Nonclassical Logics And Their Applications
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Nonclassical Logics And Their Applications
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Author : Shier Ju
language : en
Publisher: Springer Nature
Release Date : 2020-01-31
Nonclassical Logics And Their Applications written by Shier Ju and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-31 with Philosophy categories.
This edited book focuses on non-classical logics and their applications, highlighting the rapid advances and the new perspectives that are emerging in this area. Non-classical logics are logical formalisms that violate or go beyond classical logic laws, and their specific features make them particularly suited to describing and reason about aspects of social interaction. The richness and diversity of non-classical logics mean that this area is a natural catalyst for ideas and insights from many different fields, from information theory to game theory and business science. This volume is the post-proceedings of the 8th International Conference on Logic and Cognition, held at Sun Yat-Sen University Institute of Logic and Cognition (ILC) in Guangzhou, China in December 2016. The conference series started in 2001, and is organized by the ILC, often in collaboration with various international research groups. This eighth installment was jointly organized by ILC and Alessandra Palmigiano's Applied Logic research group. The conference series aims to foster the development of effective logical tools to study social behavior from a philosophical, cognitive and formal perspective in order to challenge the field of logic in ways that open up new and exciting research directions. Chapter "The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms" of this book is available open access under a CC BY 4.0 license at link.springer.com
Nonclassical Logics And Their Applications
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Author :
language : en
Publisher:
Release Date : 2020
Nonclassical Logics And Their Applications written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Cognition categories.
This edited book focuses on non-classical logics and their applications, highlighting the rapid advances and the new perspectives that are emerging in this area. Non-classical logics are logical formalisms that violate or go beyond classical logic laws, and their specific features make them particularly suited to describing and reason about aspects of social interaction. The richness and diversity of non-classical logics mean that this area is a natural catalyst for ideas and insights from many different fields, from information theory to game theory and business science. This volume is the post-proceedings of the 8th International Conference on Logic and Cognition, held at Sun Yat-Sen University Institute of Logic and Cognition (ILC) in Guangzhou, China in December 2016. The conference series started in 2001, and is organized by the ILC, often in collaboration with various international research groups. This eighth installment was jointly organized by ILC and Alessandra Palmigiano's Applied Logic research group. The conference series aims to foster the development of effective logical tools to study social behavior from a philosophical, cognitive and formal perspective in order to challenge the field of logic in ways that open up new and exciting research directions. Chapter "The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms" of this book is available open access under a CC BY 4.0 license at link.springer.com.
Non Classical Logics And Their Applications To Fuzzy Subsets
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Author : Ulrich Höhle
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Non Classical Logics And Their Applications To Fuzzy Subsets written by Ulrich Höhle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Non-Classical Logics and their Applications to Fuzzy Subsets is the first major work devoted to a careful study of various relations between non-classical logics and fuzzy sets. This volume is indispensable for all those who are interested in a deeper understanding of the mathematical foundations of fuzzy set theory, particularly in intuitionistic logic, Lukasiewicz logic, monoidal logic, fuzzy logic and topos-like categories. The tutorial nature of the longer chapters, the comprehensive bibliography and index make it suitable as a valuable and important reference for graduate students as well as research workers in the field of non-classical logics. The book is arranged in three parts: Part A presents the most recent developments in the theory of Heyting algebras, MV-algebras, quantales and GL-monoids. Part B gives a coherent and current account of topos-like categories for fuzzy set theory based on Heyting algebra valued sets, quantal sets of M-valued sets. Part C addresses general aspects of non-classical logics including epistemological problems as well as recursive properties of fuzzy logic.
Labelled Non Classical Logics
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Author : Luca Viganò
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Labelled Non Classical Logics written by Luca Viganò and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Philosophy categories.
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
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Author : Graham Priest
language : en
Publisher: Cambridge University Press
Release Date : 2001-02-22
An Introduction To Non Classical Logic written by Graham Priest and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-02-22 with Mathematics categories.
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.
An Introduction To Non Classical Logic
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Author : Graham Priest
language : en
Publisher: Cambridge University Press
Release Date : 2008-04-10
An Introduction To Non Classical Logic written by Graham Priest and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-10 with Science categories.
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.
Logics For Computer Science
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Author : Anita Wasilewska
language : en
Publisher: Springer
Release Date : 2018-11-03
Logics For Computer Science written by Anita Wasilewska and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-03 with Computers categories.
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.
Classical And Nonclassical Logics
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Author : Eric Schechter
language : en
Publisher: Princeton University Press
Release Date : 2020-10-06
Classical And Nonclassical Logics written by Eric Schechter and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-06 with Mathematics categories.
So-called classical logic--the logic developed in the early twentieth century by Gottlob Frege, Bertrand Russell, and others--is computationally the simplest of the major logics, and it is adequate for the needs of most mathematicians. But it is just one of the many kinds of reasoning in everyday thought. Consequently, when presented by itself--as in most introductory texts on logic--it seems arbitrary and unnatural to students new to the subject. In Classical and Nonclassical Logics, Eric Schechter introduces classical logic alongside constructive, relevant, comparative, and other nonclassical logics. Such logics have been investigated for decades in research journals and advanced books, but this is the first textbook to make this subject accessible to beginners. While presenting an assortment of logics separately, it also conveys the deeper ideas (such as derivations and soundness) that apply to all logics. The book leads up to proofs of the Disjunction Property of constructive logic and completeness for several logics. The book begins with brief introductions to informal set theory and general topology, and avoids advanced algebra; thus it is self-contained and suitable for readers with little background in mathematics. It is intended primarily for undergraduate students with no previous experience of formal logic, but advanced students as well as researchers will also profit from this book.
Structural Analysis Of Non Classical Logics
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Author : Syraya Chin-Mu Yang
language : en
Publisher: Springer
Release Date : 2015-10-16
Structural Analysis Of Non Classical Logics written by Syraya Chin-Mu Yang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-16 with Philosophy categories.
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.
Logic For Applications
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Author : Anil Nerode
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Logic For Applications written by Anil Nerode and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the re cent dramatic growth in the applications oflogic to computer science. Thus, our choice oftopics has been heavily influenced by such applications. Of course, we cover the basic traditional topics: syntax, semantics, soundnes5, completeness and compactness as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much ofour book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic especially in its application to Logic Programming and PRO LOG. We deal extensively with the mathematical foundations ofall three ofthese subjects. In addition, we include two chapters on nonclassical logics - modal and intuitionistic - that are becoming increasingly important in computer sci ence. We develop the basic material on the syntax and semantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method in troduced for classical logic. We indicate how it can easily be adapted to various other special types of modal logics. A number of more advanced topics (includ ing nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.