Many-Valued Logics 2 : Automated Reasoning and Practical Applications

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Many-Valued Logics 2 : Automated Reasoning and Practical Applications

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  • 製本 Hardcover:ハードカバー版/ページ数 298 p.
  • 言語 ENG
  • 商品コード 9783540645078
  • DDC分類 511.3

Full Description


Many-valued logics are becoming increasingly important in all areas of computer science. This is the second volume of an authoritative two-volume handbook on many valued logics by two leading figures in the field. While the first volume was mainly concerned with theoretical foundations, this volume emphasizes automated reasoning, practical applications, and the latest developments in fuzzy logic and rough set theory. Among the applications presented are those in software specification and electronic circuit verification.

Table of Contents

Introduction: The History of Automated Reasoning   1  (6)
Basic Notions and Results 7 (32)
Basic Notions of Algebra 7 (7)
Finite Algebras 14 (7)
Completeness of Function Sets 21 (12)
Some Properties of the Sets Zn 33 (6)
Gentzen Systems for n-Valued Logical Calculi 39 (32)
General Remarks 39 (1)
Some Identities in Post Algebras 39 (4)
A Language for the n-Valued Logical 43 (1)
Calculus and Its Semantics
A Gentzen System for the n-Valued 44 (10)
Propositional Calculus
An Alternative Gentzen System for 54 (2)
Finite-Valued Logics
A Gentzen System for the n-Valued 56 (13)
First-Order Predicate Calculus
Completeness of the Sequential Predicate 69 (2)
Calculus
Multisequent Systems of Takahashi and 71 (28)
Rousseau for Finite-Valued Logics
Notational Remarks 71 (1)
Many-Valued Propositional Calculi 71 (4)
Many-Valued Predicate Calculus 75 (7)
Gentzen Takahashi Systems for 82 (8)
Finite-Valued Logics
A Gentzen System for a Particular Class 90 (9)
of Finite-Valued Logics
The Resolution Principle in n-Valued Logics 99 (18)
Historical Remarks 99 (1)
The Language of Multi-Valued Predicate 100(1)
Calculus
A Supplement on the Semantics 101(1)
Unifying Substitutions 102(2)
Resolution Proof Systems for 104(13)
Finite-Valued Propositional Logics
Minimization Problems in Resolution Proof 117(32)
Systems
A Supplement on Propositional Calculi 117(2)
Semantic Trees 119(1)
Proof Trees 120(1)
More About Resolution Proof Systems 121(3)
Matrices Induced by Resolution Proof 124(7)
Systems
Minimal Resolution Proof Systems 131(6)
Disjunctive Logics 137(2)
Polarization 139(10)
Resolution in Finite-Valued First-Order 149(20)
Predicate Calculi
Introductory Remarks and Supplements to 149(1)
Semantics
Some Identities in Finite Post Algebras 149(5)
Satisfiability Theorems 154(6)
Canonical Models for n-Valued Logics 160(4)
The Resolution Principle for the n-Valued 164(5)
Predicate Calculus
Overview of Applications 169(30)
Software Specification and Verification 172(7)
Motivation 172(1)
Analytic Tableau Method 173(6)
Conclusions 179(1)
Interval Arithmetic 179(12)
Introduction 179(1)
GL3 Logic 180(3)
Definition of I System and Its 183(2)
Properties
Axiomatization A 185(2)
Conclusions 187(4)
Verification of Electronic Circuits 191(8)
Introduction 191(3)
Logic 194(2)
Example 196(1)
Conclusions 197(2)
Selected Applications of Fuzzy Set Theory 199(50)
Introduction 199(1)
Basic Definitions 200(4)
Operations on Fuzzy Sets and Fuzzy 204(45)
Relations
Union and Intersection of Sets 204(3)
Complement of a Set 207(1)
Composition of Relations 208(1)
Fuzzy Modifiers 209(2)
The Extension Principle 211(7)
Lattice Fuzzy Sets 218(7)
Fuzzy Logics as Generalized Many-Valued 225(2)
Logics
Fuzzy Logics as Linguistic Logics 227(3)
A Generalization of the Modus Ponens 230(19)
Rule
Selected Applications of Rough Set Theory 249(40)
Introduction 249(1)
Approximate Knowledge and Rough Sets 250(5)
Knowledge Base 250(3)
Knowledge Approximation 253(1)
Degrees of Knowledge Accuracy 254(1)
Knowledge Reduction 255(6)
Knowledge Reduct and Kernel 255(3)
Category Reduction 258(2)
Dependencies in a Knowledge Base 260(1)
Knowledge Representation Systems 261(3)
Inference from Rough Knowledge 264(3)
Introduction 264(3)
Decision Logic 267(7)
Language of Decision Logic 267(1)
Semantics of Decision Logic 268(3)
Inference 271(1)
Decision Algorithms 272(2)
Reduction of Decision Algorithms 274(15)
Bibliography 289(10)
Index 299