Proof Theory For Fuzzy Logics

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Proof Theory for Fuzzy Logics

George Metcalfe,Nicola Olivetti,Dov M. Gabbay
Proof Theory for Fuzzy Logics Book PDF

Author : George Metcalfe,Nicola Olivetti,Dov M. Gabbay
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 51,8 Mb
Release : 2008-11-27
Category : Mathematics
ISBN : 9781402094095

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Proof Theory for Fuzzy Logics by George Metcalfe,Nicola Olivetti,Dov M. Gabbay Pdf

Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems (including key standard completeness results) and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations.

Handbook of Mathematical Fuzzy Logic

Petr Cintula,Christian G Fermueller,Carles Noguera
Handbook of Mathematical Fuzzy Logic Book PDF

Author : Petr Cintula,Christian G Fermueller,Carles Noguera
Publisher : Unknown
Page : 384 pages
File Size : 49,5 Mb
Release : 2015-12-31
Category : Mathematics
ISBN : 1848901933

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Handbook of Mathematical Fuzzy Logic by Petr Cintula,Christian G Fermueller,Carles Noguera Pdf

Originating as an attempt to provide solid logical foundations for fuzzy set theory, and motivated also by philosophical and computational problems of vagueness and imprecision, Mathematical Fuzzy Logic (MFL) has become a significant subfield of mathematical logic. Research in this area focuses on many-valued logics with linearly ordered truth values and has yielded elegant and deep mathematical theories and challenging problems, thus continuing to attract an ever increasing number of researchers. This handbook provides, through its several volumes, an up-to-date systematic presentation of the best-developed areas of MFL. Its intended audience is researchers working on MFL or related fields, that may use the text as a reference book, and anyone looking for a comprehensive introduction to MFL. This handbook will be useful not only for readers interested in pure mathematical logic, but also for those interested in logical foundations of fuzzy set theory or in a mathematical apparatus suitable for dealing with some philosophical and linguistic issues related to vagueness. This third volume starts with three chapters on semantics of fuzzy logics, namely, on the structure of linearly ordered algebras, on semantic games, and on Ulam-Renyi games; it continues with an introduction to fuzzy logics with evaluated syntax, a survey of fuzzy description logics, and a study of probability on MV-algebras; and it ends with a philosophical chapter on the role of fuzzy logics in theories of vagueness."

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 : 50,6 Mb
Release : 2021-07-30
Category : Philosophy
ISBN : 9783030712587

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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.

Mathematical Intuitionism

Al'bert Grigor'evi_ Dragalin
Mathematical Intuitionism Book PDF

Author : Al'bert Grigor'evi_ Dragalin
Publisher : American Mathematical Soc.
Page : 228 pages
File Size : 52,9 Mb
Release : 1988-12-31
Category : Mathematics
ISBN : 9780821845202

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Mathematical Intuitionism by Al'bert Grigor'evi_ Dragalin Pdf

In the area of mathematical logic, a great deal of attention is now being devoted to the study of nonclassical logics. This book intends to present the most important methods of proof theory in intuitionistic logic and to acquaint the reader with the principal axiomatic theories based on intuitionistic logic.

Fuzzy Logic and Mathematics

Radim Bělohlávek,Joseph W. Dauben,George J. Klir
Fuzzy Logic and Mathematics Book PDF

Author : Radim Bělohlávek,Joseph W. Dauben,George J. Klir
Publisher : Oxford University Press
Page : 545 pages
File Size : 51,6 Mb
Release : 2017
Category : Mathematics
ISBN : 9780190200015

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Fuzzy Logic and Mathematics by Radim Bělohlávek,Joseph W. Dauben,George J. Klir Pdf

The main part of the book is a comprehensive overview of the development of fuzzy logic and its applications in various areas of human affair since its genesis in the mid 1960s. This overview is then employed for assessing the significance of fuzzy logic and mathematics based on fuzzy logic.

