Results for 'Modality (Logic'

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  1. Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford, England: Oxford University Press.
    Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.
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  2. Modal Logic: Graph. Darst.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2002 - Cambridge University Press.
    This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.
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  3. Modal Logic: An Introduction.Brian F. Chellas - 1980 - Cambridge University Press.
    A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's (...)
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  4. Modal Logic and Philosophy.Sten Lindström & Krister Segerberg - 2007 - In Patrick Blackburn, Johan van Benthem & Frank Wolter (eds.), Handbook of Modal Logic. Amsterdam, the Netherlands: Elsevier. pp. 1149-1214.
    Modal logic is one of philosophy’s many children. As a mature adult it has moved out of the parental home and is nowadays straying far from its parent. But the ties are still there: philosophy is important to modal logic, modal logic is important for philosophy. Or, at least, this is a thesis we try to defend in this chapter. Limitations of space have ruled out any attempt at writing a survey of all the work going on (...)
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  5.  4
    Introductory Modal Logic.Kenneth J. Konyndyk - 1986 - University of Notre Dame Press.
    Modal logic, developed as an extension of classical propositional logic and first-order quantification theory, integrates the notions of possibility and necessity and necessary implication. Arguments whose understanding depends on some fundamental knowledge of modal logic have always been important in philosophy of religion, metaphysics, and epistemology. Moreover, modal logic has become increasingly important with the use of the concept of "possible worlds" in these areas. Introductory Modal Logic fills the need for a basic text on (...)
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  6.  11
    The Modal Logic of Stepwise Removal.Johan van Benthem, Krzysztof Mierzewski & Francesca Zaffora Blando - 2022 - Review of Symbolic Logic 15 (1):36-63.
    We investigate the modal logic of stepwise removal of objects, both for its intrinsic interest as a logic of quantification without replacement, and as a pilot study to better understand the complexity jumps between dynamic epistemic logics of model transformations and logics of freely chosen graph changes that get registered in a growing memory. After introducing this logic (MLSR) and its corresponding removal modality, we analyze its expressive power and prove a bisimulation characterization theorem. We then (...)
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  7.  23
    Modal Logic.Yde Venema, Alexander Chagrov & Michael Zakharyaschev - 2000 - Philosophical Review 109 (2):286.
    Modern modal logic originated as a branch of philosophical logic in which the concepts of necessity and possibility were investigated by means of a pair of dual operators that are added to a propositional or first-order language. The field owes much of its flavor and success to the introduction in the 1950s of the “possible-worlds” semantics in which the modal operators are interpreted via some “accessibility relation” connecting possible worlds. In subsequent years, modal logic has received attention (...)
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  8. Modal Logic.Alexander Chagrov - 1997 - Oxford, England: Oxford University Press.
    For a novice this book is a mathematically-oriented introduction to modal logic, the discipline within mathematical logic studying mathematical models of reasoning which involve various kinds of modal operators. It starts with very fundamental concepts and gradually proceeds to the front line of current research, introducing in full details the modern semantic and algebraic apparatus and covering practically all classical results in the field. It contains both numerous exercises and open problems, and presupposes only minimal knowledge in mathematics. (...)
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  9.  1
    Modal Logic for Open Minds.Johan van Benthem - 2010 - Stanford, CA, USA: Center for the Study of Language and Information.
    In _Modal Logic for Open Minds,_ Johan van Benthem provides an up-to-date introduction to the field of modal logic, outlining its major ideas and exploring the numerous ways in which various academic fields have adopted it. Van Benthem begins with the basic theories of modal logic, semantics, bisimulation, and axiomatics, and also covers more advanced topics, such as expressive power and computational complexity. The book then moves to a wide range of applications, including new developments in information (...)
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  10.  53
    Modal Logic.Yde Venema - 2000 - Philosophical Review 109 (2):286-289.
    Modern modal logic originated as a branch of philosophical logic in which the concepts of necessity and possibility were investigated by means of a pair of dual operators that are added to a propositional or first-order language. The field owes much of its flavor and success to the introduction in the 1950s of the “possible-worlds” semantics in which the modal operators are interpreted via some “accessibility relation” connecting possible worlds. In subsequent years, modal logic has received attention (...)
