Fuzzy Sets, Logics and Reasoning About Knowledge

by Dubois, Didier; Prade, Henri M.; Klement, Erich Peter

• ISBN13: 9780792359777
• ISBN10: 0792359771
• Format: Hardcover
• Copyright: 2000-04-01
• Publisher: Kluwer Academic Pub

Summary

Fuzzy Sets, Logics and Reasoning about Knowledge 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. Readership: Scholars and graduate students in logic, algebra, knowledge representation, and formal aspects of artificial intelligence.

Table of Contents

Editorial Preface	ix
Dov M. Gabbay
Introduction: Bridging the Gap between Multiple-valued Logics, Fuzzy Logic, Uncertain Reasoning and Reasoning about Knowledge	1	(6)
Didier Dubois
Henri Prade
Erich Peter Klement
Part I: Advances in Multiple-valued Logics
The Poincare Paradox and Non-classical Logics	7	(10)
Ulrich Hohle
Propositional Fuzzy Logics based on Frank t-norms: A comparison	17	(22)
Erich Peter Klement
Mirko Navara
A Resolution-based Axiomatisation of `Bold' Propositional Fuzzy Logic	39	(12)
Stephan Lehmke
How to Make Your Logic Fuzzy: Fibred Semantics and The Weaving of Logics	51	(34)
Dov M. Gabbay
Introducing Grade to Some Metalogical Notions	85	(16)
Mihir K. Chakraborty
Sanjukta Basu
Closure Operators, Fuzzy Logic and Constraints	101	(20)
Giangiacomo Gerla
Part II: Algebraic Aspects of Multiple-valued Logics
Ulam Game, the Logic of MaxSat, and Many-valued Partitions	121	(18)
Daniele Mundici
A Many-valued Generalisation of the Ultrapower Construction	139	(12)
Costas A. Drossos
Gabriel Filters and the Spectrum of an MV-Algebra	151	(10)
Panagis Karazeris
Conditional States in Finite-valued Logics	161	(14)
Antonio Di Nola
George Georgescu
Ada Lettieri
Conditioning on MV-algebras and Additive Measures---further results	175	(26)
Siegfried Weber
Part III: Advances in Approximate Reasoning
Toward Adequacy Conditions for Inference Schemata in Approximate Reasoning: The Case of the Rule of Syllogism	201	(12)
Siegfried Gottwald
Formal Theories in Fuzzy Logic	213	(24)
Vilem Novak
A Note on Fuzzy Inference as Deduction	237	(6)
Lluis Godo
Petr Hajek
The Role of Similarity in Fuzzy Reasoning	243	(12)
Frank Klawonn
T-indistinguishability Operators and Approximate Reasoning via CRI	255	(14)
Dionis Boixader
Joan Jacas
About Similarity-based Logical Systems	269	(20)
Francesco Esteva
Pere Garcia
Lluis Godo
On Similarity-based Fuzzy Clusterings	289	(12)
Helmut Thiele
Part IV: Reasoning about Information and Knowledge
Informational Representability: Abstract Models versus Concrete Models	301	(14)
Stephane Demri
Ewa Orlowska
From Possibilistic Information to Kleene's Strong Multi-valued Logics	315	(10)
Gert De Cooman
A Roadmap of Qualitative Independence	325	(26)
D. Dubois
L. Farinas del Cerro
A. Herzig
H. Prade
Truth Functionality and Measure-based Logics	351	(30)
Luca Boldrin
Claudio Sossai
Logic Programs with Context-dependent Preferences	381	(14)
Gerhard Brewka
An Overview of Inconsistency-tolerant Inferences in Prioritized Knowledge Bases	395	(24)
Salem Benferhat
Didier Dubois
Henri Prade
Index	419