Petr Hájek On Mathematical Fuzzy Logic

Author : Franco Montagna
Publisher : Springer
Page : 318 pages
File Size : 51,8 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.

Author : Franco Montagna
Publisher : Unknown
Page : 128 pages
File Size : 51,7 Mb
Release : 2015
Category : Electronic books
ISBN : OCLC:1026460429

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Petr Hájek on Mathematical Fuzzy Logic by Franco Montagna Pdf

Author : Petr Hájek
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 41,5 Mb
Release : 2013-12-01
Category : Philosophy
ISBN : 9789401153003

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Metamathematics of Fuzzy Logic by Petr Hájek Pdf

This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. It aims to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named ‘fuzzy inference’ can be naturally understood as logical deduction. It is for mathematicians, logicians, computer scientists, specialists in artificial intelligence and knowledge engineering, and developers of fuzzy logic.

Author : Petr Cintula
Publisher : Unknown
Page : 405 pages
File Size : 52,7 Mb
Release : 2009
Category : Mathematics
ISBN : 190498763X

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Witnessed Years by Petr Cintula Pdf

Readers of this volume are invited on a journey through a logician's life, as witnessed by his colleagues and friends. They will have the opportunity to immerse themselves in the regions of set theory, arithmetic, data analysis, algebra, fuzzy logic and other topics that Petr Hajek has shared with the contributors. Each of the contributions is unique in its approach as well as its personal envoi, helping to create a full-blooded, vivid and genuine picture of the man who has been so emphatically influential to so many of us. Mature and fresh ideas blend in the texts which will, hopefully, make an interesting and enjoyable reading for Petr Hajek as well as for any keen logician.

Author : Stanisław Krajewski,Stephen Krajewski
Publisher : IOS Press
Page : 380 pages
File Size : 55,5 Mb
Release : 2007
Category : Mathematics
ISBN : 1586038141

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Topics in Logic, Philosophy and Foundations of Mathematics, and Computer Science by Stanisław Krajewski,Stephen Krajewski Pdf

This volume honors Professor Andrzej Grzegorczyk, the nestor of Polish logicians, on his 85th anniversary. The editors would like to express the respect and sympathy they have for him. His textbook The Outline of Mathematical Logic has been published in many editions and translated into several languages. It was this textbook that introduced many of us into the world of mathematical logic. Professor Grzegorczyk has made fundamental contributions to logic and to philosophy. His results, mainly on hierarchy of primitive recursive functions, known as the Grzegorczyk hierarchy, are of fundamental importance to theoretical computer science. In particular, they were precursory for the computational complexity theory. The editors would like to stress that this special publication celebrates a scientist who is still actively pursuing genuinely innovative directions of research. Quite recently, Andrzej Grzegorczyk gave a new proof of undecidability of the first order functional calculus. His proof does not use the arithmetization of Kurt Gödel. In recognition of his merits, the University of Clermont-Ferrand conferred to Professor Andrzej Grzegorczyk the Doctorat Honoris Causa. The work and life of Professor Andrzej Grzegorczyk is presented in the article by Professors Stanislaw Krajewski and Jan Wolenski. The papers in this collection have been submitted on invitational basis.

Author : Umberto Straccia
Publisher : CRC Press
Page : 386 pages
File Size : 49,7 Mb
Release : 2016-04-19
Category : Computers
ISBN : 9781439853481

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Foundations of Fuzzy Logic and Semantic Web Languages by Umberto Straccia Pdf

Managing vagueness/fuzziness is starting to play an important role in Semantic Web research, with a large number of research efforts underway. Foundations of Fuzzy Logic and Semantic Web Languages provides a rigorous and succinct account of the mathematical methods and tools used for representing and reasoning with fuzzy information within Semantic

Author : Dov M. Gabbay,John Woods
Publisher : Elsevier
Page : 691 pages
File Size : 44,5 Mb
Release : 2007-08-13
Category : Mathematics
ISBN : 9780080549392

