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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,Valentin B. Shehtman,Dmitrij P. Skvortsov
Publisher : Unknown
Release : 2009
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Quantification in Nonclassical Logic book written by Dov M. Gabbay,Valentin B. Shehtman,Dmitrij P. Skvortsov, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

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.

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.

Quantifiers Propositions and Identity

Quantifiers  Propositions and Identity Book
Author : Robert Goldblatt
Publisher : Cambridge University Press
Release : 2011-07-14
ISBN : 1107010527
Language : En, Es, Fr & De

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Book Description :

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.

Hiroakira Ono on Substructural Logics

Hiroakira Ono on Substructural Logics Book
Author : Nikolaos Galatos,Kazushige Terui
Publisher : Springer Nature
Release : 2021-12-13
ISBN : 3030769208
Language : En, Es, Fr & De

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Book Description :

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.

Neighborhood Semantics for Modal Logic

Neighborhood Semantics for Modal Logic Book
Author : Eric Pacuit
Publisher : Springer
Release : 2017-11-15
ISBN : 3319671499
Language : En, Es, Fr & De

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Book Description :

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.

Essays on Non Classical Logic

Essays on Non Classical Logic Book
Author : Heinrich Wansing
Publisher : World Scientific
Release : 2001-09-25
ISBN : 9814490202
Language : En, Es, Fr & De

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Book Description :

This book covers a broad range of up-to-date issues in non-classical logic that are of interest not only to philosophical and mathematical logicians but also to computer scientists and researchers in artificial intelligence. The problems addressed range from methodological issues in paraconsistent and deontic logic to the revision theory of truth and infinite Turing machines. The book identifies a number of important current trends in contemporary non-classical logic. Among them are dialogical and substructural logic, the classification of concepts of negation, truthmaker theory, and mathematical and foundational aspects of modal and temporal logic. Contents:Fine-Grained Theories of Time (P Blackburn)Revision Sequences and Computers with an Infinite Amount of Time (B Löwe)On Frege's Nightmare: A Combination of Intuitionistic, Free and Paraconsistent Logics (S Rahman)Truthmakers, Entailment and Necessity (S Read)Global Definability in Basic Modal Logic (M de Rijke & H Sturm)Ackermann's Implication for Typefree Logic (K Robering)Why Dialogical Logic? (H Rückert)Semantics for Constructive Negations (Y Shramko)Recent Trends in Paraconsistent Logic (M Urchs)Obligations, Authorities, and History Dependence (H Wansing) Readership: Graduate students and researchers in philosophical logic and mathematical logic, as well as computer scientists in artificial intelligence. Keywords:Modal Logic;Tense Logic;Deontic Logic;Paraconsistent Logic;Free Logic;Substructural Logics;Dialogical Logic;Constructive Negation;Revision Theory of Truth;Truthmakers

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.

Kripke s Worlds

Kripke   s Worlds Book
Author : Olivier Gasquet,Andreas Herzig,Bilal Said,François Schwarzentruber
Publisher : Springer Science & Business Media
Release : 2013-11-20
ISBN : 3764385049
Language : En, Es, Fr & De

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Book Description :

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.

Arnon Avron on Semantics and Proof Theory of Non Classical Logics

Arnon Avron on Semantics and Proof Theory of Non Classical Logics Book
Author : Ofer Arieli,Anna Zamansky
Publisher : Springer Nature
Release : 2021-07-30
ISBN : 3030712583
Language : En, Es, Fr & De

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Book Description :

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.

Categories for the Working Philosopher

Categories for the Working Philosopher Book
Author : Elaine Landry
Publisher : Oxford University Press
Release : 2017-10-19
ISBN : 019874899X
Language : En, Es, Fr & De

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Book Description :

This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, in an accessible waythat builds on the concepts that are already familiar to philosophers working in these areas.

Logic Language and Computation

Logic  Language  and Computation Book
Author : Martin Aher,Daniel Hole,Emil Jeřábek,Clemens Kupke
Publisher : Springer
Release : 2015-05-04
ISBN : 3662469065
Language : En, Es, Fr & De

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Book Description :

This book constitutes the refereed proceedings of the 10th International Tbilisi Symposium on Logic, Language and Computation, TbiLLC 2013, held in Gudauri, Georgia, in September 2013. The conference series is centered around the interaction between logic, language and computation. The contributions represent these three fields and the symposia aim to foster interaction between them. The book consists of 16 papers that were carefully reviewed and selected from 26 submissions. Each paper has passed through a rigorous peer-review process before being accepted for publication. The volume also contains two summaries of the tutorials that took place at the symposium: the one on admissible rules and the one on the formal semantics of aspectual meaning from a cross-linguistic perspective.

