Petr Hájek on Mathematical Fuzzy Logic

Nonfiction, Science & Nature, Mathematics, Logic, Religion & Spirituality, Philosophy
Cover of the book Petr Hájek on Mathematical Fuzzy Logic by , Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: ISBN: 9783319062334
Publisher: Springer International Publishing Publication: September 23, 2014
Imprint: Springer Language: English
Author:
ISBN: 9783319062334
Publisher: Springer International Publishing
Publication: September 23, 2014
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Design Thinking Research by
Cover of the book Modern Approaches to Discrete Curvature by
Cover of the book Ergodic Optimization in the Expanding Case by
Cover of the book Geology and Paleontology of the Quaternary of Uruguay by
Cover of the book Minority Youth and Social Integration by
Cover of the book The Quality of Democracy in Africa by
Cover of the book Sociolinguistics in African Contexts by
Cover of the book Critical Infrastructures, Key Resources, Key Assets by
Cover of the book Being Participatory: Researching with Children and Young People by
Cover of the book The Semantics of Gradability, Vagueness, and Scale Structure by
Cover of the book Advances in Computational Intelligence by
Cover of the book Understanding the Mathematical Way of Thinking – The Registers of Semiotic Representations by
Cover of the book DataFlow Supercomputing Essentials by
Cover of the book Noise Tolerant Data Authentication for Wireless Communication by
Cover of the book Digital Mammography by
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy