Fuzzy Sets, Logics and Reasoning about Knowledge

2000
ISBN: 978-0-7923-5977-7
Verlag: Springer Netherlands

Buch, Englisch, 425 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1750 g

Reihe: Applied Logic Series

reports recent results concerning the genuinely logical aspects of fuzzy sets in relation to algebraic considerations, knowledge representation and commonsense reasoning. It takes a state-of-the-art look at multiple-valued and fuzzy set-based logics, in an artificial intelligence perspective. The papers, all of which are written by leading contributors in their respective fields, are grouped into four sections.
The first section presents a panorama of many-valued logics in connection with fuzzy sets. The second explores algebraic foundations, with an emphasis on MV algebras. The third is devoted to approximate reasoning methods and similarity-based reasoning. The fourth explores connections between fuzzy knowledge representation, especially possibilistic logic and prioritized knowledge bases.
: Scholars and graduate students in logic, algebra, knowledge representation, and formal aspects of artificial intelligence.

Zielgruppe

Research

Autoren/Hrsg.

Dubois, Didier

Klement, Erich Peter

Prade, Henri

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Wissensbasierte Systeme, Expertensysteme
• Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Robotik
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik

Inhaltsverzeichnis

Introduction: Bridging the Gap between Multiple-valued Logics, Fuzzy Logic, Uncertain Reasoning and Reasoning about Knowledge.- I: Advances in Mutiple-valued Logics.- The Poincaré Paradox and Non-classical Logics.- Propositional Fuzzy Logics based on Frank t-norms: A comparison.- A Resolution-based Axiomatisation of ‘Bold’ Propositional Fuzzy Logic.- How to Make Your Logic Fuzzy: Fibred Semantics and The Weaving of Logics.- Introducing Grade to Some Metalogical Notions.- Closure Operators, Fuzzy Logic and Constraints.- II: Algebraic Aspects of Multiple-valued Logics.- Ulam Game, the Logic of MaxSat, and Many-valued Partitions.- A Many-valued Generalisation of the Ultrapower Construction.- Gabriel Filters and the Spectrum of an MV-Algebra.- Conditional States in Finite-valued Logics.- Conditioning on MV-algebras and Additive Measures—further results.- III: Advances in Approximate Reasoning.- Toward Adequacy Conditions for Inference Schemata in Approximate Reasoning: The Case of the Rule of Syllogism.- Formal Theories in Fuzzy Logic.- A Note on Fuzzy Inference as Deduction.- The Role of Similarity in Fuzzy Reasoning.- T-indistinguishability Operators and Approximate Reasoning via CRI.- About Similarity-based Logical Systems.- On Similarity-based Fuzzy Clusterings.- IV: Reasoning about Information and Knowledge.- Informational Representability: Abstract Models versus Concrete Models.- From Possibilistic Information to Kleene’s Strong Multi-valued Logics.- A Roadmap of Qualitative Independence.- Truth Functionality and Measure-based Logics.- Logic Programs with Context-dependent Preferences.- An Overview of Inconsistency-tolerant Inferences in Prioritized Knowledge Bases.