Proof Theory and Automated Deduction

Jean Goubault-Larrecq,I. Mackie
Proof Theory and Automated Deduction Book PDF

Author : Jean Goubault-Larrecq,I. Mackie
Publisher : Springer Science & Business Media
Page : 448 pages
File Size : 54,8 Mb
Release : 2001-11-30
Category : Computers
ISBN : 1402003684

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Proof Theory and Automated Deduction by Jean Goubault-Larrecq,I. Mackie Pdf

Interest in computer applications has led to a new attitude to applied logic in which researchers tailor a logic in the same way they define a computer language. In response to this attitude, this text for undergraduate and graduate students discusses major algorithmic methodologies, and tableaux and resolution methods. The authors focus on first-order logic, the use of proof theory, and the computer application of automated searches for proofs of mathematical propositions. Annotation copyrighted by Book News, Inc., Portland, OR

Theory of Graded Consequence

Mihir Kumar Chakraborty,Soma Dutta
Theory of Graded Consequence Book PDF

Author : Mihir Kumar Chakraborty,Soma Dutta
Publisher : Springer
Page : 224 pages
File Size : 55,8 Mb
Release : 2019-07-22
Category : Philosophy
ISBN : 9789811388965

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Theory of Graded Consequence by Mihir Kumar Chakraborty,Soma Dutta Pdf

This book introduces the theory of graded consequence (GCT) and its mathematical formulation. It also compares the notion of graded consequence with other notions of consequence in fuzzy logics, and discusses possible applications of the theory in approximate reasoning and decision-support systems. One of the main points where this book emphasizes on is that GCT maintains the distinction between the three different levels of languages of a logic, namely object language, metalanguage and metametalanguage, and thus avoids the problem of violation of the principle of use and mention; it also shows, gathering evidences from existing fuzzy logics, that the problem of category mistake may arise as a result of not maintaining distinction between levels.

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 : 54,6 Mb
Release : 2019-08-02
Category : Philosophy
ISBN : 9789811379970

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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.

Proof Theory

Katalin Bimbo
Proof Theory Book PDF

Author : Katalin Bimbo
Publisher : CRC Press
Page : 386 pages
File Size : 48,5 Mb
Release : 2014-08-20
Category : Mathematics
ISBN : 9781466564688

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Proof Theory by Katalin Bimbo Pdf

Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi

Theoretical Advances and Applications of Fuzzy Logic and Soft Computing

Oscar Castillo,Patricia Melin,Oscar Montiel Ross,Roberto Sepúlveda Cruz,Witold Pedrycz
Theoretical Advances and Applications of Fuzzy Logic and Soft Computing Book PDF

Author : Oscar Castillo,Patricia Melin,Oscar Montiel Ross,Roberto Sepúlveda Cruz,Witold Pedrycz
Publisher : Springer Science & Business Media
Page : 626 pages
File Size : 44,9 Mb
Release : 2007-10-10
Category : Technology & Engineering
ISBN : 9783540724346

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Theoretical Advances and Applications of Fuzzy Logic and Soft Computing by Oscar Castillo,Patricia Melin,Oscar Montiel Ross,Roberto Sepúlveda Cruz,Witold Pedrycz Pdf

This book comprises a selection of papers on theoretical advances and applications of fuzzy logic and soft computing from the IFSA 2007 World Congress, held in Cancun, Mexico, June 2007. These papers constitute an important contribution to the theory and applications of fuzzy logic and soft computing methodologies.

Petr Hájek on Mathematical Fuzzy Logic

Franco Montagna
Petr H jek on Mathematical Fuzzy Logic Book PDF

Author : Franco Montagna
Publisher : Springer
Page : 318 pages
File Size : 53,7 Mb
Release : 2014-09-23
Category : Mathematics
ISBN : 9783319062334

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Petr Hájek on Mathematical Fuzzy Logic by Franco Montagna Pdf

This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work. The book opens with a discussion on Hájek's contribution to mathematical fuzzy logic and with a scientific biography of him, progresses to include two articles with a foundation flavour, that demonstrate some important aspects of Hájek's production, namely, a paper on the development of fuzzy sets and another paper on some fuzzy versions of set theory and arithmetic. Articles in the volume also focus on the treatment of vagueness, building connections between Hájek's favorite fuzzy logic and linguistic models of vagueness. Other articles introduce alternative notions of consequence relation, namely, the preservation of truth degrees, which is discussed in a general context, and the differential semantics. For the latter, a surprisingly strong standard completeness theorem is proved. Another contribution also looks at two principles valid in classical logic and characterize the three main t-norm logics in terms of these principles. Other articles, with an algebraic flavour, offer a summary of the applications of lattice ordered-groups to many-valued logic and to quantum logic, as well as an investigation of prelinearity in varieties of pointed lattice ordered algebras that satisfy a weak form of distributivity and have a very weak implication. The last part of the volume contains an article on possibilistic modal logics defined over MTL chains, a topic that Hájek discussed in his celebrated work, Metamathematics of Fuzzy Logic, and another one where the authors, besides offering unexpected premises such as proposing to call Hájek's basic fuzzy logic HL, instead of BL, propose a very weak system, called SL as a candidate for the role of the really basic fuzzy logic. The paper also provides a generalization of the prelinearity axiom, which was investigated by Hájek in the context of fuzzy logic.