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  11.  46
    Modal Logic for Philosophers.James W. Garson - 2006 - Cambridge and New York: Cambridge University Press.
    Designed for use by philosophy students, this book provides an accessible, yet technically sound treatment of modal logic and its philosophical applications. Every effort has been made to simplify the presentation by using diagrams in place of more complex mathematical apparatus. These and other innovations provide philosophers with easy access to a rich variety of topics in modal logic, including a full coverage of quantified modal logic, non-rigid designators, definite descriptions, and the de-re de-dictio distinction. Discussion of (...)
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  12.  12
    A Modal Logic for Supervised Learning.Alexandru Baltag, Dazhu Li & Mina Young Pedersen - 2022 - Journal of Logic, Language and Information 31 (2):213-234.
    Formal learning theory formalizes the process of inferring a general result from examples, as in the case of inferring grammars from sentences when learning a language. In this work, we develop a general framework—the supervised learning game—to investigate the interaction between Teacher and Learner. In particular, our proposal highlights several interesting features of the agents: on the one hand, Learner may make mistakes in the learning process, and she may also ignore the potential relation between different hypotheses; on the other (...)
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  13. Modal Logic with Names.George Gargov & Valentin Goranko - 1993 - Journal of Philosophical Logic 22 (6):607 - 636.
    We investigate an enrichment of the propositional modal language L with a "universal" modality ■ having semantics x ⊧ ■φ iff ∀y(y ⊧ φ), and a countable set of "names" - a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒ $_{c}$ proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(⍯) of ℒ, where ⍯ is an additional modality with the semantics x (...)
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  14. A New Introduction to Modal Logic.M. J. Cresswell & G. E. Hughes - 1996 - Routledge.
    This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: _An Introduction to Modal Logic_ and _A Companion to Modal Logic_. _A New Introduction to Modal Logic_ is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works. (...)
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  15.  27
    An Introduction to Modal Logic.G. E. Hughes - 1968 - London: Methuen.
    Modal propositional logic; Modal predicate logic; A survey of modal logic.
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  16.  9
    Modal Logic for Open Minds -.Johan van Benthem - 2010 - Stanford, CA, USA: Center for the Study of Language and Inf.
    In _Modal Logic for Open Minds,_ Johan van Benthem provides an up-to-date introduction to the field of modal logic, outlining its major ideas and exploring the numerous ways in which various academic fields have adopted it. Van Benthem begins with the basic theories of modal logic, semantics, bisimulation, and axiomatics, and also covers more advanced topics, such as expressive power and computational complexity. The book then moves to a wide range of applications, including new developments in information (...)
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  17.  2
    Modal Logics and Philosophy.Rod Girle - 2000 - Mcgill-Queen's University Press.
    In Part 1 the reader is introduced to some standard systems of modal logic and encouraged through a series of exercises to become proficient in manipulating these logics. The emphasis is on possible world semantics for modal logics and the semantic emphasis is carried into the formal method, Jeffrey-style truth-trees. Standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 systematically explores the applications of modal logic to philosophical issues such (...)
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  18.  3
    Modal Logic for Philosophers.James W. Garson - 2006 - Cambridge and New York: Cambridge University Press.
    Designed for use by philosophy students, this 2006 book provides an accessible, yet technically sound treatment of modal logic and its philosophical applications. Every effort has been made to simplify the presentation by using diagrams in place of more complex mathematical apparatus. These and other innovations provide philosophers with easy access to a rich variety of topics in modal logic, including a full coverage of quantified modal logic, non-rigid designators, definite descriptions, and the de-re de-dictio distinction. Discussion (...)
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  19.  23
    A Short Introduction to Modal Logic.Grigori Mints - 1992 - Stanford, CA, USA: Center for the Study of Language and Information.
    A Short Introduction to Modal Logic presents both semantic and syntactic features of the subject and illustrates them by detailed analyses of the three best-known modal systems S5, S4 and T. The book concentrates on the logical aspects of ...
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  20. Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism.Hasen Khudairi - 2019 - In Matteo Vincenzo D'Alfonso & Don Berkich (eds.), On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence. Springer. pp. 65-82.