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The Many Valued and Nonmonotonic Turn in Logic by Dov M. Gabbay,John Woods Pdf

The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20th century non-classical logic. These are many-valuedness and non-monotonicity. On the one approach, in deference to vagueness, temporal or quantum indeterminacy or reference-failure, sentences that are classically non-bivalent are allowed as inputs and outputs to consequence relations. Many-valued, dialetheic, fuzzy and quantum logics are, among other things, principled attempts to regulate the flow-through of sentences that are neither true nor false. On the second, or non-monotonic, approach, constraints are placed on inputs (and sometimes on outputs) of a classical consequence relation, with a view to producing a notion of consequence that serves in a more realistic way the requirements of real-life inference. Many-valued logics produce an interesting problem. Non-bivalent inputs produce classically valid consequence statements, for any choice of outputs. A major task of many-valued logics of all stripes is to fashion an appropriately non-classical relation of consequence.The chief preoccupation of non-monotonic (and default) logicians is how to constrain inputs and outputs of the consequence relation. In what is called “left non-monotonicity , it is forbidden to add new sentences to the inputs of true consequence-statements. The restriction takes notice of the fact that new information will sometimes override an antecedently (and reasonably) derived consequence. In what is called “right non-monotonicity , limitations are imposed on outputs of the consequence relation. Most notably, perhaps, is the requirement that the rule of or-introduction not be given free sway on outputs. Also prominent is the effort of paraconsistent logicians, both preservationist and dialetheic, to limit the outputs of inconsistent inputs, which in classical contexts are wholly unconstrained.In some instances, our two themes coincide. Dialetheic logics are a case in point. Dialetheic logics allow certain selected sentences to have, as a third truth value, the classical values of truth and falsity together. So such logics also admit classically inconsistent inputs. A central task is to construct a right non-monotonic consequence relation that allows for these many-valued, and inconsistent, inputs.The Many Valued and Non-Monotonic Turn in Logic is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science, AI, linguistics, cognitive science, argumentation theory, and the history of ideas. Detailed and comprehensive chapters covering the entire range of modal logic. Contains the latest scholarly discoveries and interprative insights that answers many questions in the field of logic.

Author : Radim Belohlavek,Joseph W. Dauben,George J. Klir
Publisher : Oxford University Press
Page : 480 pages
File Size : 40,8 Mb
Release : 2017-05-03
Category : Philosophy
ISBN : 9780190200022

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

The term "fuzzy logic," as it is understood in this book, stands for all aspects of representing and manipulating knowledge based on the rejection of the most fundamental principle of classical logic---the principle of bivalence. According to this principle, each declarative sentence is required to be either true or false. In fuzzy logic, these classical truth values are not abandoned. However, additional, intermediate truth values between true and false are allowed, which are interpreted as degrees of truth. This opens a new way of thinking---thinking in terms of degrees rather than absolutes. For example, it leads to the definition of a new kind of sets, referred to as fuzzy sets, in which membership is a matter of degree. The book examines the genesis and development of fuzzy logic. It surveys the prehistory of fuzzy logic and inspects circumstances that eventually lead to the emergence of fuzzy logic. The book explores in detail the development of propositional, predicate, and other calculi that admit degrees of truth, which are known as fuzzy logic in the narrow sense. Fuzzy logic in the broad sense, whose primary aim is to utilize degrees of truth for emulating common-sense human reasoning in natural language, is scrutinized as well. The book also examines principles for developing mathematics based on fuzzy logic and provides overviews of areas in which this has been done most effectively. It also presents a detailed survey of established and prospective applications of fuzzy logic in various areas of human affairs, and provides an assessment of the significance of fuzzy logic as a new paradigm.

Author : Petr Cintula,Christian G Fermueller,Carles Noguera
Publisher : Unknown
Page : 384 pages
File Size : 50,8 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."

