Neighborhood Semantics For Modal Logic

Author: Eric Pacuit
Editor: Springer
ISBN: 3319671499
File Size: 59,75 MB
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This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic (the so-called non-normal modal logics). In addition, the book discusses a broad range of topics, including standard modal logic results (i.e., completeness, decidability and definability); bisimulations for neighborhood models and other model-theoretic constructions; comparisons with other semantics for modal logic (e.g., relational models, topological models, plausibility models); neighborhood semantics for first-order modal logic, applications in game theory (coalitional logic and game logic); applications in epistemic logic (logics of evidence and belief); and non-normal modal logics with dynamic modalities. The book can be used as the primary text for seminars on philosophical logic focused on non-normal modal logics; as a supplemental text for courses on modal logic, logic in AI, or philosophical logic (either at the undergraduate or graduate level); or as the primary source for researchers interested in learning about the uses of neighborhood semantics in philosophical logic and game theory.

Common Knowledge

Author: Luc Lismont
Editor:
ISBN:
File Size: 75,52 MB
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Common Knowledge

Author: L. Lismont
Editor:
ISBN:
File Size: 55,99 MB
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Modal Logic

Author: Source Wikipedia
Editor: University-Press.org
ISBN: 9781230552279
File Size: 17,74 MB
Format: PDF
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 79. Chapters: Godel's ontological proof, Potentiality and actuality, Accessibility relation, Counterpart theory, Admissible rule, Kripke semantics, Dynamic logic, Interior algebra, Epistemic modal logic, Doxastic logic, Essence, Deontic logic, Logico-linguistic modeling, Possible world, General frame, Problem of future contingents, Formal ethics, Modal companion, Fiction theory, Two dimensionalism, Rigid designator, Actualism, Contingency, Subjunctive possibility, De dicto and de re, Modal operator, Impossible world, Frege-Church ontology, Accident, Sahlqvist formula, Imperative logic, Autoepistemic logic, Standard translation, Epistemic possibility, Strict conditional, Modal -calculus, Logical possibility, Modal depth, Condition of possibility, S5, Provability logic, Barcan formula, Neighborhood semantics, Apodicticity, Hybrid logic, KK thesis, Multimodal logic, Metaphysical necessity, Alethic modality, Non-rigid designator, Guarded logic, Modal algebra, Finite model property, Predicate abstraction, Axiom S5, Impossible event, Classical modal logic, Hennessy-Milner logic, Window operator, Alternating-time Temporal Logic, Normal modal logic, Modal fictionalism, Interpretability logic, Conceptual necessity, Assertoric, Gabbay's separation theorem, Regular modal logic.

An Essay In Classical Modal Logic

Author: Krister Segerberg
Editor:
ISBN:
File Size: 75,61 MB
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Mathematics Logic And Their Philosophies

Author: Mojtaba Mojtahedi
Editor: Springer Nature
ISBN: 3030536548
File Size: 21,59 MB
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Subjunctive Conditional Modal Logic

Author: David Owen Butcher
Editor:
ISBN:
File Size: 39,82 MB
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A Note On Incompleteness Of Modal Logics With Respect To Neighbourhood Semantics

Author: W. Dziobiak
Editor:
ISBN:
File Size: 79,59 MB
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Logic Methodology And Philosophy Of Science Vi

Author: International Congress of Logic, Methodology and Philosophy of Science
Editor: North Holland
ISBN:
File Size: 80,68 MB
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Logic, Methodology and Philosophy of Science VI.

Lectures On Propositional Calculi

Author: Ryszard Wójcicki
Editor:
ISBN:
File Size: 65,65 MB
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Polyadic Modal Logics With Applications In Normative Reasoning

Author: Kam Sing Leung
Editor:
ISBN:
File Size: 15,34 MB
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The study of modal logic often starts with that of unary operators applied to sentences, denoting some notions of necessity or possibility. However, we adopt a more general approach in this dissertation. We begin with object languages that possess multi-ary modal operators, and interpret them in relational semantics, neighbourhood semantics and algebraic semantics. Some topics on this subject have been investigated by logicians for some time, and we present a survey of their results. But there remain areas to be explored, and we examine them in order to gain more knowledge of our territory. More specifically, we propose polyadic modal axioms that correspond to seriality, reflexivity, symmetry, transitivity and euclideanness of multi-ary relations, and prove soundness and completeness of normal systems based on these axioms. We also put forward polyadic classical systems determined by classes of neighbourhood frames of finite types such as superset-closed frames, quasi-filtroids and filtroids. Equivalences between categories of modal algebras and categories of relational frames and neighbourhood frames are demonstrated. Furthermore some of the systems studied in this dissertation are shown to be translationally equivalent. While the first part of our study is purely formal, we take a different route in the second part. The multi-ary modal operators, previously interpreted in classes of mathematical structures, are given meanings in ordinary discourse. We read them as modalities in normative thinking, for instance, as the "ought" when we say "̀you ought to visit your parents, or at least call them if you cannot visit them". A series of polyadic modal logics, called systems of deontic residuation, are proposed. They represent real-life situations involving, for example, normative conflicts and contrary-to-duty obligations better than traditional deontic logics based on unary modal operators do.

The Bulletin Of Symbolic Logic

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File Size: 56,95 MB
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American Philosophers 1950 2000

Author: Matthew J. Bruccoli
Editor: Gale / Cengage Learning
ISBN:
File Size: 34,44 MB
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Essays on American philosophers engaged with philosophical topics; focuses on the rise of analytic philosophy as the dominant philosophical movement in the English-speaking world for most of the twentieth century. Also covers libertarianism, a political philosophy that holds that individuals are the sole legitimate owners of their own minds and bodies and that they should be free to do as they please.

What Logics Mean

Author: James W. Garson
Editor: Cambridge University Press
ISBN: 110703910X
File Size: 46,95 MB
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This book explains how the meanings of the symbols of logic are determined by the rules that govern them.

Mathematical Reviews

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ISBN:
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Reports On Mathematical Logic

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File Size: 18,52 MB
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Intensional Logic Programming

Author: Mehmet Ali Orgun
Editor:
ISBN:
File Size: 50,25 MB
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Synthesizing Semantics For Extensions Of Propositional Logic

Author: Hans Jürgen Ohlbach
Editor:
ISBN:
File Size: 27,27 MB
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Abstract: "Given a Hilbert-style specification of a propositional extension of standard propositional logic, it is shown how the basic model theoretic semantics can be obtained from the axioms by syntactic transformations. The transformations are designed in such a way that they eliminate certain derived theorems from the Hilbert axiomatization by turning them into tautologies. The following transformations are considered. Elimination of the reflexivity and transitivity of a binary consequence relation yields the basic possible worlds framework. Elimination of the congruence properties of the connectives yields weak neighbourhood semantics. Elimination of certain monotonicity properties yields a stronger neighbourhood semantics. Elimination of certain closure properties yields relational possible worlds semantics for the connectives. If propositional logic is the basis of the specification, the translated Hilbert axioms can be simplified by eliminating the formula variables with a quantifier elimination algorithm. This way we obtain the frame conditions for the semantic structures. All transformations work for arbitrary n-place connectives. The steps can be fully automated by means of PL1 theorem provers and quantifier elimination algorithms. The meta theory guarantees soundness and completeness of all transformation steps. As a by-product, translations into multi-modal logic are developed."