An Introduction To Non Classical Logic

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An Introduction to Non-Classical Logic

Graham Priest
An Introduction to Non Classical Logic Book PDF

Author : Graham Priest
Publisher : Cambridge University Press
Page : 128 pages
File Size : 47,5 Mb
Release : 2008-04-10
Category : Science
ISBN : 1139469673

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An Introduction to Non-Classical Logic by Graham Priest Pdf

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.

Classical and Nonclassical Logics

Eric Schechter
Classical and Nonclassical Logics Book PDF

Author : Eric Schechter
Publisher : Princeton University Press
Page : 530 pages
File Size : 52,8 Mb
Release : 2005-08-28
Category : Mathematics
ISBN : 0691122792

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Classical and Nonclassical Logics by Eric Schechter Pdf

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).

Labelled Non-Classical Logics

Luca Viganò
Labelled Non Classical Logics Book PDF

Author : Luca Viganò
Publisher : Springer Science & Business Media
Page : 295 pages
File Size : 52,5 Mb
Release : 2013-04-17
Category : Philosophy
ISBN : 9781475732085

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Labelled Non-Classical Logics by Luca Viganò Pdf

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.

An Introduction to Non-Classical Logic

Graham Priest
An Introduction to Non Classical Logic Book PDF

Author : Graham Priest
Publisher : Cambridge University Press
Page : 268 pages
File Size : 47,9 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 052179434X

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An Introduction to Non-Classical Logic by Graham Priest Pdf

This book is an introduction to non-classical propositional logics. It brings together for the first time in a textbook a range of topics in logic, many of them of relatively recent origin, including modal, conditional, intuitionist, many-valued, paraconsistent, relevant and fuzzy logics. The material is unified by the underlying theme of world-semantics. All of the topics are explained clearly and accessibly, using devices such as tableaux proofs, and their relation to current philosophical issues and debates is discussed. Students with a basic understanding of classical logic will find this an invaluable introduction to an area that has become of central importance in both logic and philosophy, but which, until now, could be studied only through the research literature. It will interest those studying logic, those who need to know about non-classical logics because of their philosophical importance, and, more widely, readers working in mathematics and computer science.

Logics for Computer Science

Anita Wasilewska
Logics for Computer Science Book PDF

Author : Anita Wasilewska
Publisher : Springer
Page : 535 pages
File Size : 48,7 Mb
Release : 2018-11-03
Category : Computers
ISBN : 9783319925912

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Logics for Computer Science by Anita Wasilewska Pdf

Providing an in-depth introduction to fundamental classical and non-classical logics, this textbook offers a comprehensive survey of logics for computer scientists. Logics for Computer Science contains intuitive introductory chapters explaining the need for logical investigations, motivations for different types of logics and some of their history. They are followed by strict formal approach chapters. All chapters contain many detailed examples explaining each of the introduced notions and definitions, well chosen sets of exercises with carefully written solutions, and sets of homework. While many logic books are available, they were written by logicians for logicians, not for computer scientists. They usually choose one particular way of presenting the material and use a specialized language. Logics for Computer Science discusses Gentzen as well as Hilbert formalizations, first order theories, the Hilbert Program, Godel's first and second incompleteness theorems and their proofs. It also introduces and discusses some many valued logics, modal logics and introduces algebraic models for classical, intuitionistic, and modal S4 and S5 logics. The theory of computation is based on concepts defined by logicians and mathematicians. Logic plays a fundamental role in computer science, and this book explains the basic theorems, as well as different techniques of proving them in classical and some non-classical logics. Important applications derived from concepts of logic for computer technology include Artificial Intelligence and Software Engineering. In addition to Computer Science, this book may also find an audience in mathematics and philosophy courses, and some of the chapters are also useful for a course in Artificial Intelligence.

Introduction to Logic

Alfred Tarski
Introduction to Logic Book PDF

Author : Alfred Tarski
Publisher : Courier Corporation
Page : 272 pages
File Size : 44,6 Mb
Release : 2013-07-04
Category : Mathematics
ISBN : 9780486318899

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Introduction to Logic by Alfred Tarski Pdf

This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.

Logic and Implication

Petr Cintula,Carles Noguera
Logic and Implication Book PDF

Author : Petr Cintula,Carles Noguera
Publisher : Springer Nature
Page : 465 pages
File Size : 54,9 Mb
Release : 2022-01-01
Category : Philosophy
ISBN : 9783030856755

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Logic and Implication by Petr Cintula,Carles Noguera Pdf

This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to (abstract) algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions. Based on their recent work, the authors develop a powerful uniform framework for the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics. The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics.

Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs

Ivo Düntsch,Edwin Mares
Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs Book PDF

Author : Ivo Düntsch,Edwin Mares
Publisher : Springer Nature
Page : 591 pages
File Size : 55,6 Mb
Release : 2021-09-24
Category : Philosophy
ISBN : 9783030714307

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Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs by Ivo Düntsch,Edwin Mares Pdf

This book is dedicated to the work of Alasdair Urquhart. The book starts out with an introduction to and an overview of Urquhart’s work, and an autobiographical essay by Urquhart. This introductory section is followed by papers on algebraic logic and lattice theory, papers on the complexity of proofs, and papers on philosophical logic and history of logic. The final section of the book contains a response to the papers by Urquhart. Alasdair Urquhart has made extremely important contributions to a variety of fields in logic. He produced some of the earliest work on the semantics of relevant logic. He provided the undecidability of the logics R (of relevant implication) and E (of relevant entailment), as well as some of their close neighbors. He proved that interpolation fails in some of those systems. Urquhart has done very important work in complexity theory, both about the complexity of proofs in classical and some nonclassical logics. In pure algebra, he has produced a representation theorem for lattices and some rather beautiful duality theorems. In addition, he has done important work in the history of logic, especially on Bertrand Russell, including editing Volume four of Russell’s Collected Papers.