Author : Alexandru Baltag,Jeremy Seligman,Tomoyuki Yamada
Publisher : Springer
Page : 694 pages
File Size : 43,8 Mb
Release : 2017-09-01
Category : Mathematics
ISBN : 9783662556658

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Logic, Rationality, and Interaction by Alexandru Baltag,Jeremy Seligman,Tomoyuki Yamada Pdf

This LNCS volume is part of FoLLI book serie and contains the papers presented at the 6th International Workshop on Logic, Rationality and Interaction/ (LORI-VI), held in September 2017 in Sapporo, Japan. The focus of the workshop is on following topics: Agency, Argumentation and Agreement, Belief Revision and Belief Merging, Belief Representation, Cooperation, Decision making and Planning, Natural Language, Philosophy and Philosophical Logic, and Strategic Reasoning.

Author : A.J. Tallón-Ballesteros,K. Li
Publisher : IOS Press
Page : 990 pages
File Size : 47,7 Mb
Release : 2018-11-06
Category : Computers
ISBN : 9781614999270

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Fuzzy Systems and Data Mining IV by A.J. Tallón-Ballesteros,K. Li Pdf

Big Data Analytics is on the rise in the last years of the current decade. Data are overwhelming the computation capacity of high performance servers. Cloud, grid, edge and fog computing are a few examples of the current hype. Computational Intelligence offers two faces to deal with the development of models: on the one hand, the crisp approach, which considers for every variable an exact value and, on the other hand, the fuzzy focus, which copes with values between two boundaries. This book presents 114 papers from the 4th International Conference on Fuzzy Systems and Data Mining (FSDM 2018), held in Bangkok, Thailand, from 16 to 19 November 2018. All papers were carefully reviewed by program committee members, who took into consideration the breadth and depth of the research topics that fall within the scope of FSDM. The acceptance rate was 32.85% . Offering a state-of-the-art overview of fuzzy systems and data mining, the publication will be of interest to all those whose work involves data science.

Author : Petr Cintula,Carles Noguera
Publisher : Springer Nature
Page : 465 pages
File Size : 51,8 Mb
Release : 2022-01-01
Category : Philosophy
ISBN : 9783030856755

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Logic and Implication by Petr Cintula,Carles Noguera Pdf

This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to (abstract) algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions. Based on their recent work, the authors develop a powerful uniform framework for the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics. The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics.

Author : Samuel R. Buss,Petr Hájek,Pavel Pudlák
Publisher : Cambridge University Press
Page : 128 pages
File Size : 54,7 Mb
Release : 2017-03-30
Category : Mathematics
ISBN : 9781108618489

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Logic Colloquium '98 by Samuel R. Buss,Petr Hájek,Pavel Pudlák Pdf

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the thirteenth publication in the Lecture Notes in Logic series, collects the proceedings of the European Summer Meeting of the Association for Symbolic Logic held at the University of Economics in Prague, August 9–15, 1988. It includes surveys and research from preeminent logicians. The papers in this volume range over all areas of mathematical logic, including proof theory, set theory, model theory, computability theory and philosophy. This book will be of interest to all students and researchers in mathematical logic.

Author : Radim Bělohlávek,Joseph W. Dauben,George J. Klir
Publisher : Oxford University Press
Page : 545 pages
File Size : 41,9 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.

Author : Alfredo Petrosino,Vincenzo Loia,Witold Pedrycz
Publisher : Springer
Page : 281 pages
File Size : 51,6 Mb
Release : 2017-02-06
Category : Computers
ISBN : 9783319529622

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Fuzzy Logic and Soft Computing Applications by Alfredo Petrosino,Vincenzo Loia,Witold Pedrycz Pdf

This book constitutes the proceedings of the 11th International Workshop on Fuzzy Logic and Applications, WILF 2016, held in Naples, Italy, in December 2016. The 22 revised full papers presented together with 2 invited lectures were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on fuzzy measures and transforms; granularity and multi-logics, clustering and learning; knowledge systems; and soft computing and applications.