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Title Petr Hájek on mathematical fuzzy logic / Franco Montagna, editor.

Published Cham : Springer, [2014]


Location Call No. Status
Physical description 1 online resource (xii, 318 pages) : illustrations.
Series Outstanding Contributions to Logic, 2211-2758 ; volume 6
Outstanding contributions to logic ; v.6. 2211-2758
Springer English/International eBooks 2015 - Full Set
Contents Preface; Contents; Contributors; Part IIntroduction; 1 Introduction; 1.1 Mathematical Fuzzy Logic; 1.2 The Beginning; 1.3 The Monograph ̀̀Metamathematics of Fuzzy Logic''; 1.4 First-Order Fuzzy Logics; 1.5 Computational Complexity of Fuzzy Logics; 1.6 Logics Weaker than BL; 1.7 Further Logics Related to BL; 1.7.1 Rational Pavelka Logic; 1.7.2 Logics of Probability, of Possibility and of Belief; 1.7.3 Fuzzy Modal Logics; 1.7.4 Fuzzy Description Logic; 1.7.5 Logics with Truth Hedges; 1.8 Mathematical Theories Over Fuzzy Logic; 1.9 Petr's Failures; References
2 Petr H©Łjek: A Scientific Biography2.1 Introduction; 2.2 Early Years and Set Theory; 2.3 Arithmetic; 2.4 Logic Applied to Computer Science; 2.5 Fuzzy Logic; 2.6 Sources and Acknowledgements; References; Part II Foundational Aspects of MathematicalFuzzy Logic; 3 The Logic of Fuzzy Set Theory: A Historical Approach; 3.1 Introduction; 3.2 The ̀̀Fuzzy Sets'' of Zadeh; 3.2.1 Relating the Zadeh Approach to Non-classical Logics; 3.3 The ̀̀Many-Valued Sets'' of Klaua; 3.4 A Betting Approach; 3.5 Invoking T-Norms; 3.6 Logics of T-Norms; 3.6.1 The Logic of all Continuous T-Norms
3.6.2 The Logic of all Left-Continuous T-Norms3.6.3 First-Order Logics; 3.6.4 Some More Recent Extensions; 3.7 Basing fuzzy Set Theory on t-norm Logics; 3.7.1 ZF-Style Approaches; 3.7.2 A Cantor-Style Approach; 3.7.3 Fuzzified Mathematical Theories and Fuzzy Type Theories; 3.8 Conclusion; References; 4 Set Theory and Arithmetic in Fuzzy Logic; 4.1 Introduction; 4.2 Preliminaries; 4.3 ZF-Style Set Theories in Fuzzy Logic; 4.4 Arithmetic and the Truth Predicate; 4.4.1 Classical Arithmetic and the Truth Predicate; 4.4.2 Arithmetic with a Fuzzy Truth Predicate
4.4.3 Non-arithmeticity of Product Logic4.5 Cantor -- Łukasiewicz Set Theory; 4.5.1 Basic Notions of Cantor -- Łukasiewicz Set Theory; 4.5.2 Arithmetic in Cantor -- Łukasiewicz Set Theory; 4.5.3 Naïve Comprehension over MTL; 4.6 Conclusions; References; 5 Bridges Between Contextual Linguistic Models of Vagueness and T-Norm Based Fuzzy Logic; 5.1 Introduction; 5.2 A Contextual Linguistic Approach to Vagueness; 5.3 Extracting Fuzzy Sets from Contexts; 5.4 Saturated Contexts; 5.5 Dialogue Semantics; 5.6 Contexts and Similarity Based Reasoning; 5.7 Summary and Outlook; References
Part III Semantics and Consequence Relation inMany-Valued Logic6 Consequence and Degrees of Truth in Many-Valued Logic; 6.1 Introduction; 6.2 Some Motivation and Some History; 6.3 The Łukasiewicz Case; 6.4 Widening the Scope: Fuzzy and Substructural Logics; 6.5 Abstract algebraic logic classification; 6.6 The Deduction Theorem; 6.7 Axiomatizations; 6.7.1 In the Gentzen style; 6.7.2 In the Hilbert style; 6.8 Conclusions; References; 7 The Differential Semantics of Łukasiewicz Syntactic Consequence; 7.1 Prelude: Semantics for H©Łjek Propositional Basic Logic
Summary This volume celebrates the work of Petr H©Łjek 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 H©Łjek'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 H©Łjek'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 vague.
Other author Montagna, Franco, editor.
SpringerLink issuing body.
Subject Hájek, Petr.
Fuzzy logic.
Fuzzy mathematics.
Electronic books.
Electronic books.
Electronic books.
ISBN 9783319062334
Standard Number 10.1007/978-3-319-06233-4