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Author: Sergei Odintsov
Publisher: Springer Science & Business Media
Published: 2008-03-19
Total Pages: 241
ISBN-13: 1402068670
DOWNLOAD EBOOKHere is an account of recent investigations into the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity, and the strong negation. These concepts are studied in the setting of paraconsistent logic.
Author: Holger Andreas
Publisher: Springer
Published: 2016-12-02
Total Pages: 221
ISBN-13: 331940220X
DOWNLOAD EBOOKThis book covers work written by leading scholars from different schools within the research area of paraconsistency. The authors critically investigate how contemporary paraconsistent logics can be used to better understand human reasoning in science and mathematics. Offering a variety of perspectives, they shed a new light on the question of whether paraconsistent logics can function as the underlying logics of inconsistent but useful scientific and mathematical theories. The great variety of paraconsistent logics gives rise to various, interrelated questions, such as what are the desiderata a paraconsistent logic should satisfy, is there prospect of a universal approach to paraconsistent reasoning with axiomatic theories, and to what extent is reasoning about sets structurally analogous to reasoning about truth. Furthermore, the authors consider paraconsistent logic’s status as either a normative or descriptive discipline (or one which falls in between) and which inconsistent but non-trivial axiomatic theories are well understood by which types of paraconsistent approaches. This volume addresses such questions from different perspectives in order to (i) obtain a representative overview of the state of the art in the philosophical debate on paraconsistency, (ii) come up with fresh ideas for the future of paraconsistency, and most importantly (iii) provide paraconsistent logic with a stronger philosophical foundation, taking into account the developments within the different schools of paraconsistency.
Author: Can Başkent
Publisher: Springer Nature
Published: 2020-01-01
Total Pages: 698
ISBN-13: 3030253651
DOWNLOAD EBOOKThis 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 .
Author: Arnold Koslow
Publisher: Birkhäuser
Published: 2015-06-10
Total Pages: 607
ISBN-13: 3319153684
DOWNLOAD EBOOKThis second volume of a collection of papers offers new perspectives and challenges in the study of logic. It is presented in honor of the fiftieth birthday of Jean-Yves Béziau. The papers touch upon a wide range of topics including paraconsistent logic, quantum logic, geometry of oppositions, categorical logic, computational logic, fundamental logic notions (identity, rule, quantification) and history of logic (Leibniz, Peirce, Hilbert). The volume gathers personal recollections about Jean-Yves Béziau and an autobiography, followed by 25 papers written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Irving Anellis, Dov Gabbay, Ivor Grattan-Guinness, Istvan Németi, Henri Prade. These essays will be of interest to all students and researchers interested in the nature and future of logic.
Author: Vasco Brattka
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2014-09-04
Total Pages: 389
ISBN-13: 1614519404
DOWNLOAD EBOOKPublished in honor of Victor L. Selivanov, the 17 articles collected in this volume inform on the latest developments in computability theory and its applications in computable analysis; descriptive set theory and topology; and the theory of omega-languages; as well as non-classical logics, such as temporal logic and paraconsistent logic. This volume will be of interest to mathematicians and logicians, as well as theoretical computer scientists.
Author: Davide Fazio
Publisher: Springer Nature
Published: 2020-11-07
Total Pages: 193
ISBN-13: 303052163X
DOWNLOAD EBOOKThis volume presents the state of the art in the algebraic investigation into substructural logics. It features papers from the workshop AsubL (Algebra & Substructural Logics - Take 6). Held at the University of Cagliari, Italy, this event is part of the framework of the Horizon 2020 Project SYSMICS: SYntax meets Semantics: Methods, Interactions, and Connections in Substructural logics. Substructural logics are usually formulated as Gentzen systems that lack one or more structural rules. They have been intensively studied over the past two decades by logicians of various persuasions. These researchers include mathematicians, philosophers, linguists, and computer scientists. Substructural logics are applicable to the mathematical investigation of such processes as resource-conscious reasoning, approximate reasoning, type-theoretical grammar, and other focal notions in computer science. They also apply to epistemology, economics, and linguistics. The recourse to algebraic methods -- or, better, the fecund interplay of algebra and proof theory -- has proved useful in providing a unifying framework for these investigations. The AsubL series of conferences, in particular, has played an important role in these developments. This collection will appeal to students and researchers with an interest in substructural logics, abstract algebraic logic, residuated lattices, proof theory, universal algebra, and logical semantics.
