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Quantification In Nonclassical Logic

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Quantification in Nonclassical Logic

Quantification in Nonclassical Logic Book
Author : Dov M. Gabbay,Dimitrij Skvortsov,Valentin Shehtman
Publisher : Elsevier
Release : 2009-06-20
ISBN : 008093112X
Language : En, Es, Fr & De

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Book Description :

Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy and language in ancient times; they were studied by traditional informal methods until the 20th century. In the last century the tools became highly 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.

Quantification in Nonclassical Logic

Quantification in Nonclassical Logic Book
Author : Dov M. Gabbay,Dimitrij Skvortsov,Valentin Shehtman
Publisher : Elsevier Science
Release : 2009-08-01
ISBN : 9780444520128
Language : En, Es, Fr & De

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Book Description :

Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy and language in ancient times; they were studied by traditional informal methods until the 20th century. In the last century the tools became highly 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.

An Introduction to Non Classical Logic

An Introduction to Non Classical Logic Book
Author : Graham Priest
Publisher : Cambridge University Press
Release : 2008-04-10
ISBN : 9781139469678
Language : En, Es, Fr & De

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Book Description :

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.

Intro to Non Classical Logic 2ed

Intro to Non Classical Logic 2ed Book
Author : Anonim
Publisher : Unknown
Release : 2008
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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.

Labelled Non Classical Logics

Labelled Non Classical Logics Book
Author : Luca Viganò
Publisher : Springer Science & Business Media
Release : 2013-04-17
ISBN : 1475732082
Language : En, Es, Fr & De

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Book Description :

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 Book
Author : Syraya Chin-Mu Yang,Duen-Min Deng,Hanti Lin
Publisher : Springer
Release : 2015-10-16
ISBN : 3662483572
Language : En, Es, Fr & De

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Book Description :

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.

Compiled Labelled Deductive Systems

Compiled Labelled Deductive Systems Book
Author : Krysia Broda
Publisher : Research Studies PressLtd
Release : 2004
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

This book introduces a general framework, called Compiled Labelled Deductive System (CLDS), for a unified presentation of logics. It shows how this technique is applied to various families of non-classical logics widely used in Computer Science and Artificial Intelligence. It includes complete natural deduction proof systems, together with proofs and examples, for the families of propositional and predicate modal logics, propositional conditional logics of normality, multiplicative linear logic and for Lukasiewicz fuzzy logic. The CLDS framework generalises the notion of a logical theory to a structured theory consisting of labelled formulas and relations between the labels. This formalisation makes the logics more amenable to applications. Moreover, the framework provides a semantic approach based on a first-order translation, which can be uniformly applied to any logic whose semantics is first-order axiomatisable. Such a semantic approach also facilitates the development of automated theorem provers for non-classical logics.

The Journal of Non classical Logic

The Journal of Non classical Logic Book
Author : Anonim
Publisher : Unknown
Release : 1991
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download The Journal of Non classical Logic book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Journal of Applied Non classical Logics

Journal of Applied Non classical Logics Book
Author : Anonim
Publisher : Unknown
Release : 2005
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Algebraic Methods in Logic and in Computer Science

Algebraic Methods in Logic and in Computer Science Book
Author : Cecylia Rauszer
Publisher : Unknown
Release : 1993
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Algebraic Methods in Logic and in Computer Science book written by Cecylia Rauszer, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Logic Language and Computation

Logic  Language and Computation Book
Author : S. Akama
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 9401156387
Language : En, Es, Fr & De

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Book Description :

The editors of the Applied Logic Series are happy to present to the reader the fifth volume in the series, a collection of papers on Logic, Language and Computation. One very striking feature of the application of logic to language and to computation is that it requires the combination, the integration and the use of many diverse systems and methodologies - all in the same single application. The papers in this volume will give the reader a glimpse into the problems of this active frontier of logic. The Editors CONTENTS Preface IX 1. S. AKAMA Recent Issues in Logic, Language and Computation 1 2. M. J. CRESSWELL Restricted Quantification 27 3. B. H. SLATER The Epsilon Calculus' Problematic 39 4. K. VON HEUSINGER Definite Descriptions and Choice Functions 61 5. N. ASHER Spatio-Temporal Structure in Text 93 6. Y. NAKAYAMA DRT and Many-Valued Logics 131 7. S. AKAMA On Constructive Modality 143 8. H. W ANSING Displaying as Temporalizing: Sequent Systems for Subintuitionistic Logics 159 9. L. FARINAS DEL CERRO AND V. LUGARDON 179 Quantification and Dependence Logics 10. R. SYLVAN Relevant Conditionals, and Relevant Application Thereof 191 Index 245 Preface This is a collection of papers by distinguished researchers on Logic, Lin guistics, Philosophy and Computer Science. The aim of this book is to address a broad picture of the recent research on related areas. In particular, the contributions focus on natural language semantics and non-classical logics from different viewpoints.

