Quantification In Nonclassical Logic

Quantification In Nonclassical Logic Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Quantification In Nonclassical Logic book. This book definitely worth reading, it is an incredibly well-written.

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 : 44,5 Mb
Release : 2009-06-20
Category : Mathematics
ISBN : 9780080931128

Get Book

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.

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 : 51,5 Mb
Release : 2013-04-17
Category : Philosophy
ISBN : 9781475732085

Get Book

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 : 128 pages
File Size : 40,5 Mb
Release : 2008-04-10
Category : Science
ISBN : 1139469673

Get Book

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 : 46,9 Mb
Release : 2005-08-28
Category : Mathematics
ISBN : 0691122792

Get Book

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).

V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics

Alex Citkin,Ioannis M. Vandoulakis
V A Yankov on Non Classical Logics History and Philosophy of Mathematics Book PDF

Author : Alex Citkin,Ioannis M. Vandoulakis
Publisher : Springer Nature
Page : 319 pages
File Size : 52,7 Mb
Release : 2022-11-08
Category : Mathematics
ISBN : 9783031068430

Get Book

V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics by Alex Citkin,Ioannis M. Vandoulakis Pdf

This book is dedicated to V.A. Yankov’s seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic. The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov’s results and their applications in algebraic logic, the theory of admissible rules and refutation systems is included in the book. In addition, the reader can find the studies on splitting and join-splitting in intermediate propositional logics that are based on Yankov-type formulas which are closely related to canonical formulas, and the study of properties of predicate extensions of non-classical propositional logics. The book also contains an exposition of Yankov’s revolutionary approach to constructive proof theory. The editors also include Yankov’s contributions to history and philosophy of mathematics and foundations of mathematics, as well as an examination of his original interpretation of history of Greek philosophy and mathematics.

Structural Analysis of Non-Classical Logics

Syraya Chin-Mu Yang,Duen-Min Deng,Hanti Lin
Structural Analysis of Non Classical Logics Book PDF

Author : Syraya Chin-Mu Yang,Duen-Min Deng,Hanti Lin
Publisher : Springer
Page : 278 pages
File Size : 49,5 Mb
Release : 2015-10-16
Category : Philosophy
ISBN : 9783662483572

Get Book

Structural Analysis of Non-Classical Logics by Syraya Chin-Mu Yang,Duen-Min Deng,Hanti Lin Pdf

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, Language and Computation

S. Akama
Logic Language and Computation Book PDF

Author : S. Akama
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Philosophy
ISBN : 9789401156387

Get Book

Logic, Language and Computation by S. Akama Pdf

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.

Kit Fine on Truthmakers, Relevance, and Non-classical Logic

Federico L. G. Faroldi,Frederik Van De Putte
Kit Fine on Truthmakers Relevance and Non classical Logic Book PDF

Author : Federico L. G. Faroldi,Frederik Van De Putte
Publisher : Springer Nature
Page : 796 pages
File Size : 46,5 Mb
Release : 2023-11-25
Category : Philosophy
ISBN : 9783031294150

Get Book

Kit Fine on Truthmakers, Relevance, and Non-classical Logic by Federico L. G. Faroldi,Frederik Van De Putte Pdf

This book explores some of Kit Fine's outstanding contributions to logic, philosophy of language, philosophy of mathematics, and metaphysics, among others. Contributing authors address in-depth issues about truthmaker semantics, counterfactual conditionals, grounding, vagueness, non-classical consequence relations, and arbitrary objects, offering critical reflections and novel research contributions. Each chapter is accompanied by an extensive commentary, in which Kit Fine offers detailed responses to the ideas and themes raised by the contributors. The book includes a brief autobiography and exhaustive list of his publications to this date. This book is of interest to logicians of all stripes and to analytic philosophers more generally.

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 : 48,8 Mb
Release : 2019-08-02
Category : Philosophy
ISBN : 9789811379970

Get Book

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.

Generalized Galois Logics

Katalin Bimbó,J. Michael Dunn
Generalized Galois Logics Book PDF

Author : Katalin Bimbó,J. Michael Dunn
Publisher : Center for the Study of Language and Information Publica Tion
Page : 400 pages
File Size : 40,6 Mb
Release : 2008
Category : Language Arts & Disciplines
ISBN : UOM:39015079336692

Get Book

Generalized Galois Logics by Katalin Bimbó,J. Michael Dunn Pdf

Nonclassical logics have played an increasing role in recent years in disciplines ranging from mathematics and computer science to linguistics and philosophy. Generalized Galois Logics develops a uniform framework of relational semantics to mediate between logical calculi and their semantics through algebra. This volume addresses normal modal logics such as K and S5, and substructural logics, including relevance logics, linear logic, and Lambek calculi. The authors also treat less-familiar and new logical systems with equal deftness.

