Arnon Avron On Semantics And Proof Theory Of Non Classical Logics
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Arnon Avron On Semantics And Proof Theory Of Non Classical Logics
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Author : Ofer Arieli
language : en
Publisher: Springer Nature
Release Date : 2021-07-30
Arnon Avron On Semantics And Proof Theory Of Non Classical Logics written by Ofer Arieli and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-30 with Philosophy categories.
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.
Arnon Avron On Semantics And Proof Theory Of Non Classical Logics
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Author : Ofer Arieli
language : en
Publisher:
Release Date : 2021
Arnon Avron On Semantics And Proof Theory Of Non Classical Logics written by Ofer Arieli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
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.
Goal Directed Proof Theory
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Author : Dov M. Gabbay
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Goal Directed Proof Theory written by Dov M. Gabbay 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.
Goal Directed Proof Theory presents a uniform and coherent methodology for automated deduction in non-classical logics, the relevance of which to computer science is now widely acknowledged. The methodology is based on goal-directed provability. It is a generalization of the logic programming style of deduction, and it is particularly favourable for proof search. The methodology is applied for the first time in a uniform way to a wide range of non-classical systems, covering intuitionistic, intermediate, modal and substructural logics. The book can also be used as an introduction to these logical systems form a procedural perspective. Readership: Computer scientists, mathematicians and philosophers, and anyone interested in the automation of reasoning based on non-classical logics. The book is suitable for self study, its only prerequisite being some elementary knowledge of logic and proof theory.
What Is Negation
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Author : Dov M. Gabbay
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
What Is Negation written by Dov M. Gabbay 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 2013-06-29 with Philosophy categories.
The notion of negation is one of the central logical notions. It has been studied since antiquity and has been subjected to thorough investigations in the development of philosophical logic, linguistics, artificial intelligence and logic programming. The properties of negation-in combination with those of other logical operations and structural features of the deducibility relation-serve as gateways among logical systems. Therefore negation plays an important role in selecting logical systems for particular applications. At the moment negation is a 'hot topic', and there is an urgent need for a comprehensive account of this logical key concept. We therefore have asked leading scholars in various branches of logic to contribute to a volume on "What is Negation?". The result is the present neatly focused collection of re search papers bringing together different approaches toward a general characteri zation of kinds of negation and classifications thereof. The volume is structured into four interrelated thematic parts. Part I is centered around the themes of Models, Relevance and Impossibility. In Chapter 1 (Negation: Two Points of View), Arnon Avron develops two characteri zations of negation, one semantic the other proof-theoretic. Interestingly and maybe provokingly, under neither of these accounts intuitionistic negation emerges as a genuine negation. J. Michael Dunn in Chapter 2 (A Comparative Study of Various Model-theoretic Treatments of Negation: A History of Formal Negation) surveys a detailed correspondence-theoretic classifcation of various notions of negation in terms of properties of a binary relation interpreted as incompatibility.
Analysis And Synthesis Of Logics
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Author : Walter Carnielli
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-22
Analysis And Synthesis Of Logics written by Walter Carnielli 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 2008-01-22 with Mathematics categories.
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 (for instance, two Hilbert calculi or a Hilbert calculus and a tableau calculus). The important issue of preservation of properties is extensively addressed. For instance, sufficient conditions are provided for a combined logic to be sound and complete when the original component logics are known to be sound and complete. The book brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). It also provides examples of potential applications in emergent fields like security protocols, quantum computing, networks and argumentation theory, besides discussing more classical applications like software specification, knowledge representation, computational linguistics and modular automated reasoning. This monograph will be of interest to researchers and graduate students in mathematical logic, theory of computation and philosophical logic with no previous knowledge of the subject of combining and decomposing logics, but with a working knowledge of first-order logic. The book will also be relevant for people involved in research projects where logic is used as a tool and the need for working with several logics at the same time is mandatory (for instance, temporal, epistemic and probabilistic logics).
Relevance Logic
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Author : Shay Allen Logan
language : en
Publisher:
Release Date : 2024-05-10
Relevance Logic written by Shay Allen Logan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-10 with Philosophy categories.
