The Resource Petr Hájek on mathematical fuzzy logic, Franco Montagna, editor

Petr Hájek on mathematical fuzzy logic, Franco Montagna, editor

Label
Petr Hájek on mathematical fuzzy logic
Title
Petr Hájek on mathematical fuzzy logic
Statement of responsibility
Franco Montagna, editor
Contributor
Editor
Subject
Genre
Language
eng
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
Member of
Cataloging source
GW5XE
Dewey number
511.3/13
Illustrations
illustrations
Index
no index present
LC call number
QA9.64
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Montagna, Franco
Series statement
Outstanding Contributions to Logic,
Series volume
volume 6
http://library.link/vocab/subjectName
  • Hájek, Petr
  • Fuzzy logic
  • Fuzzy mathematics
  • MATHEMATICS
  • Fuzzy logic
  • Fuzzy mathematics
  • Philosophy: logic
  • Mathematical foundations
Label
Petr Hájek on mathematical fuzzy logic, Franco Montagna, editor
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-06233-4
Instantiates
Publication
Copyright
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Extent
1 online resource (xii, 318 pages)
File format
unknown
Form of item
online
Isbn
9783319062334
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
c
Note
SpringerLink
Other control number
10.1007/978-3-319-06233-4
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)892623802
  • (OCoLC)ocn892623802
Label
Petr Hájek on mathematical fuzzy logic, Franco Montagna, editor
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-06233-4
Publication
Copyright
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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
Dimensions
unknown
Extent
1 online resource (xii, 318 pages)
File format
unknown
Form of item
online
Isbn
9783319062334
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
c
Note
SpringerLink
Other control number
10.1007/978-3-319-06233-4
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)892623802
  • (OCoLC)ocn892623802

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