Petr Hájek on Mathematical Fuzzy Logic PDF Download
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Author: Franco Montagna
Publisher: Springer
ISBN: 3319062336
Category : Mathematics
Languages : en
Pages : 324
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Book Description
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: Samuel R. Buss
Publisher: Cambridge University Press
ISBN: 1108618480
Category : Mathematics
Languages : en
Pages : 559
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Book Description
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: Sam Buss
Publisher: A K Peters/CRC Press
ISBN:
Category : Mathematics
Languages : en
Pages : 568
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Book Description
A compilation of papers presented at the 1998 European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium '98 includes surveys and research from the world's preeminent logicians. Topics cover current research from all areas of mathematical logic, including Proof Theory, Set Theory, Model Theory, Computability Theory, and Philosophy. This book will be of interest to students and researchers of mathematical logic.
Author: Rene Cori
Publisher: A K Peters/CRC Press
ISBN:
Category : Mathematics
Languages : en
Pages : 432
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Book Description
This compilation of papers presented at the 2000 European Summer Meeting of the Association for Symbolic Logic marks the centenial anniversery of Hilbert's famous lecture. Held in the same hall at La Sorbonne where Hilbert first presented his famous problems, this meeting carries special significance to the Mathematics and Logic communities. The presentations include tutorials and research articles from some of the world's preeminent logicians. Three long articles are based on tutorials given at the meeting, and present accessible expositions of devloping research in three active areas of logic: model theory, computability, and set theory. The eleven subsequent articles cover seperate research topics in all areas of mathematical logic, including: aspects in Computer Science, Proof Theory, Set Theory, Model Theory, Computability Theory, and aspects of Philosophy.
Author: Maja Pivec
Publisher: IOS Press
ISBN: 158603572X
Category : Computers
Languages : en
Pages : 332
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Book Description
The learning process can be seen as an emotional and personal experience that is addictive and motivates learners to proactive behavior. Divided in three parts, this title discusses major topics such as: emotions, motivation, games, and game-experience.
Author: Godehard Link
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 161451996X
Category : Philosophy
Languages : en
Pages : 382
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Book Description
The essays collected in this volume focus on the role of formalist aspects in mathematical theorizing and practice, examining issues such as infinity, finiteness, and proof procedures, as well as central historical figures in the field, including Frege, Russell, Hilbert and Wittgenstein. Using modern logico-philosophical tools and systematic conceptual and logical analyses, the volume provides a thorough, up-to-date account of the subject.
Author: Sven Ove Hansson
Publisher: Springer Science & Business Media
ISBN: 9400777590
Category : Philosophy
Languages : en
Pages : 432
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Book Description
The volume analyses and develops David Makinson’s efforts to make classical logic useful outside its most obvious application areas. The book contains chapters that analyse, appraise, or reshape Makinson’s work and chapters that develop themes emerging from his contributions. These are grouped into major areas to which Makinsons has made highly influential contributions and the volume in its entirety is divided into four sections, each devoted to a particular area of logic: belief change, uncertain reasoning, normative systems and the resources of classical logic. Among the contributions included in the volume, one chapter focuses on the “inferential preferential method”, i.e. the combined use of classical logic and mechanisms of preference and choice and provides examples from Makinson’s work in non-monotonic and defeasible reasoning and belief revision. One chapter offers a short autobiography by Makinson which details his discovery of modern logic, his travels across continents and reveals his intellectual encounters and inspirations. The chapter also contains an unusually explicit statement on his views on the (limited but important) role of logic in philosophy.
Author: Michel Morvan
Publisher: Springer Science & Business Media
ISBN: 9783540642305
Category : Computers
Languages : en
Pages : 652
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Book Description
This book constitutes the strictly refereed proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science, STACS 98, held in Paris, France, in February 1998. The volume presents three invited surveys together with 52 revised full papers selected from a total of 155 submissions. The papers are organized in topical sections on algorithms and data structures, logic, complexity, and automata and formal languages.
Author: Matthew Foreman
Publisher: Springer Science & Business Media
ISBN: 1402057644
Category : Mathematics
Languages : en
Pages : 2200
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Book Description
Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.
Author: Douglas Bridges
Publisher: Cambridge University Press
ISBN: 1316510867
Category : Mathematics
Languages : en
Pages : 863
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Book Description
Gives a complete overview of modern constructive mathematics and its applications through surveys by leading experts.
Author: Alexander S. Kechris
Publisher: Cambridge University Press
ISBN: 1107182999
Category : Mathematics
Languages : en
Pages : 317
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Book Description
The final volume in a series of four books presenting the seminal papers from the Caltech-UCLA 'Cabal Seminar'.
