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: 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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  3.  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 (...)
  4.  10
    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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  5. 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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  6. 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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  7.  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 (...)
  8. 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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  9.  32
    An Essay in Classical Modal Logic.Krister Segerberg - 1971 - Uppsala, Sweden: Uppsala, Filosofiska Föreningen Och Filosofiska Institutionen Vid Uppsala Universitet.
  10.  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 (...)
  11.  28
    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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  12. 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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  13.  34
    Modal Logic: The Lewis-Modal Systems.Joseph Jay Zeman - 1973 - London: Clarendon Press.
  14. Displaying Modal Logic.Heinrich Wansing - 2000 - Studia Logica 66 (3):421-426.
  15.  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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  16.  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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  17.  55
    Modal Logic and Classical Logic.Johan van Benthem - 1983 - Distributed in the U.S.A. By Humanities Press.
  18.  35
    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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  19.  4
    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 (...)
  20.  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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  21.  6
    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 (...)
  22. Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
     
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  23. 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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  24. 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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  25. Quantified Modal Logic: Non-Normal Worlds and Propositional Attitudes.Veikko Rantala - 1982 - Studia Logica 41 (1):41 - 65.
    One way to obtain a comprehensive semantics for various systems of modal logic is to use a general notion of non-normal world. In the present article, a general notion of modal system is considered together with a semantic framework provided by such a general notion of non-normal world. Methodologically, the main purpose of this paper is to provide a logical framework for the study of various modalities, notably prepositional attitudes. Some specific systems are studied together with semantics using non-normal (...)
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  26. Modal Logic Within Counterfactual Logic.Timothy Williamson - 2010 - In Bob Hale & Aviv Hoffmann (eds.), Modality: Metaphysics, Logic, and Epistemology. Oxford University Press.
  27.  9
    Connexive Modal Logic.H. Wansing - 2005 - In Renate Schmidt, Ian Pratt-Hartmann, Mark Reynolds & Heinrich Wansing (eds.), Advances in Modal Logic, Volume 5. CSLI Publications. pp. 367-383.
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  28.  53
    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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  29.  5
    On Modal Logics Between {$\roman K\times\roman K\times \roman K$} and {${\rm S}5\times{\rm S}5\times{\rm S}5$}.R. Hirsch, I. Hodkinson & A. Kurucz - 2002 - Journal of Symbolic Logic 67 (1):221-234.
    We prove that everyn-modal logic betweenKnandS5nis undecidable, whenever n ≥ 3. We also show that each of these logics is non-finitely axiomatizable, lacks the product finite model property, and there is no algorithm deciding whether a finite frame validates the logic. These results answer several questions of Gabbay and Shehtman. The proofs combine the modal logic technique of Yankov–Fine frame formulas with algebraic logic results of Halmos, Johnson and Monk, and give a reduction of the representation (...)
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  30.  4
    Connexive Modal Logic.H. Wansing - 2005 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 367-383.
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  31.  44
    First Steps in Modal Logic.Sally Popkorn - 1994 - Cambridge University Press.
    This is a first course in propositional modal logic, suitable for mathematicians, computer scientists and philosophers. Emphasis is placed on semantic aspects, in the form of labelled transition structures, rather than on proof theory. The book covers all the basic material - propositional languages, semantics and correspondence results, proof systems and completeness results - as well as some topics not usually covered in a modal logic course. It is written from a mathematical standpoint. To help the reader, the (...)
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  32. Displaying the Modal Logic of Consistency.Heinrich Wansing - 1999 - Journal of Symbolic Logic 64 (4):1573-1590.
    It is shown that the constructive four-valued logic N4 can be faithfully embedded into the modal logic S4. This embedding is used to obtain complete, cut-free display sequent calculi for N4 and C4, the modal logic of consistency over N4. C4 is a natural monotonic base system for semantics-based non-monotonic reasoning.
     
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  33.  27
    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.  68
    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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  35. 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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  36. 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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  37. Hegel, Modal Logic, and the Social Nature of Mind.Paul Redding - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy 62 (5):586-606.
    ABSTRACTHegel's Phenomenology of Spirit provides a fascinating picture of individual minds caught up in “recognitive” relations so as to constitute a realm—“spirit”—which, while necessarily embedded in nature, is not reducible to it. In this essay I suggest a contemporary path for developing Hegel's suggestive ideas in a way that broadly conforms to the demands of his own system, such that one moves from logic to a philosophy of mind. Hence I draw on Hegel's “subjective logic”, understood in the (...)
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  38.  34
    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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  39.  24
    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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  40.  15
    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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  41.  23
    The Modal Logic of Potential Infinity: Branching Versus Convergent Possibilities.Ethan Brauer - 2020 - 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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  42.  94
    Modal Logic with Subjunctive Conditionals and Dispositional Predicates.Lennart Åqvist - 1973 - Journal of Philosophical Logic 2 (1):1 - 76.
  43. 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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  44. Modal Logic, Transition Systems and Processes.Johan van Benthem, Jan van Eijck & Vera Stebletsova - unknown
    Transition systems can be viewed either as process diagrams or as Kripke structures. The rst perspective is that of process theory, the second that of modal logic. This paper shows how various formalisms of modal logic can be brought to bear on processes. Notions of bisimulation can not only be motivated by operations on transition systems, but they can also be suggested by investigations of modal formalisms. To show that the equational view of processes from process algebra is (...)
     
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  45.  86
    Modal Logic and Contingentism: A Comment on Timothy Williamsons Modal Logic as Metaphysics.Louis deRosset - 2016 - Analysis 76 (2):155-172.
    Necessitists hold that, necessarily, everything is such that, necessarily, something is identical to it. Timothy Williamson has posed a number of challenges to contingentism, the negation of necessitism. One such challenge is an argument that necessitists can more wholeheartedly embrace possible worlds semantics than can contingentists. If this charge is correct, then necessitists, but not contingentists, can unproblematically exploit the technical successes of possible worlds semantics. I will argue, however, that the charge is incorrect: contingentists can embrace possible worlds semantics (...)
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  46.  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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  47.  94
    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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  48.  74
    Modal Logic: A Semantic Perspective.Patrick Blackburn & Johan van Benthem - 1988 - Ethics 98:501-517.
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 BASIC MODAL LOGIC . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.
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  49.  6
    Medieval Modal Logic & Science: Augustine on Necessary Truth & Thomas on its Impossibility Without a First Cause.Robert C. Trundle - 1999 - Lanham, MD, USA: University Press of America.
    Medieval Modal Logic & Science uses modal reasoning in a new way to fortify the relationships between science, ethics, and politics. Robert C. Trundle accomplishes this by analyzing the role of modal logic in the work of St. Augustine and St. Thomas Aquinas, then applying these themes to contemporary issues. He incorporates Augustine's ideas involving thought and consciousness, and Aquinas's reasoning to a First Cause. The author also deals with Augustine's ties to Aristotelian modalities of thought regarding science (...)
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  50.  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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