.

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The fuzzy modality probably is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is non-expansive wrt. a suitable notion of behavioural distance. In the present paper, we provide a characterization of the expressive power of this logic based on this observation: We prove a probabilistic analogue of the classical van Benthem theorem, which states that modal logic is precisely the bisimulation-invariant fragment of first-order logic. Specifically, we show that every formula in probabilistic fuzzy first-order logic that is non-expansive wrt. behavioural distance can be approximated by concepts of bounded rank in probabilistic fuzzy description logic.
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Baltag, Alexandru, Nick Bezhanishvili, and David Fernández-Duque. "The Topology of Surprise." In 19th International Conference on Principles of Knowledge Representation and Reasoning {KR-2022}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/kr.2022/4.

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In this paper we present a topological epistemic logic, with modalities for knowledge (modeled as the universal modality), knowability (represented by the topological interior operator), and unknowability of the actual world. The last notion has a non-self-referential reading (modeled by Cantor derivative: the set of limit points of a given set) and a self-referential one (modeled by Cantor's perfect core of a given set: its largest subset without isolated points). We completely axiomatize this logic, showing that it is decidable and PSPACE-complete, and we apply it to the analysis of a famous epistemic puzzle: the Surprise Exam Paradox.
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