Model Theory for Modal Logic

Gabbay, D. M., “Model Theory for Intuitionistic Logic', Zeit. f. math. Logik und Grund. d. Math, 18(1972b), 49–54. Goldblatt, R.I., “First-order. Definability in Modal Logic", JSL 40 (1975), 35–40. Halmos, P. R., Naive Set Theory, ...

Author: K.A. Bowen

Publisher: Springer Science & Business Media

ISBN: 9789401576420

Category: Philosophy

Page: 139

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Proof Theory of Modal Logic

RELATIONAL PROOF SYSTEMS FOR MODAL LOGICS 1 INTRODUCTION The purpose of this paper is to give a survey of the relational ... Semantics and model theory : With logic L there is associated a class of relational models for L , and in these ...

Author: Heinrich Wansing

Publisher: Springer Science & Business Media

ISBN: 0792341201

Category: Computers

Page: 334

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This volume deals with formal, mechanizable reasoning in modal logics, that is, logics of necessity, possibility, belief, time computations etc. It is therefore of immense interest for various interrelated disciplines such as philosophy, AI, computer science, logic, cognitive science and linguistics. The book consists of 15 original research papers, divided into three parts. The first part contains papers which give a profound description of powerful proof-theoretic methods as applied to the normal modal logic S4. Part II is concerned with a number of generalizations of the standard proof-theoretic formats, while the third part presents new and important results on semantics-based proof systems for modal logic.
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Handbook of Modal Logic

Clearly a classical interpolant χ with |= (φ → χ) ∧ (χ → ψ), is an interpolant also in the sense of finite model theory. The modal characterisation theorem. Note how both sides of the equivalence expressed in Theorem 55 change their ...

Author: Patrick Blackburn

Publisher: Elsevier

ISBN: 0080466664

Category: Mathematics

Page: 1260

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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, suitable for beginners approaching the subject for the first time, and advanced articles, which will help those already familiar with the field to deepen their expertise. Please visit: http://people.uleth.ca/~woods/RedSeriesPromo_WP/PubSLPR.html - Compact modal logic reference - Computational approaches fully discussed - Contemporary applications of modal logic covered in depth
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Modal Logic as Metaphysics

on the semantics of its non-modal fragment: no distinctively modal parameter waits for the model to fix its value. Kripke's model theory for modal logic is quite different. The semantics of the non-modal fragment of the language leaves ...

Author: Timothy Williamson

Publisher: Oxford University Press

ISBN: 9780199552078

Category: Philosophy

Page: 481

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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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Advances in Modal Logic

Advances in Modal Logic is a unique forum for presenting the latest results and new directions of research in modal logic.

Author: Frank Wolter

Publisher: World Scientific

ISBN: 9789812776471

Category: Computers

Page: 425

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Advances in Modal Logic is a unique forum for presenting the latest results and new directions of research in modal logic. The topics dealt with are of interdisciplinary interest and range from mathematical, computational, and philosophical problems to applications in knowledge representation and formal linguistics.Volume 3 presents substantial advances in the relational model theory and the algorithmic treatment of modal logics. It contains invited and contributed papers from the third conference on OC Advances in Modal LogicOCO, held at the University of Leipzig (Germany) in October 2000. It includes papers on dynamic logic, description logic, hybrid logic, epistemic logic, combinations of modal logics, tense logic, action logic, provability logic, and modal predicate logic."
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A New Introduction to Modal Logic

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.

Author: M.J. Cresswell

Publisher: Routledge

ISBN: 9781134800278

Category: Philosophy

Page: 432

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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. The book takes readers from the most basic systems of modal propositional logic right up to systems of modal predicate with identity. It covers both technical developments such as completeness and incompleteness, and finite and infinite models, and their philosophical applications, especially in the area of modal predicate logic.
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Mathematics Models and Modality

5 MODAL MUDDLES: UNWARRANTED COMPLACENCY It is a significant historical fact that the model theory for modal logics was worked out in the late fifties and early sixties, while the distinctions among logical demonstrability, ...

Author: John P. Burgess

Publisher: Cambridge University Press

ISBN: 9781139470544

Category: Science

Page:

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John Burgess is the author of a rich and creative body of work which seeks to defend classical logic and mathematics through counter-criticism of their nominalist, intuitionist, relevantist, and other critics. This selection of his essays, which spans twenty-five years, addresses key topics including nominalism, neo-logicism, intuitionism, modal logic, analyticity, and translation. An introduction sets the essays in context and offers a retrospective appraisal of their aims. The volume will be of interest to a wide range of readers across philosophy of mathematics, logic, and philosophy of language.
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Modal Logic

A 2001 graduate text on modal logic, a field which has caught the attention of computer scientists, economists and computational linguists.

Author: Patrick Blackburn

Publisher: Cambridge University Press

ISBN: 0521527147

Category: Computers

Page: 574

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This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. Researchers in areas ranging from economics to computational linguistics have since realised its worth. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects, and applications to issues in logic and computer science such as completeness, computability and complexity are considered. Three appendices supply basic background information and numerous exercises are provided. Ideal for anyone wanting to learn modern modal logic.
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First Steps in Modal Logic

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.

Author: Sally Popkorn

Publisher: Cambridge University Press

ISBN: 9780521464826

Category: Mathematics

Page: 340

View: 697

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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.
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