    This essay examines the philosophical significance of $\Omega$-logic in Zermelo-Fraenkel set theory with choice (ZFC). The duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of $\Omega$-logical validity can then be countenanced within a coalgebraic logic, and $\Omega$-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of $\Omega$-logical validity correspond to those (...)
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  21.  53
    Modal Logic and Classical Logic.Johan van Benthem - 1983 - Distributed in the U.S.A. By Humanities Press.
  22.  14
    Tools and Techniques in Modal Logic.Marcus Kracht - 1999 - Elsevier.
    This book treats modal logic as a theory, with several subtheories, such as completeness theory, correspondence theory, duality theory and transfer theory and is intended as a course in modal logic for students who have had prior contact with modal logic and who wish to study it more deeply. It presupposes training in mathematical or logic. Very little specific knowledge is presupposed, most results which are needed are proved in this book.
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  23.  4
    Modal Logic for Philosophers.James W. Garson - 2006 - Cambridge and New York: Cambridge University Press.
    This book on modal logic is especially designed for philosophy students. It provides an accessible yet technically sound treatment of modal logic and its philosophical applications. Every effort is made to simplify the presentation by using diagrams instead of more complex mathematical apparatus. These and other innovations provide philosophers with easy access to a rich variety of topics in modal logic, including a full coverage of quantified modal logic, non-rigid designators, definite descriptions, and the de-re de-dicto (...)
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  24.  39
    Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.
    This is identical with the first edition (see 21: 2716) except for the addition of a Supplement containing 5 previously published articles and the bringing of the bibliography (now 73 items) up to date. The 5 added articles present clarifications or modifications of views expressed in the first edition. (PsycINFO Database Record (c) 2009 APA, all rights reserved).
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  25.  66
    Many-Dimensional Modal Logics: Theory and Applications.Dov M. Gabbay (ed.) - 2003 - Elsevier North Holland.
    Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects. To study (...)
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  26. Quantified Modal Logic and the Plural De Re.Phillip Bricker - 1989 - Midwest Studies in Philosophy 14 (1):372-394.
    Modal sentences of the form "every F might be G" and "some F must be G" have a threefold ambiguity. in addition to the familiar readings "de dicto" and "de re", there is a third reading on which they are examples of the "plural de re": they attribute a modal property to the F's plurally in a way that cannot in general be reduced to an attribution of modal properties to the individual F's. The plural "de re" readings of modal (...)
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  27.  34
    Modal Logic: The Lewis-Modal Systems.Joseph Jay Zeman - 1973 - London: Clarendon Press.
  28. Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
     
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  29.  97
    The Modal Logic of Gödel Sentences.Hirohiko Kushida - 2010 - Journal of Philosophical Logic 39 (5):577 - 590.
    The modal logic of Gödel sentences, termed as GS, is introduced to analyze the logical properties of 'true but unprovable' sentences in formal arithmetic. The logic GS is, in a sense, dual to Grzegorczyk's Logic, where modality can be interpreted as 'true and provable'. As we show, GS and Grzegorczyk's Logic are, in fact, mutually embeddable. We prove Kripke completeness and arithmetical completeness for GS. GS is also an extended system of the logic of (...)
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  30.  1
    Displaying Modal Logic.Heinrich Wansing - 1998 - Dordrecht, Netherland: Springer.
    The present monograph is a slightly revised version of my Habilitations schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics, successfully defended at Leipzig University, November 1997. It collects work on proof systems for modal and constructive logics I have done over the last few years. The main concern is display logic, a certain refinement of Gentzen's sequent calculus developed by Nuel D. Belnap. This book is far from offering a comprehensive presentation of generalized sequent systems for modal logics broadly (...)
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  31. A New Introduction to Modal Logic.Paolo Crivelli, Timothy Williamson, G. E. Hughes & M. J. Cresswell - 1998 - Philosophical Review 107 (3):471.
    This volume succeeds the same authors' well-known An Introduction to Modal Logic and A Companion to Modal Logic. We designate the three books and their authors NIML, IML, CML and H&C respectively. Sadly, George Hughes died partway through the writing of NIML.
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  32.  51
    The Modal Logic of Bayesian Belief Revision.Zalán Gyenis, Miklós Rédei & William Brown - 2019 - Journal of Philosophical Logic 48 (5):809-824.
