Quantification in Nonclassical Logic Book

Quantification in Nonclassical Logic


  • Author : Dov M. Gabbay
  • Publisher : Elsevier
  • Release Date : 2009-06-20
  • Genre: Mathematics
  • Pages : 640
  • ISBN 10 : 9780080931128

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Quantification in Nonclassical Logic Excerpt :

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 Book
Score: 4
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An Introduction to Non Classical Logic


  • Author : Graham Priest
  • Publisher : Cambridge University Press
  • Release Date : 2008-04-10
  • Genre: Science
  • Pages : null
  • ISBN 10 : 1139469673

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An Introduction to Non Classical Logic Excerpt :

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.

Structural Analysis of Non Classical Logics Book

Structural Analysis of Non Classical Logics


  • Author : Syraya Chin-Mu Yang
  • Publisher : Springer
  • Release Date : 2015-10-16
  • Genre: Philosophy
  • Pages : 278
  • ISBN 10 : 9783662483572

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Structural Analysis of Non Classical Logics Excerpt :

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.

Logics for Computer Science Book

Logics for Computer Science


  • Author : Anita Wasilewska
  • Publisher : Springer
  • Release Date : 2018-11-03
  • Genre: Computers
  • Pages : 535
  • ISBN 10 : 9783319925912

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Logics for Computer Science Excerpt :

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.

Quantifiers  Propositions and Identity Book

Quantifiers Propositions and Identity


  • Author : Robert Goldblatt
  • Publisher : Cambridge University Press
  • Release Date : 2011-07-14
  • Genre: Mathematics
  • Pages : 268
  • ISBN 10 : 9781107010529

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Quantifiers Propositions and Identity Excerpt :

Many systems of quantified modal logic cannot be characterised by Kripke's well-known possible worlds semantic analysis. This book shows how they can be characterised by a more general 'admissible semantics', using models in which there is a restriction on which sets of worlds count as propositions. This requires a new interpretation of quantifiers that takes into account the admissibility of propositions. The author sheds new light on the celebrated Barcan Formula, whose role becomes that of legitimising the Kripkean interpretation of quantification. The theory is worked out for systems with quantifiers ranging over actual objects, and over all possibilia, and for logics with existence and identity predicates and definite descriptions. The final chapter develops a new admissible 'cover semantics' for propositional and quantified relevant logic, adapting ideas from the Kripke-Joyal semantics for intuitionistic logic in topos theory. This book is for mathematical or philosophical logicians, computer scientists and linguists.

Handbook of Modal Logic Book
Score: 4
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Handbook of Modal Logic


  • Author : Patrick Blackburn
  • Publisher : Elsevier
  • Release Date : 2006-11-03
  • Genre: Mathematics
  • Pages : 1260
  • ISBN 10 : 0080466664

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Handbook of Modal Logic Excerpt :

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

Labelled Non Classical Logics Book

Labelled Non Classical Logics


  • Author : Luca Viganò
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-04-17
  • Genre: Philosophy
  • Pages : 292
  • ISBN 10 : 9781475732085

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Labelled Non Classical Logics Excerpt :

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.

Hiroakira Ono on Substructural Logics Book

Hiroakira Ono on Substructural Logics


  • Author : Nikolaos Galatos
  • Publisher : Springer Nature
  • Release Date : 2021-12-13
  • Genre: Philosophy
  • Pages : 375
  • ISBN 10 : 9783030769208

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Hiroakira Ono on Substructural Logics Excerpt :

This volume is dedicated to Hiroakira Ono life’s work on substructural logics. Chapters, written by well-established academics, cover topics related to universal algebra, algebraic logic and the Full Lambek calculus; the book includes a short biography about Hiroakira Ono. The book starts with detailed surveys on universal algebra, abstract algebraic logic, topological dualities, and connections to computer science. It further contains specialised contributions on connections to formal languages (recognizability in residuated lattices and connections to the finite embedding property), covering systems for modal substructural logics, results on the existence and disjunction properties and finally a study of conservativity of expansions. This book will be primarily of interest to researchers working in algebraic and non-classical logic.

Classical and Nonclassical Logics Book

Classical and Nonclassical Logics


  • Author : Eric Schechter
  • Publisher : Princeton University Press
  • Release Date : 2005-08-28
  • Genre: Mathematics
  • Pages : 507
  • ISBN 10 : 0691122792

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Classical and Nonclassical Logics Excerpt :

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).

