Labelled Non-Classical Logics
Labelled Non-Classical Logics

Author: Luca Viganò

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 295

ISBN-13: 1475732082

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I am very happy to have this opportunity to introduce Luca Vigano's book on Labelled Non-Classical Logics. I put forward the methodology of labelled deductive systems to the participants of Logic Colloquium'90 (Labelled Deductive systems, a Position Paper, In J. Oikkonen and J. Vaananen, editors, Logic Colloquium '90, Volume 2 of Lecture Notes in Logic, pages 66-68, Springer, Berlin, 1993), in an attempt to bring labelling as a recognised and significant component of our logic culture. It was a response to earlier isolated uses of labels by various distinguished authors, as a means to achieve local proof theoretic goals. Labelling was used in many different areas such as resource labelling in relevance logics, prefix tableaux in modal logics, annotated logic programs in logic programming, proof tracing in truth maintenance systems, and various side annotations in higher-order proof theory, arithmetic and analysis. This widespread local use of labels was an indication of an underlying logical pattern, namely the simultaneous side-by-side manipulation of several kinds of logical information. It was clear that there was a need to establish the labelled deductive systems methodology. Modal logic is one major area where labelling can be developed quickly and sys tematically with a view of demonstrating its power and significant advantage. In modal logic the labels can play a double role.

Structural Analysis of Non-Classical Logics
Structural Analysis of Non-Classical Logics

Author: Syraya Chin-Mu Yang

Publisher: Springer

Published: 2015-10-16

Total Pages: 285

ISBN-13: 3662483572

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This volume brings together a group of logic-minded philosophers and philosophically oriented logicians to address a diversity of topics on the structural analysis of non-classical logics. It mainly focuses on the construction of different types of models for various non-classical logics of current interest, including modal logics, epistemic logics, dynamic logics, and observational predicate logic. The book presents a wide range of applications of two well-known approaches in current research: (i) structural modeling of certain philosophical issues in the framework of non-classic logics, such as admissible models for modal logic, structural models for modal epistemology and for counterfactuals, and epistemological models for common knowledge and for public announcements; (ii) conceptual analysis of logical properties of, and formal semantics for, non-classical logics, such as sub-formula property, truthmaking, epistemic modality, behavioral strategies, speech acts and assertions. The structural analysis provided in this volume will appeal not only to graduate students and experts in non-classic logics, but also to readers from a wide range of disciplines, including computer science, cognitive science, linguistics, game theory and theory of action, to mention a few.

Quantification in Nonclassical Logic
Quantification in Nonclassical Logic

Author: Dov M. Gabbay

Publisher: Elsevier

Published: 2009-06-20

Total Pages: 641

ISBN-13: 008093112X

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Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy andlanguage in ancient times; they were studied by traditional informalmethods until the 20th century. In the last century the tools becamehighly mathematical, and both modal logic and quantification found numerous applications in Computer Science. At the same time many other kinds of nonclassical logics were investigated and applied to Computer Science. Although there exist several good books in propositional modal logics, this book is the first detailed monograph in nonclassical first-order quantification. It includes results obtained during the past thirty years. The field is very large, so we confine ourselves with only two kinds of logics: modal and superintuitionistic. The main emphasis of Volume 1 is model-theoretic, and it concentrates on descriptions of different sound semantics and completeness problem --- even for these seemingly simple questions we have our hands full. The major part of the presented material has never been published before. Some results are very recent, and for other results we either give new proofs or first proofs in full detail.

Classical and Nonclassical Logics
Classical and Nonclassical Logics

Author: Eric Schechter

Publisher: Princeton University Press

Published: 2005-08-28

Total Pages: 530

ISBN-13: 9780691122793

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Classical logic is traditionally introduced by itself, but that makes it seem arbitrary and unnatural. This text introduces classical alongside several nonclassical logics (relevant, constructive, quantative, paraconsistent).

Natural Deduction, Hybrid Systems and Modal Logics
Natural Deduction, Hybrid Systems and Modal Logics

Author: Andrzej Indrzejczak

Publisher: Springer Science & Business Media

Published: 2010-07-03

Total Pages: 515

ISBN-13: 9048187850

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This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.

An Introduction to Non-Classical Logic
An Introduction to Non-Classical Logic

Author: Graham Priest

Publisher: Cambridge University Press

Published: 2008-04-10

Total Pages: 582

ISBN-13: 1139469673

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This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

Philosophical Logic: Current Trends in Asia
Philosophical Logic: Current Trends in Asia

Author: Syraya Chin-Mu Yang

Publisher: Springer

Published: 2017-11-25

Total Pages: 308

ISBN-13: 9811063559

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This volume brings together a group of logic-minded philosophers and philosophically oriented logicians, mainly from Asia, to address a variety of logical and philosophical topics of current interest, offering a representative cross-section of the philosophical logic landscape in early 21st-century Asia. It surveys a variety of fields, including modal logic, epistemic logic, formal semantics, decidability and mereology. The book proposes new approaches and constructs more powerful frameworks, such as cover theory, an algebraic approach to cut-elimination, and a Boolean approach to causal discovery, to name but a few. Readers may find a wide range of applications of these original works in current research of philosophical logic, especially in the structural and conceptual analysis of some significant semantic properties and formal systems. The variety of topics and issues discussed here will appeal to readers from a broad spectrum of disciplines, ranging from mathematical/philosophical logic, computing science, cognitive science and artificial intelligence, to linguistics, game theory and beyond.

An Introduction to Many-Valued and Fuzzy Logic
An Introduction to Many-Valued and Fuzzy Logic

Author: Merrie Bergmann

Publisher: Cambridge University Press

Published: 2008-01-14

Total Pages: 7

ISBN-13: 1139468782

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Professor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical systems - Lukasiewicz, Gödel, and product logics - are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems.