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: 317

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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: 464

View: 266

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Are there such things as merely possible people, who would have lived if our ancestors had acted differently? Are there future people, who have not yet been conceived? Questions like those raise deep issues about both the nature of being and its logical relations with contingency and change. In Modal Logic as Metaphysics, Timothy Williamson argues for positive answers to those questions on the basis of an integrated approach to the issues, applying thetechnical resources of modal logic to provide structural cores for metaphysical theories. He rejects the search for a metaphysically neutral logic as futile, and proposes higher-order modal logic as a new settingin which to resolve such metaphysical questions scientifically, by the construction of systematic logical theories embodying rival answers and their comparison by normal scientific standards.
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Effective Completeness Theorems for Modal Logics

We initiate the study of computable model theory of modal logic, by establishing effective completeness theorems for a variety of modal logics.

Author: Suman Ganguli

Publisher:

ISBN: CORNELL:31924088882281

Category:

Page: 292

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We initiate the study of computable model theory of modal logic, by establishing effective completeness theorems for a variety of modal logics. For each of the logics we consider, we give a natural definition of a decidable Kripke model, and then show how to construct such a decidable Kripke model of a given decidable theory.
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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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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: Modality

Page: 424

View: 647

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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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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: 554

View: 290

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

The satisfiability problem is the following: for a fixed class of models, to determine whether a given formula φ is satisfiable in some model of that class (a more precise definition will follow). The general picture is that modal logic ...

Author: Erich Grädel

Publisher: Springer Science & Business Media

ISBN: 9783540688044

Category: Computers

Page: 440

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Finite model theory,as understoodhere, is an areaof mathematicallogic that has developed in close connection with applications to computer science, in particular the theory of computational complexity and database theory. One of the fundamental insights of mathematical logic is that our understanding of mathematical phenomena is enriched by elevating the languages we use to describe mathematical structures to objects of explicit study. If mathematics is the science of patterns, then the media through which we discern patterns, as well as the structures in which we discern them, command our attention. It isthis aspect oflogicwhichis mostprominentin model theory,“thebranchof mathematical logic which deals with the relation between a formal language and its interpretations”. No wonder, then, that mathematical logic, and ?nite model theory in particular, should ?nd manifold applications in computer science: from specifying programs to querying databases, computer science is rife with phenomena whose understanding requires close attention to the interaction between language and structure. This volume gives a broadoverviewof some central themes of ?nite model theory: expressive power, descriptive complexity, and zero–one laws, together with selected applications to database theory and arti?cial intelligence, es- cially constraint databases and constraint satisfaction problems. The ?nal chapter provides a concise modern introduction to modal logic,which emp- sizes the continuity in spirit and technique with ?nite model theory.
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