Arnon Avron on Semantics and Proof Theory of Non-Classical Logics

Ofer Arieli,Anna Zamansky
Arnon Avron on Semantics and Proof Theory of Non Classical Logics Book PDF

Author : Ofer Arieli,Anna Zamansky
Publisher : Springer Nature
Page : 369 pages
File Size : 47,9 Mb
Release : 2021-07-30
Category : Philosophy
ISBN : 9783030712587

Get Book

Arnon Avron on Semantics and Proof Theory of Non-Classical Logics by Ofer Arieli,Anna Zamansky Pdf

This book is a collection of contributions honouring Arnon Avron’s seminal work on the semantics and proof theory of non-classical logics. It includes presentations of advanced work by some of the most esteemed scholars working on semantic and proof-theoretical aspects of computer science logic. Topics in this book include frameworks for paraconsistent reasoning, foundations of relevance logics, analysis and characterizations of modal logics and fuzzy logics, hypersequent calculi and their properties, non-deterministic semantics, algebraic structures for many-valued logics, and representations of the mechanization of mathematics. Avron’s foundational and pioneering contributions have been widely acknowledged and adopted by the scientific community. His research interests are very broad, spanning over proof theory, automated reasoning, non-classical logics, foundations of mathematics, and applications of logic in computer science and artificial intelligence. This is clearly reflected by the diversity of topics discussed in the chapters included in this book, all of which directly relate to Avron’s past and present works. This book is of interest to computer scientists and scholars of formal logic.

Quantifiers, Propositions and Identity

Robert Goldblatt
Quantifiers Propositions and Identity Book PDF

Author : Robert Goldblatt
Publisher : Cambridge University Press
Page : 283 pages
File Size : 52,7 Mb
Release : 2011-07-14
Category : Mathematics
ISBN : 9781107010529

Get Book

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.

Logics for Computer Science

Anita Wasilewska
Logics for Computer Science Book PDF

Author : Anita Wasilewska
Publisher : Springer
Page : 535 pages
File Size : 46,5 Mb
Release : 2018-11-03
Category : Computers
ISBN : 9783319925912

Get Book

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.

Handbook of Modal Logic

Patrick Blackburn,Johan F.A.K. van Benthem,Frank Wolter
Handbook of Modal Logic Book PDF

Author : Patrick Blackburn,Johan F.A.K. van Benthem,Frank Wolter
Publisher : Elsevier
Page : 1260 pages
File Size : 51,7 Mb
Release : 2006-11-03
Category : Mathematics
ISBN : 0080466664

Get Book

Handbook of Modal Logic by Patrick Blackburn,Johan F.A.K. van Benthem,Frank Wolter Pdf

The Handbook of Modal Logic contains 20 articles, which collectively introduce contemporary modal logic, survey current research, and indicate the way in which the field is developing. The articles survey the field from a wide variety of perspectives: the underling theory is explored in depth, modern computational approaches are treated, and six major applications areas of modal logic (in Mathematics, Computer Science, Artificial Intelligence, Linguistics, Game Theory, and Philosophy) are surveyed. The book contains both well-written expository articles, suitable for beginners approaching the subject for the first time, and advanced articles, which will help those already familiar with the field to deepen their expertise. Please visit: http://people.uleth.ca/~woods/RedSeriesPromo_WP/PubSLPR.html - Compact modal logic reference - Computational approaches fully discussed - Contemporary applications of modal logic covered in depth

Analysis and Synthesis of Logics

Walter Carnielli,Marcelo Coniglio,Dov M. Gabbay,Paula Gouveia,Cristina Sernadas
Analysis and Synthesis of Logics Book PDF

Author : Walter Carnielli,Marcelo Coniglio,Dov M. Gabbay,Paula Gouveia,Cristina Sernadas
Publisher : Springer Science & Business Media
Page : 612 pages
File Size : 47,8 Mb
Release : 2008-01-22
Category : Mathematics
ISBN : 9781402067822

Get Book

Analysis and Synthesis of Logics by Walter Carnielli,Marcelo Coniglio,Dov M. Gabbay,Paula Gouveia,Cristina Sernadas Pdf

Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature. The issue of preservation of properties is addressed.