Neighborhood Semantics For Modal Logic

Author : Eric Pacuit
Publisher : Springer
Page : 154 pages
File Size : 51,6 Mb
Release : 2017-11-15
Category : Philosophy
ISBN : 9783319671499

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Neighborhood Semantics for Modal Logic by Eric Pacuit Pdf

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.

Author : David Harel,Dexter Kozen,Jerzy Tiuryn
Publisher : MIT Press
Page : 492 pages
File Size : 44,5 Mb
Release : 2000-09-29
Category : Computers
ISBN : 0262263025

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Dynamic Logic by David Harel,Dexter Kozen,Jerzy Tiuryn Pdf

This book provides the first comprehensive introduction to Dynamic Logic. Among the many approaches to formal reasoning about programs, Dynamic Logic enjoys the singular advantage of being strongly related to classical logic. Its variants constitute natural generalizations and extensions of classical formalisms. For example, Propositional Dynamic Logic (PDL) can be described as a blend of three complementary classical ingredients: propositional calculus, modal logic, and the algebra of regular events. In First-Order Dynamic Logic (DL), the propositional calculus is replaced by classical first-order predicate calculus. Dynamic Logic is a system of remarkable unity that is theoretically rich as well as of practical value. It can be used for formalizing correctness specifications and proving rigorously that those specifications are met by a particular program. Other uses include determining the equivalence of programs, comparing the expressive power of various programming constructs, and synthesizing programs from specifications. This book provides the first comprehensive introduction to Dynamic Logic. It is divided into three parts. The first part reviews the appropriate fundamental concepts of logic and computability theory and can stand alone as an introduction to these topics. The second part discusses PDL and its variants, and the third part discusses DL and its variants. Examples are provided throughout, and exercises and a short historical section are included at the end of each chapter.

Author : Nino B. Cocchiarella,Max A. Freund
Publisher : Oxford University Press
Page : 288 pages
File Size : 41,9 Mb
Release : 2008-08-04
Category : Mathematics
ISBN : 0199710635

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Modal Logic by Nino B. Cocchiarella,Max A. Freund Pdf

In this text, a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision and philosophical insight. All of the S1-S5 modal logics of Lewis and Langford, among others, are constructed. A matrix, or many-valued semantics, for sentential modal logic is formalized, and an important result that no finite matrix can characterize any of the standard modal logics is proven. Exercises, some of which show independence results, help to develop logical skills. A separate sentential modal logic of logical necessity in logical atomism is also constructed and shown to be complete and decidable. On the first-order level of the logic of logical necessity, the modal thesis of anti-essentialism is valid and every de re sentence is provably equivalent to a de dicto sentence. An elegant extension of the standard sentential modal logics into several first-order modal logics is developed. Both a first-order modal logic for possibilism containing actualism as a proper part as well as a separate modal logic for actualism alone are constructed for a variety of modal systems. Exercises on this level show the connections between modal laws and quantifier logic regarding generalization into, or out of, modal contexts and the conditions required for the necessity of identity and non-identity. Two types of second-order modal logics, one possibilist and the other actualist, are developed based on a distinction between existence-entailing concepts and concepts in general. The result is a deeper second-order analysis of possibilism and actualism as ontological frameworks. Exercises regarding second-order predicate quantifiers clarify the distinction between existence-entailing concepts and concepts in general. Modal Logic is ideally suited as a core text for graduate and undergraduate courses in modal logic, and as supplementary reading in courses on mathematical logic, formal ontology, and artificial intelligence.

Author : Judit Madarász,Gergely Székely
Publisher : Springer Nature
Page : 517 pages
File Size : 40,6 Mb
Release : 2021-05-31
Category : Philosophy
ISBN : 9783030641870

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Hajnal Andréka and István Németi on Unity of Science by Judit Madarász,Gergely Székely Pdf

This book features more than 20 papers that celebrate the work of Hajnal Andréka and István Németi. It illustrates an interaction between developing and applying mathematical logic. The papers offer new results as well as surveys in areas influenced by these two outstanding researchers. They also provide details on the after-life of some of their initiatives. Computer science connects the papers in the first part of the book. The second part concentrates on algebraic logic. It features a range of papers that hint at the intricate many-way connections between logic, algebra, and geometry. The third part explores novel applications of logic in relativity theory, philosophy of logic, philosophy of physics and spacetime, and methodology of science. They include such exciting subjects as time travelling in emergent spacetime. The short autobiographies of Hajnal Andréka and István Németi at the end of the book describe an adventurous journey from electric engineering and Maxwell’s equations to a complex system of computer programs for designing Hungary’s electric power system, to exploring and contributing deep results to Tarskian algebraic logic as the deepest core theory of such questions, then on to applications of the results in such exciting new areas as relativity theory in order to rejuvenate logic itself.

Author : Mojtaba Mojtahedi,Shahid Rahman,Mohammad Saleh Zarepour
Publisher : Springer Nature
Page : 493 pages
File Size : 41,9 Mb
Release : 2021-02-09
Category : Philosophy
ISBN : 9783030536541

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Mathematics, Logic, and their Philosophies by Mojtaba Mojtahedi,Shahid Rahman,Mohammad Saleh Zarepour Pdf

This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. The third category contains papers on Avicenna’s logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community.

Author : Robert Goldblatt
Publisher : Cambridge University Press
Page : 283 pages
File Size : 43,9 Mb
Release : 2011-07-14
Category : Mathematics
ISBN : 9781107010529

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Quantifiers, Propositions and Identity by Robert Goldblatt Pdf

Develops new semantical characterisations of many logical systems with quantification that are incomplete under the traditional Kripkean possible worlds interpretation. This book is for mathematical or philosophical logicians, computer scientists and linguists, including academic researchers, teachers and advanced students.

