Physical description 
1 online resource (xii, 318 pages) : illustrations. 
Series 
Outstanding Contributions to Logic, 22112758 ; volume 6


Outstanding contributions to logic ; v.6. 22112758


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 FirstOrder 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 Nonclassical Logics; 3.3 The ̀̀ManyValued Sets'' of Klaua; 3.4 A Betting Approach; 3.5 Invoking TNorms; 3.6 Logics of TNorms; 3.6.1 The Logic of all Continuous TNorms 

3.6.2 The Logic of all LeftContinuous TNorms3.6.3 FirstOrder Logics; 3.6.4 Some More Recent Extensions; 3.7 Basing fuzzy Set Theory on tnorm Logics; 3.7.1 ZFStyle Approaches; 3.7.2 A CantorStyle 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 ZFStyle 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 Nonarithmeticity 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 TNorm 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 inManyValued Logic6 Consequence and Degrees of Truth in ManyValued 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 

3319062336 

9783319062327 
Standard Number 
10.1007/9783319062334 
