Petr Hájek on mathematical fuzzy logic. ([2014])

• Record Type: Book
• Further Information: Note: Franco Montagna, editor.
• Editors: Montagna, Franco
• 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.
• Publisher Details: Cham : Springer
• Publication Date: 2014
• Copyright Date: 2015
• Extent: 1 online resource (xii, 318 pages), illustrations
• Subjects: 511.3/13; Mathematics; Fuzzy logic; Fuzzy mathematics; MATHEMATICS -- General; Fuzzy logic; Fuzzy mathematics; Philosophy -- Logic; Philosophy: logic; Logic, Symbolic and mathematical; Logic; Mathematics -- Logic; Mathematical foundations; Electronic books
• Languages: English
• ISBNs: 9783319062334; 3319062336; 3319062328; 9783319062327
• Related ISBNs: 9783319062327
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (SpringerLink, viewed October 9, 2014).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.