Author : Heinrich Wansing
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 52,6 Mb
Release : 2013-03-14
Category : Philosophy
ISBN : 9789401712804

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Displaying Modal Logic by Heinrich Wansing Pdf

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 conceived. The proof-theory of non-classical logics is a rapidly developing field, and even the generalizations of the ordinary notion of sequent listed in Chapter 1 can hardly be presented in great detail within a single volume. In addition to further investigating the various approaches toward generalized Gentzen systems, it is important to compare them and to discuss their relative advantages and disadvantages. An initial attempt at bringing together work on different kinds of proof systems for modal logics has been made in [188]. Another step in the same direction is [196]. Since Chapter 1 contains introductory considerations and, moreover, every remaining chapter begins with some surveying or summarizing remarks, in this preface I shall only emphasize a relation to philosophy that is important to me, register the sources of papers that have entered this book in some form or another, and acknowledge advice and support.

Author : Alexandru Baltag,Jeremy Seligman,Tomoyuki Yamada
Publisher : Springer
Page : 694 pages
File Size : 53,6 Mb
Release : 2017-09-01
Category : Mathematics
ISBN : 9783662556658

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Logic, Rationality, and Interaction by Alexandru Baltag,Jeremy Seligman,Tomoyuki Yamada Pdf

This LNCS volume is part of FoLLI book serie and contains the papers presented at the 6th International Workshop on Logic, Rationality and Interaction/ (LORI-VI), held in September 2017 in Sapporo, Japan. The focus of the workshop is on following topics: Agency, Argumentation and Agreement, Belief Revision and Belief Merging, Belief Representation, Cooperation, Decision making and Planning, Natural Language, Philosophy and Philosophical Logic, and Strategic Reasoning.

Author : Marcelo Esteban Coniglio
Publisher : Springer Nature
Page : 330 pages
File Size : 43,8 Mb
Release : 2024-06-14
Category : Electronic
ISBN : 9783031565953

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Many-valued Semantics and Modal Logics: Essays in Honour of Yuriy Vasilievich Ivlev by Marcelo Esteban Coniglio Pdf

Author : Joao Paulo Carvalho,Marie-Jeanne Lesot,Uzay Kaymak,Susana Vieira,Bernadette Bouchon-Meunier,Ronald R. Yager
Publisher : Springer
Page : 836 pages
File Size : 54,7 Mb
Release : 2016-06-10
Category : Computers
ISBN : 9783319405810

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Information Processing and Management of Uncertainty in Knowledge-Based Systems by Joao Paulo Carvalho,Marie-Jeanne Lesot,Uzay Kaymak,Susana Vieira,Bernadette Bouchon-Meunier,Ronald R. Yager Pdf

This two volume set (CCIS 610 and 611) constitute the proceedings of the 16th International Conference on Information processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2016, held in Eindhoven, The Netherlands, in June 2016. The 127 revised full papers presented together with four invited talks were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on fuzzy measures and integrals; uncertainty quantification with imprecise probability; textual data processing; belief functions theory and its applications; graphical models; fuzzy implications functions; applications in medicine and bioinformatics; real-world applications; soft computing for image processing; clustering; fuzzy logic, formal concept analysis and rough sets; graded and many-valued modal logics; imperfect databases; multiple criteria decision methods; argumentation and belief revision; databases and information systems; conceptual aspects of data aggregation and complex data fusion; fuzzy sets and fuzzy logic; decision support; comparison measures; machine learning; social data processing; temporal data processing; aggregation.

Author : Mohua Banerjee,Krishna S.
Publisher : Springer
Page : 236 pages
File Size : 48,7 Mb
Release : 2014-11-22
Category : Mathematics
ISBN : 9783662458242

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Logic and Its Applications by Mohua Banerjee,Krishna S. Pdf

This book collects the refereed proceedings of the 6th Indian Conference on Logic and Its Applications, ICLA 2015, held in Mumbai, India, in January 2015. The volume contains 13 full revised papers along with 3 invited talks presented at the conference. The papers were selected after rigorous review, from 23 submissions. They cover topics related to pure and applied formal logic, foundations and philosophy of mathematics and the sciences, set theory, model theory, proof theory, areas of theoretical computer science, artificial intelligence, systems of logic in the Indian tradition, and other disciplines which are of direct interest to mathematical and philosophical logic.

Author : M.J. Cresswell,G.E. Hughes
Publisher : Routledge
Page : 432 pages
File Size : 47,8 Mb
Release : 2012-08-06
Category : Philosophy
ISBN : 9781134800278

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A New Introduction to Modal Logic by M.J. Cresswell,G.E. Hughes Pdf

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.

Author : Brian F. Chellas
Publisher : Cambridge University Press
Page : 316 pages
File Size : 41,6 Mb
Release : 1980-02-29
Category : Mathematics
ISBN : 0521295157

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Modal Logic by Brian F. Chellas Pdf

An introductory textbook on modal logic the logic of necessity and possibility.

Author : M. Fitting,Richard L. Mendelsohn
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Philosophy
ISBN : 9789401152921

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First-Order Modal Logic by M. Fitting,Richard L. Mendelsohn Pdf

This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.

Author : Kevin Scharp
Publisher : Oxford University Press
Page : 342 pages
File Size : 44,8 Mb
Release : 2013-07-11
Category : Philosophy
ISBN : 9780199653850

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Replacing Truth by Kevin Scharp Pdf

Kevin Scharp proposes an original account of the nature and logic of truth, on which truth is an inconsistent concept that should be replaced for certain theoretical purposes. He argues that truth is best understood as an inconsistent concept; develops an axiomatic theory of truth; and offers a new kind of possible-worlds semantics for this theory.