Author: Jair Minoro Abe
Publisher: Springer
Published: 2015-06-22
Total Pages: 312
ISBN-13: 3319197223
DOWNLOAD EBOOKThis book presents some of the latest applications of new theories based on the concept of paraconsistency and correlated topics in informatics, such as pattern recognition (bioinformatics), robotics, decision-making themes, and sample size. Each chapter is self-contained, and an introductory chapter covering the logic theoretical basis is also included. The aim of the text is twofold: to serve as an introductory text on the theories and applications of new logic, and as a textbook for undergraduate or graduate-level courses in AI. Today AI frequently has to cope with problems of vagueness, incomplete and conflicting (inconsistent) information. One of the most notable formal theories for addressing them is paraconsistent (paracomplete and non-alethic) logic.
Author: Katalin Bimbo
Publisher: Springer
Published: 2016-04-02
Total Pages: 469
ISBN-13: 3319293001
DOWNLOAD EBOOKThis book celebrates and expands on J. Michael Dunn’s work on informational interpretations of logic. Dunn, in his Ph.D. thesis (1966), introduced a semantics for first-degree entailments utilizing the idea that a sentence can provide positive or negative information about a topic, possibly supplying both or neither. He later published a related interpretation of the logic R-mingle, which turned out to be one of the first relational semantics for a relevance logic. An incompatibility relation between information states lends itself to a definition of negation and it has figured into Dunn's comprehensive investigations into representations of various negations. The informational view of semantics is also a prominent theme in Dunn’s research on other logics, such as quantum logic and linear logic, and led to the encompassing theory of generalized Galois logics (or "gaggles"). Dunn’s latest work addresses informational interpretations of the ternary accessibility relation and the very nature of information. The book opens with Dunn’s autobiography, followed by a list of his publications. It then presents a series of papers written by respected logicians working on different aspects of information-based logics. The topics covered include the logic R-mingle, which was introduced by Dunn, and its applications in mathematical reasoning as well as its importance in obtaining results for other relevance logics. There are also interpretations of the accessibility relation in the semantics of relevance and other non-classical logics using different notions of information. It also presents a collection of papers that develop semantics for various logics, including certain modal and many-valued logics. The publication of this book is well timed, since we are living in an "information age.” Providing new technical findings, intellectual history and careful expositions of intriguing ideas, it appeals to a wide audience of scholars and researchers.
Author: Gemma Robles
Publisher: Academic Press
Published: 2018-01-02
Total Pages: 160
ISBN-13: 0128045094
DOWNLOAD EBOOKRoutley-Meyer Ternary Relational Semantics for Intuitionistic-type Negations examines how to introduce intuitionistic-type negations into RM-semantics. RM-semantics is highly malleable and capable of modeling families of logics which are very different from each other. This semantics was introduced in the early 1970s, and was devised for interpreting relevance logics. In RM-semantics, negation is interpreted by means of the Routley operator, which has been almost exclusively used for modeling De Morgan negations. This book provides research on particular features of intuitionistic-type of negations in RM-semantics, while also defining the basic systems and many of their extensions by using models with or without a set of designated points. - Provides a clear development of the fundamentals of RM-semantics in a new application - Covers the most general research on ternary relational semantics - Includes scrutiny of constructive negation from the ternary relational perspective
Author: Lawrence S. Moss
Publisher: Springer
Published: 2018-06-26
Total Pages: 342
ISBN-13: 3662576694
DOWNLOAD EBOOKEdited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 25th Workshop on Logic, Language, Information and Communication, WoLLIC 2018, held inBogota, Colombia, in July 2018. The 16 full papers together with 3 short papers and 3 invited talks presented were fully reviewed and selected from 30 submissions. The vision for the conference is to provide an annual forum which is large enough to provide meaningful interactions between logic and the sciences related to information and computation.