    In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using Bayes’ rule. We define a hierarchy of modal logics that capture the logical features of Bayesian belief revision. Elements in the hierarchy are distinguished by the cardinality of the set of elementary propositions on which the agent’s prior is defined. Inclusions among the modal logics in the hierarchy are determined. By linking the modal logics in the hierarchy to the strongest modal (...)
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  33.  26
    The Modal Logic of Agreement and Noncontingency.Lloyd Humberstone - 2002 - Notre Dame Journal of Formal Logic 43 (2):95-127.
    The formula A (it is noncontingent whether A) is true at a point in a Kripke model just in case all points accessible to that point agree on the truth-value of A. We can think of -based modal logic as a special case of what we call the general modal logic of agreement, interpreted with the aid of models supporting a ternary relation, S, say, with OA (which we write instead of A to emphasize the generalization involved) true (...)
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  34.  28
    Metaphysical Nihilism and Modal Logic.Ethan Brauer - 2022 - Philosophical Studies 179 (9):2751-2763.
    In this paper I argue, that if it is metaphysically possible for it to have been the case that nothing existed, then it follows that the right modal logic cannot extend D, ruling out popular modal logics S4 and S5. I provisionally defend the claim that it is possible for nothing to have existed. I then consider the various ways of resisting the conclusion that the right modal logic is weaker than D.
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  35.  26
    An Essay in Classical Modal Logic.Krister Segerberg - 1971 - Uppsala, Sweden: Uppsala, Filosofiska Föreningen Och Filosofiska Institutionen Vid Uppsala Universitet.
  36. Which Modal Logic Is the Right One?John P. Burgess - 1999 - Notre Dame Journal of Formal Logic 40 (1):81-93.
    The question, "Which modal logic is the right one for logical necessity?," divides into two questions, one about model-theoretic validity, the other about proof-theoretic demonstrability. The arguments of Halldén and others that the right validity argument is S5, and the right demonstrability logic includes S4, are reviewed, and certain common objections are argued to be fallacious. A new argument, based on work of Supecki and Bryll, is presented for the claim that the right demonstrability logic must be (...)
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  37.  34
    Modal Logic Over Finite Structures.Eric Rosen - 1997 - Journal of Logic, Language and Information 6 (4):427-439.
    We investigate properties of propositional modal logic over the classof finite structures. In particular, we show that certain knownpreservation theorems remain true over this class. We prove that aclass of finite models is defined by a first-order sentence and closedunder bisimulations if and only if it is definable by a modal formula.We also prove that a class of finite models defined by a modal formulais closed under extensions if and only if it is defined by a -modal formula.
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  38. The Modal Logic of Inequality.Maarten de Rijke - 1992 - Journal of Symbolic Logic 57 (2):566-584.
    We consider some modal languages with a modal operator $D$ whose semantics is based on the relation of inequality. Basic logical properties such as definability, expressive power and completeness are studied. Also, some connections with a number of other recent proposals to extend the standard modal language are pointed at.
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  39.  33
    Modal Logics with Belnapian Truth Values.Serge P. Odintsov & Heinrich Wansing - 2010 - Journal of Applied Non-Classical Logics 20 (3):279-304.
    Various four- and three-valued modal propositional logics are studied. The basic systems are modal extensions BK and BS4 of Belnap and Dunn's four-valued logic of firstdegree entailment. Three-valued extensions of BK and BS4 are considered as well. These logics are introduced semantically by means of relational models with two distinct evaluation relations, one for verification and the other for falsification. Axiom systems are defined and shown to be sound and complete with respect to the relational semantics and with respect (...)
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  40.  22
    The Modal Logic of Potential Infinity: Branching Versus Convergent Possibilities.Ethan Brauer - forthcoming - Erkenntnis:1-19.
    Modal logic provides an elegant way to understand the notion of potential infinity. This raises the question of what the right modal logic is for reasoning about potential infinity. In this article I identify a choice point in determining the right modal logic: Can a potentially infinite collection ever be expanded in two mutually incompatible ways? If not, then the possible expansions are convergent; if so, then the possible expansions are branching. When possible expansions are convergent, the (...)