The Bulletin of Symbolic Logic

The Bulletin of Symbolic Logic Book
Author : Anonim
Publisher : Unknown
Release : 2009
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download The Bulletin of Symbolic Logic book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Philosophical Logic

Philosophical Logic Book
Author : John P. Burgess
Publisher : Princeton University Press
Release : 2012-08-26
ISBN : 0691156336
Language : En, Es, Fr & De

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Book Description :

Philosophical Logic is a clear and concise critical survey of nonclassical logics of philosophical interest written by one of the world's leading authorities on the subject. After giving an overview of classical logic, John Burgess introduces five central branches of nonclassical logic (temporal, modal, conditional, relevantistic, and intuitionistic), focusing on the sometimes problematic relationship between formal apparatus and intuitive motivation. Requiring minimal background and arranged to make the more technical material optional, the book offers a choice between an overview and in-depth study, and it balances the philosophical and technical aspects of the subject. The book emphasizes the relationship between models and the traditional goal of logic, the evaluation of arguments, and critically examines apparatus and assumptions that often are taken for granted. Philosophical Logic provides an unusually thorough treatment of conditional logic, unifying probabilistic and model-theoretic approaches. It underscores the variety of approaches that have been taken to relevantistic and related logics, and it stresses the problem of connecting formal systems to the motivating ideas behind intuitionistic mathematics. Each chapter ends with a brief guide to further reading. Philosophical Logic addresses students new to logic, philosophers working in other areas, and specialists in logic, providing both a sophisticated introduction and a new synthesis.

Comptes Rendus Philosophiques

Comptes Rendus Philosophiques Book
Author : Anonim
Publisher : Unknown
Release : 2002
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Dag Prawitz on Proofs and Meaning

Dag Prawitz on Proofs and Meaning Book
Author : Heinrich Wansing
Publisher : Springer
Release : 2014-11-27
ISBN : 3319110411
Language : En, Es, Fr & De

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Book Description :

This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of p roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence.

Essays on Wittgenstein in Honour of G H Von Wright

Essays on Wittgenstein in Honour of G H  Von Wright Book
Author : Jaakko Hintikka
Publisher : Unknown
Release : 1976
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Essays on Wittgenstein in Honour of G H Von Wright book written by Jaakko Hintikka, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Reports on Mathematical Logic

Reports on Mathematical Logic Book
Author : Anonim
Publisher : Unknown
Release : 1984
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Reports on Mathematical Logic book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Mathematical Reviews

Mathematical Reviews Book
Author : Anonim
Publisher : Unknown
Release : 2006
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Mathematical Reviews book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

The Philosopher s Index

The Philosopher s Index Book
Author : Anonim
Publisher : Unknown
Release : 1978
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download The Philosopher s Index book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Philosophy of Logics

Philosophy of Logics Book
Author : Susan Haack
Publisher : Cambridge University Press
Release : 1978-07-27
ISBN : 1107392764
Language : En, Es, Fr & De

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Book Description :

The first systematic exposition of all the central topics in the philosophy of logic, Susan Haack's book has established an international reputation (translated into five languages) for its accessibility, clarity, conciseness, orderliness, and range as well as for its thorough scholarship and careful analyses. Haack discusses the scope and purpose of logic, validity, truth-functions, quantification and ontology, names, descriptions, truth, truth-bearers, the set-theoretical and semantic paradoxes, and modality. She also explores the motivations for a whole range of non-classical systems of logic, including many-valued logics, fuzzy logic, moddal and tense logics, and relevance logics. Persupposing only an elementary knowledge of formal logic, this book includes many useful summary tables and diagrams, as well as a helpful glossary of technical terms. Wide-ranging, informative, and eminently readable, this book has proven a valuable resource for generations of students and scholars in a variety of disciplines outside philosophy needing guidance on the philosophy of logic.