Neighborhood Semantics for Modal Logic Book

Neighborhood Semantics for Modal Logic


  • Author : Eric Pacuit
  • Publisher : Springer
  • Release Date : 2017-11-15
  • Genre: Philosophy
  • Pages : 154
  • ISBN 10 : 9783319671499

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Neighborhood Semantics for Modal Logic Excerpt :

This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic (the so-called non-normal modal logics). In addition, the book discusses a broad range of topics, including standard modal logic results (i.e., completeness, decidability and definability); bisimulations for neighborhood models and other model-theoretic constructions; comparisons with other semantics for modal logic (e.g., relational models, topological models, plausibility models); neighborhood semantics for first-order modal logic, applications in game theory (coalitional logic and game logic); applications in epistemic logic (logics of evidence and belief); and non-normal modal logics with dynamic modalities. The book can be used as the primary text for seminars on philosophical logic focused on non-normal modal logics; as a supplemental text for courses on modal logic, logic in AI, or philosophical logic (either at the undergraduate or graduate level); or as the primary source for researchers interested in learning about the uses of neighborhood semantics in philosophical logic and game theory.

Logic  Epistemology  and the Unity of Science Book

Logic Epistemology and the Unity of Science


  • Author : Shahid Rahman
  • Publisher : Springer Science & Business Media
  • Release Date : 2009-03-16
  • Genre: Philosophy
  • Pages : 626
  • ISBN 10 : 9789048124862

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Logic Epistemology and the Unity of Science Excerpt :

The first volume in this new series explores, through extensive co-operation, new ways of achieving the integration of science in all its diversity. The book offers essays from important and influential philosophers in contemporary philosophy, discussing a range of topics from philosophy of science to epistemology, philosophy of logic and game theoretical approaches. It will be of interest to philosophers, computer scientists and all others interested in the scientific rationality.

Kripke   s Worlds Book

Kripke s Worlds


  • Author : Olivier Gasquet
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-11-20
  • Genre: Mathematics
  • Pages : 198
  • ISBN 10 : 9783764385040

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Kripke s Worlds Excerpt :

Possible worlds models were introduced by Saul Kripke in the early 1960s. Basically, a possible world's model is nothing but a graph with labelled nodes and labelled edges. Such graphs provide semantics for various modal logics (alethic, temporal, epistemic and doxastic, dynamic, deontic, description logics) and also turned out useful for other nonclassical logics (intuitionistic, conditional, several paraconsistent and relevant logics). All these logics have been studied intensively in philosophical and mathematical logic and in computer science, and have been applied increasingly in domains such as program semantics, artificial intelligence, and more recently in the semantic web. Additionally, all these logics were also studied proof theoretically. The proof systems for modal logics come in various styles: Hilbert style, natural deduction, sequents, and resolution. However, it is fair to say that the most uniform and most successful such systems are tableaux systems. Given logic and a formula, they allow one to check whether there is a model in that logic. This basically amounts to trying to build a model for the formula by building a tree. This book follows a more general approach by trying to build a graph, the advantage being that a graph is closer to a Kripke model than a tree. It provides a step-by-step introduction to possible worlds semantics (and by that to modal and other nonclassical logics) via the tableaux method. It is accompanied by a piece of software called LoTREC (www.irit.fr/Lotrec). LoTREC allows to check whether a given formula is true at a given world of a given model and to check whether a given formula is satisfiable in a given logic. The latter can be done immediately if the tableau system for that logic has already been implemented in LoTREC. If this is not yet the case LoTREC offers the possibility to implement a tableau system in a relatively easy way via a simple, graph-based, interactive language.

Intro to Non Classical Logic 2ed Book

Intro to Non Classical Logic 2ed


  • Author : Anonim
  • Publisher : Unknown
  • Release Date : 2008
  • Genre: Uncategoriezed
  • Pages : null
  • ISBN 10 : OCLC:741249613

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Intro to Non Classical Logic 2ed Excerpt :

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.

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

Arnon Avron on Semantics and Proof Theory of Non Classical Logics


  • Author : Ofer Arieli
  • Publisher : Springer Nature
  • Release Date : 2021-07-30
  • Genre: Philosophy
  • Pages : 339
  • ISBN 10 : 9783030712587

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Arnon Avron on Semantics and Proof Theory of Non Classical Logics Excerpt :

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.