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  41.  94
    The Modal Logic of Set-Theoretic Potentialism and the Potentialist Maximality Principles.Joel David Hamkins & Øystein Linnebo - 2022 - Review of Symbolic Logic 15 (1):1-35.
    We analyze the precise modal commitments of several natural varieties of set-theoretic potentialism, using tools we develop for a general model-theoretic account of potentialism, building on those of Hamkins, Leibman and Löwe [14], including the use of buttons, switches, dials and ratchets. Among the potentialist conceptions we consider are: rank potentialism, Grothendieck–Zermelo potentialism, transitive-set potentialism, forcing potentialism, countable-transitive-model potentialism, countable-model potentialism, and others. In each case, we identify lower bounds for the modal validities, which are generally either S4.2 or S4.3, (...)
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  42.  3
    Modal Logics and Philosophy.Rod Girle - 2000 - Routledge.
    The first edition, published by Acumen in 2000, became a prescribed textbook on modal logic courses. The second edition has been fully revised in response to readers' suggestions, including two new chapters on conditional logic, which was not covered in the first edition. "Modal Logics and Philosophy" is a fully comprehensive introduction to modal logics and their application suitable for course use. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, "Modal (...)
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  43. Semantical Considerations on Modal Logic.Saul A. Kripke - 1963 - Acta Philosophica Fennica 16:83-94.
  44.  21
    Philosophical Applications of Modal Logic.Lloyd Humberstone - 2016 - College Publications.
    This text aims to convey some of the interest and charm of modal logic, and to put a reader new to the subject in a position to have an informed opinion as to its applicability to each of several areas of philosophical concern in which the merits of a modal approach' have been controversial. he main focus, for these purposes, is on normal modal logics, though some attention is given to the non-normal side of the picture.
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  45.  41
    Modal Logic Without Contraction in a Metatheory Without Contraction.Patrick Girard & Zach Weber - 2019 - Review of Symbolic Logic 12 (4):685-701.
    Standard reasoning about Kripke semantics for modal logic is almost always based on a background framework of classical logic. Can proofs for familiar definability theorems be carried out using a nonclassical substructural logic as the metatheory? This article presents a semantics for positive substructural modal logic and studies the connection between frame conditions and formulas, via definability theorems. The novelty is that all the proofs are carried out with a noncontractive logic in the background. This (...)
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  46.  5
    The Modal Logic of Bayesian Belief Revision.William Brown, Zalán Gyenis & Miklós Rédei - 2019 - Journal of Philosophical Logic 48 (5):809-824.
    In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using Bayes’ rule. We define a hierarchy of modal logics that capture the logical features of Bayesian belief revision. Elements in the hierarchy are distinguished by the cardinality of the set of elementary propositions on which the agent’s prior is defined. Inclusions among the modal logics in the hierarchy are determined. By linking the modal logics in the hierarchy to the strongest modal (...)
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  47.  70
    Intensional and Higher-Order Modal Logic.Daniel Gallin - 1972 - [Berkeley.
    INTENSIONAL LOGIC §1. Natural Language and Intensional Logic When we speak of a theory of meaning for a natural language such as English, we have in mind an ...
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  48.  47
    Modal Logic.James W. Garson - 2009 - Stanford Encyclopedia of Philosophy.
  49. Intensional and Higher-Order Modal Logic: With Applications to Montague Semantics.Daniel Gallin - 1975 - Amsterdam, Netherlands: American Elsevier Pub. Co..
    CHAPTER 1. INTENSIONAL LOGIC §1. Natural Language and Intensional Logic When we speak of a theory of meaning for a natural language such as English, ...
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  50.  93
    Handbook of Modal Logic.Patrick Blackburn, Johan van Benthem & Frank Wolter (eds.) - 2006 - Elsevier.
    The Handbook of Modal Logic contains 20 articles, which collectively introduce contemporary modal logic, survey current research, and indicate the way in which the field is developing. The articles survey the field from a wide variety of perspectives: the underling theory is explored in depth, modern computational approaches are treated, and six major applications areas of modal logic (in Mathematics, Computer Science, Artificial Intelligence, Linguistics, Game Theory, and Philosophy) are surveyed. The book contains both well-written expository articles, (...)
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