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.
Author(s): Didier Dubois, Henri Prade, Erich Peter Klement (auth.), Didier Dubois, Henri Prade, Erich Peter Klement (eds.)
Series: Applied Logic Series 15
Edition: 1
Publisher: Springer Netherlands
Year: 1999
Language: English
Pages: 425
Tags: Logic; Mathematical Logic and Foundations; Artificial Intelligence (incl. Robotics); Order, Lattices, Ordered Algebraic Structures
Front Matter....Pages i-ix
Introduction: Bridging the Gap between Multiple-Valued Logics, Fuzzy Logic, Uncertain Reasoning and Reasoning about Knowledge....Pages 1-6
The Poincaré Paradox and Non-Classical Logics....Pages 7-16
Propositional Fuzzy Logics Based on Frank T-Norms: A Comparison....Pages 17-38
A Resolution-Based Axiomatisation of ‘Bold’ Propositional Fuzzy Logic....Pages 39-50
How to Make Your Logic Fuzzy: Fibred Semantics and the Weaving of Logics....Pages 51-83
Introducing Grade to Some Metalogical Notions....Pages 85-99
Closure Operators, Fuzzy Logic and Constraints....Pages 101-120
Ulam Game, the Logic of Maxsat, and Many-Valued Partitions....Pages 121-137
A Many-Valued Generalization of the Ultrapower Construction....Pages 139-150
Gabriel Filters and the Spectrum of an MV-Algebra....Pages 151-160
Conditional States in Finite-Valued Logics....Pages 161-174
Conditioning on MV-Algebras and Additive Measures, Further Results....Pages 175-199
Toward Adequacy Conditions for Inference Schemata in Approximate Reasoning: The Case of the Rule of Syllogism....Pages 201-211
Formal Theories in Fuzzy Logic....Pages 213-235
A Note on Fuzzy Inference as Deduction....Pages 237-241
The Role of Similarity in Fuzzy Reasoning....Pages 243-253
T-indistinguishability Operators and Approximate Reasoning via CRI....Pages 255-268
About Similarity-Based Logical Systems....Pages 269-287
On Similarity-Based Fuzzy Clusterings....Pages 289-299
Informational Representability: Abstract Models Versus Concrete Models....Pages 301-314
From Possibilistic Information to Kleene’s Strong Multi-Valued Logics....Pages 315-323
A Roadmap of Qualitative Independence....Pages 325-350
Truth Functionality and Measure-Based Logics....Pages 351-380
Logic Programs with Context-Dependent Preferences....Pages 381-394
An Overview of Inconsistency-Tolerant Inferences in Prioritized Knowledge Bases....Pages 395-417
Back Matter....Pages 419-425