An Introduction to Formal Logic

Peter Smith
An Introduction to Formal Logic Book PDF

Author : Peter Smith
Publisher : Cambridge University Press
Page : 370 pages
File Size : 51,5 Mb
Release : 2003-11-06
Category : Mathematics
ISBN : 0521008042

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An Introduction to Formal Logic by Peter Smith Pdf

Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.

Logic for Philosophy

Theodore Sider
Logic for Philosophy Book PDF

Author : Theodore Sider
Publisher : Oxford University Press
Page : 305 pages
File Size : 46,9 Mb
Release : 2010-01-07
Category : Philosophy
ISBN : 9780192658814

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Logic for Philosophy by Theodore Sider Pdf

Logic for Philosophy is an introduction to logic for students of contemporary philosophy. It is suitable both for advanced undergraduates and for beginning graduate students in philosophy. It covers (i) basic approaches to logic, including proof theory and especially model theory, (ii) extensions of standard logic that are important in philosophy, and (iii) some elementary philosophy of logic. It emphasizes breadth rather than depth. For example, it discusses modal logic and counterfactuals, but does not prove the central metalogical results for predicate logic (completeness, undecidability, etc.) Its goal is to introduce students to the logic they need to know in order to read contemporary philosophical work. It is very user-friendly for students without an extensive background in mathematics. In short, this book gives you the understanding of logic that you need to do philosophy.

Proof Theory and Algebra in Logic

Hiroakira Ono
Proof Theory and Algebra in Logic Book PDF

Author : Hiroakira Ono
Publisher : Springer
Page : 160 pages
File Size : 50,6 Mb
Release : 2019-08-02
Category : Philosophy
ISBN : 9789811379970

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Proof Theory and Algebra in Logic by Hiroakira Ono Pdf

This book offers a concise introduction to both proof-theory and algebraic methods, the core of the syntactic and semantic study of logic respectively. The importance of combining these two has been increasingly recognized in recent years. It highlights the contrasts between the deep, concrete results using the former and the general, abstract ones using the latter. Covering modal logics, many-valued logics, superintuitionistic and substructural logics, together with their algebraic semantics, the book also provides an introduction to nonclassical logic for undergraduate or graduate level courses.The book is divided into two parts: Proof Theory in Part I and Algebra in Logic in Part II. Part I presents sequent systems and discusses cut elimination and its applications in detail. It also provides simplified proof of cut elimination, making the topic more accessible. The last chapter of Part I is devoted to clarification of the classes of logics that are discussed in the second part. Part II focuses on algebraic semantics for these logics. At the same time, it is a gentle introduction to the basics of algebraic logic and universal algebra with many examples of their applications in logic. Part II can be read independently of Part I, with only minimum knowledge required, and as such is suitable as a textbook for short introductory courses on algebra in logic.

An Introduction to Many-Valued and Fuzzy Logic

Merrie Bergmann
An Introduction to Many Valued and Fuzzy Logic Book PDF

Author : Merrie Bergmann
Publisher : Cambridge University Press
Page : 7 pages
File Size : 51,6 Mb
Release : 2008-01-14
Category : Mathematics
ISBN : 9781139468787

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An Introduction to Many-Valued and Fuzzy Logic by Merrie Bergmann Pdf

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.

Quantification in Nonclassical Logic

Dov M. Gabbay,Dimitrij Skvortsov,Valentin Shehtman
Quantification in Nonclassical Logic Book PDF

Author : Dov M. Gabbay,Dimitrij Skvortsov,Valentin Shehtman
Publisher : Elsevier
Page : 641 pages
File Size : 54,9 Mb
Release : 2009-06-20
Category : Mathematics
ISBN : 9780080931128

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Quantification in Nonclassical Logic by Dov M. Gabbay,Dimitrij Skvortsov,Valentin Shehtman Pdf

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.

Doubt Truth to be a Liar

Graham Priest
Doubt Truth to be a Liar Book PDF

Author : Graham Priest
Publisher : Oxford University Press
Page : 239 pages
File Size : 54,9 Mb
Release : 2006
Category : Language Arts & Disciplines
ISBN : 9780199263288

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Doubt Truth to be a Liar by Graham Priest Pdf

"The book is required reading for anyone who wishes to understand dialetheism; (especially) for anyone who wishes to continue to endorse the old Aristotelian orthodoxy; and, more generally, for anyone who wishes to understand the role that contradiction plays in our thinking."--BOOK JACKET.

Modal Logic

Brian F. Chellas
Modal Logic Book PDF

Author : Brian F. Chellas
Publisher : Cambridge University Press
Page : 316 pages
File Size : 55,8 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.