Outstanding Contributions to Logic

Petr Hájek on Mathematical Fuzzy Logic

Editors: Montagna, Franco (Ed.)

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  • Offers new developments in fuzzy logic
  • Presents the work of prominent logicians and how their own work has been influenced by that of Petr Ha’jek
  • Provides a range of articles from an overview of the development of fuzzy set theory to surprising proposition to call Hajek's basic fuzzy logic H, instead of BL
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  • ISBN 978-3-319-06233-4
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Hardcover $139.99
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Softcover $129.00
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  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week). Pre-ordered printed titles are excluded from promotions.
  • Due: October 28, 2016
  • ISBN 978-3-319-38295-1
  • Free shipping for individuals worldwide
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  • Please be advised Covid-19 shipping restrictions apply. Please review prior to ordering
About this book

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.

About the authors

Franco Montagna is Professor of Mathematical Logic at the University of Siena. He is author of 110 publications which appeared in prestigious scientific journals of Logic, Algebra and Computer Science. Franco Montagna was the leader of several research projects and participates very often at scientific meetings as an invited speaker. He is an Editor of Soft Computing. His main interest is many-valued logic. In this field, he obtained relevant results with a high number of citations.

Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook $99.00
price for USA in USD
  • ISBN 978-3-319-06233-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
Softcover $129.00
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week). Pre-ordered printed titles are excluded from promotions.
  • Due: October 28, 2016
  • ISBN 978-3-319-38295-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Please be advised Covid-19 shipping restrictions apply. Please review prior to ordering
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Bibliographic Information

Bibliographic Information
Book Title
Petr Hájek on Mathematical Fuzzy Logic
Editors
  • Franco Montagna
Series Title
Outstanding Contributions to Logic
Series Volume
6
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-06233-4
DOI
10.1007/978-3-319-06233-4
Hardcover ISBN
978-3-319-06232-7
Softcover ISBN
978-3-319-38295-1
Series ISSN
2211-2758
Edition Number
1
Number of Pages
XII, 318
Number of Illustrations
9 b/w illustrations
Topics