A Proof Theory for Description Logics

Alexandre Rademaker
A Proof Theory for Description Logics Book PDF

Author : Alexandre Rademaker
Publisher : Springer Science & Business Media
Page : 106 pages
File Size : 47,8 Mb
Release : 2012-05-17
Category : Mathematics
ISBN : 9781447140023

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A Proof Theory for Description Logics by Alexandre Rademaker Pdf

Description Logics (DLs) is a family of formalisms used to represent knowledge of a domain. They are equipped with a formal logic-based semantics. Knowledge representation systems based on description logics provide various inference capabilities that deduce implicit knowledge from the explicitly represented knowledge. A Proof Theory for Description Logics introduces Sequent Calculi and Natural Deduction for some DLs (ALC, ALCQ). Cut-elimination and Normalization are proved for the calculi. The author argues that such systems can improve the extraction of computational content from DLs proofs for explanation purposes.

Lectures on Soft Computing and Fuzzy Logic

Antonio Di Nola,Giangiacomo Gerla
Lectures on Soft Computing and Fuzzy Logic Book PDF

Author : Antonio Di Nola,Giangiacomo Gerla
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 46,9 Mb
Release : 2013-06-05
Category : Computers
ISBN : 9783790818185

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Lectures on Soft Computing and Fuzzy Logic by Antonio Di Nola,Giangiacomo Gerla Pdf

The present volume collects selected papers arising from lectures delivered by the authors at the School on Fuzzy Logic and Soft Computing held during the years 1996/97/98/99 and sponsored by the Salerno University. The authors contributing to this volume agreed with editors to write down, to enlarge and, in many cases, to rethink their original lectures, in order to offer to readership, a more compact presentation of the proposed topics. The aim of the volume is to offer a picture, as a job in progress, of the effort that is coming in founding and developing soft computing's techniques. The volume contains papers aimed to report on recent results containing genuinely logical aspects of fuzzy logic. The topics treated in this area cover algebraic aspects of Lukasiewicz Logic, Fuzzy Logic as the logic of continuous t-norms, Intuitionistic Fuzzy Logic. Aspects of fuzzy logic based on similar ity relation are presented in connection with the problem of flexible querying in deductive database. Departing from fuzzy logic, some papers present re sults in Probability Logic treating computational aspects, results based on indishernability relation and a non commutative version of generalized effect algebras. Several strict applications of soft computing are presented in the book. Indeed we find applications ranging among pattern recognition, image and signal processing, evolutionary agents, fuzzy cellular networks, classi fication in fuzzy environments. The volume is then intended to serve as a reference work for foundational logico-algebraic aspect of Soft Computing and for concrete applications of soft computing technologies.

Ways of Proof Theory

Ralf Schindler
Ways of Proof Theory Book PDF

Author : Ralf Schindler
Publisher : Walter de Gruyter
Page : 495 pages
File Size : 53,9 Mb
Release : 2013-05-02
Category : Philosophy
ISBN : 9783110324907

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Ways of Proof Theory by Ralf Schindler Pdf

On the occasion of the retirement of Wolfram Pohlers the Institut für Mathematische Logik und Grundlagenforschung of the University of Münster organized a colloquium and a workshop which took place July 17 – 19, 2008. This event brought together proof theorists from many parts of the world who have been acting as teachers, students and collaborators of Wolfram Pohlers and who have been shaping the field of proof theory over the years. The present volume collects papers by the speakers of the colloquium and workshop; and they produce a documentation of the state of the art of contemporary proof theory.

Proof Theory

Gaisi Takeuti
Proof Theory Book PDF

Author : Gaisi Takeuti
Publisher : Courier Corporation
Page : 514 pages
File Size : 44,5 Mb
Release : 2013-01-01
Category : Mathematics
ISBN : 9780486490731

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Proof Theory by Gaisi Takeuti Pdf

Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other twentieth-century logicians. The text explores applications of proof theory to logic as well as other areas of mathematics. Suitable for advanced undergraduates and graduate students of mathematics, this long-out-of-print monograph forms a cornerstone for any library in mathematical logic and related topics. The three-part treatment begins with an exploration of first order systems, including a treatment of predicate calculus involving Gentzen's cut-elimination theorem and the theory of natural numbers in terms of Gödel's incompleteness theorem and Gentzen's consistency proof. The second part, which considers second order and finite order systems, covers simple type theory and infinitary logic. The final chapters address consistency problems with an examination of consistency proofs and their applications.