Philosophical Logic Current Trends in Asia

Philosophical Logic  Current Trends in Asia Book
Author : Syraya Chin-Mu Yang,Kok Yong Lee,Hiroakira Ono
Publisher : Springer
Release : 2017-11-25
ISBN : 9811063559
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, mainly from Asia, to address a variety of logical and philosophical topics of current interest, offering a representative cross-section of the philosophical logic landscape in early 21st-century Asia. It surveys a variety of fields, including modal logic, epistemic logic, formal semantics, decidability and mereology. The book proposes new approaches and constructs more powerful frameworks, such as cover theory, an algebraic approach to cut-elimination, and a Boolean approach to causal discovery, to name but a few. Readers may find a wide range of applications of these original works in current research of philosophical logic, especially in the structural and conceptual analysis of some significant semantic properties and formal systems. The variety of topics and issues discussed here will appeal to readers from a broad spectrum of disciplines, ranging from mathematical/philosophical logic, computing science, cognitive science and artificial intelligence, to linguistics, game theory and beyond.

New Frontiers in Artificial Intelligence

New Frontiers in Artificial Intelligence Book
Author : Yoichi Motomura,Alastair Butler,Daisuke Bekki
Publisher : Springer
Release : 2013-07-19
ISBN : 3642399312
Language : En, Es, Fr & De

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Book Description :

This book constitutes the thoroughly refereed post-conference proceedings of the JSAI-isAI 2012 Workshops LENLS, JURISIN, ALSIP, MiMI, which tool place on November/December 2012, respectively, in Miyazaki, Japan. The 17 contributions in this volume were carefully reviewed and selected from 42 submissions.They are an excellent selection of papers that are representative of topics of AI research both in Japan an in other parts of the world. LENLS (Logic and Engineering of Natural Language Semantics) is an annual international workshop on formal semantics and pragmatics; its topics are the formal and theoretical aspects of natural language. JURISIN (Juris-Informatics) deals with juris-informatics. This workshop brings together people from various backgrounds such as law, social science, information and intelligent technology, logic and philosophy, including the conventional “AI and law” area. MiMI (Multimodality in Multispace Interaction) focuses on how multispace is managed in socially, temporally, and sequentially complex environments.

Leo Esakia on Duality in Modal and Intuitionistic Logics

Leo Esakia on Duality in Modal and Intuitionistic Logics Book
Author : Guram Bezhanishvili
Publisher : Springer
Release : 2014-06-03
ISBN : 940178860X
Language : En, Es, Fr & De

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Book Description :

This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia’s original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area. Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations to weak Heyting algebras and implicative semilattices. The book also dives into the Blok-Esakia theorem and provides an outline of the intuitionistic modal logic KM which is closely related to the Gödel-Löb provability logic GL. One chapter scrutinizes Esakia’s work interpreting modal diamond as the derivative of a topological space within the setting of point-free topology. The final chapter in the volume is dedicated to the derivational semantics of modal logic and other related issues.

Alternative Logics Do Sciences Need Them

Alternative Logics  Do Sciences Need Them  Book
Author : Paul A. Weingartner
Publisher : Springer Science & Business Media
Release : 2013-03-09
ISBN : 3662056798
Language : En, Es, Fr & De

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Book Description :

Initially proposed as rivals of classical logic, alternative logics have become increasingly important in sciences such as quantum physics, computer science, and artificial intelligence. The contributions collected here address the question whether the usage of logic in the sciences, especially in modern physics, requires a deviation from classical mathematical logic. The articles in the first part of the book set the scene by describing the context and the dilemma when applying logic in science. In Part II the authors offer several logics that deviate in different ways. The twelve papers in Part III investigate in detail specific aspects such as quantum logic, quantum computation, computer-science considerations, praxic logic, and quantum probability. The monograph provides a succinct picture of recent research in alternative logics as they have been developed for applications in the sciences.

Logical Foundations of Computer Science

Logical Foundations of Computer Science Book
Author : Sergei Artemov,Anil Nerode
Publisher : Springer Nature
Release : 2019-12-13
ISBN : 303036755X
Language : En, Es, Fr & De

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Book Description :

This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2020, held in Deerfield Beach, FL, USA, in January 2020. The 17 revised full papers were carefully reviewed and selected from 30 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; other logics in computer science.

Proof Reconstruction in Classical and Non Classical Logics

Proof Reconstruction in Classical and Non Classical Logics Book
Author : Stephanie Schmitt
Publisher : IOS Press
Release : 2000-04
ISBN : 9781586031299
Language : En, Es, Fr & De

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Book Description :

Download Proof Reconstruction in Classical and Non Classical Logics book written by Stephanie Schmitt, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.