Relevance logics are a misunderstood lot. Despite being the subject of intense study for nearly a century, they remain maligned as too complicated, too abstruse, or too silly to be worth learning much about. This Element aims to dispel these misunderstandings. By focusing on the weak relevant logic B, the discussion provides an entry point into a rich and diverse family of logics. Also, it contains the first-ever textbook treatment of quantification in relevance logics, as well as an overview of the cutting edge on variable sharing results and a guide to further topics in the field.
Saul Kripke On Modal Logic
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Author : Yale Weiss
language : en
Publisher: Springer Nature
Release Date : 2024-10-02
Saul Kripke On Modal Logic written by Yale Weiss and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-02 with Philosophy categories.
This edited volume brings together papers by both eminent and rising scholars to celebrate Saul Kripke’s singular contributions to modal logic. Kripke’s work on modal logic helped usher in a new semantic epoch for the field and made facility with modal logic indispensable not only to technically oriented philosophers but to theoretical computer scientists and others as well. This volume features previously unpublished work of Kripke’s as well as a brief intellectual biography recounting the story of how Kripke became interested in, and made his first contributions to, modal logic. However, the majority of the volume’s contributions are forward-looking, and produce new philosophical and technical insights by engaging with ideas tracing back to Kripke.
Justification Logic
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Author : Sergei Artemov
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-02
Justification Logic written by Sergei Artemov 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 2019-05-02 with Mathematics categories.
Develops a new logic paradigm which emphasizes evidence tracking, including theory, connections to other fields, and sample applications.
Graham Priest On Dialetheism And Paraconsistency
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Author : Can Başkent
language : en
Publisher: Springer Nature
Release Date : 2020-01-01
Graham Priest On Dialetheism And Paraconsistency written by Can Başkent and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-01 with Philosophy categories.
This book presents the state of the art in the fields of formal logic pioneered by Graham Priest. It includes advanced technical work on the model and proof theories of paraconsistent logic, in contributions from top scholars in the field. Graham Priest’s research has had a considerable influence on the field of philosophical logic, especially with respect to the themes of dialetheism—the thesis that there exist true but inconsistent sentences—and paraconsistency—an account of deduction in which contradictory premises do not entail the truth of arbitrary sentences. Priest’s work has regularly challenged researchers to reappraise many assumptions about rationality, ontology, and truth. This book collects original research by some of the most esteemed scholars working in philosophical logic, whose contributions explore and appraise Priest’s work on logical approaches to problems in philosophy, linguistics, computation, and mathematics. They provide fresh analyses, critiques, and applications of Priest’s work and attest to its continued relevance and topicality. The book also includes Priest’s responses to the contributors, providing a further layer to the development of these themes .
60 Years Of Connexive Logic
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Author : Hitoshi Omori
language : en
Publisher: Springer Nature
Release Date : 2025-02-01
60 Years Of Connexive Logic written by Hitoshi Omori and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-01 with Philosophy categories.
This book provides deep insights into current research in the rapidly developing field of connexive logic and includes contributions from leading scholars in the field. Unlike the most well known systems of non-classical logic, systems of connexive logic are contra-classical in that they both reject certain classically valid principles and validate schemata that are not valid classically. The history of modern formal connexive logic may be seen to have started with Storrs McCall’s dissertation “Non-classical Propositional Calculi" (Oxford) 1963, thus roughly 60 years ago. While at the turn of the 21st century connexive logic was a virtually dead research programme, the situation has changed significantly after the inclusion of an entry on connexive logic in the Stanford Encyclopedia of Philosophy in 2006 and the beginning of a series of annual workshops on connexive logic in 2015. Nowadays, connexive logic is a vibrant area, and the present volume offers an exciting glimpse on recent work in connexive logic. The topics range from discussions of the notion of connexivity in logic, to conditional logic, relevance logic, and experimental philosophy. The volume contains an introduction that puts the various chapters into perspective and concludes with a list of open problems in connexive logic. The volume will be of interest to logicians and philosophers interested in non-classical logic. Chapters 1, 9 and 10, are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.