# Classical and Fuzzy Concepts in Mathematical Logic and Applications, Professional Version

CRC Press, May 20, 1998 - Mathematics - 384 pages
Classical and Fuzzy Concepts in Mathematical Logic and Applications provides a broad, thorough coverage of the fundamentals of two-valued logic, multivalued logic, and fuzzy logic.
Exploring the parallels between classical and fuzzy mathematical logic, the book examines the use of logic in computer science, addresses questions in automatic deduction, and describes efficient computer implementation of proof techniques.
Specific issues discussed include:
• Propositional and predicate logic
• Logic networks
• Logic programming
• Proof of correctness
• Semantics
• Syntax
• Completenesss
• Theorems of Herbrand and Kalman
The authors consider that the teaching of logic for computer science is biased by the absence of motivations, comments, relevant and convincing examples, graphic aids, and the use of color to distinguish language and metalanguage. Classical and Fuzzy Concepts in Mathematical Logic and Applications discusses how the presence of these facts trigger a stirring, decisive insight into the understanding process. This view shapes this work, reflecting the authors' subjective balance between the scientific and pedagogic components of the textbook.
Usually, problems in logic lack relevance, creating a gap between classroom learning and applications to real-life problems. The book includes a variety of application-oriented problems at the end of almost every section, including programming problems in PROLOG III. With the possibility of carrying out proofs with PROLOG III and other software packages, readers will gain a first-hand experience and thus a deeper understanding of the idea of formal proof.
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### Contents

 Introduction to Naive Mathematical Logic 1 PROPOSITIONAL LOGIC 15 The Formal Language of Propositional Logic 23 The Truth Structure on 0 in Semantic Version 37 The Truth Structure on 0 in The Syntactic Version 69 Connections Between the Truth Structures on 0 97 Other Syntactic Versions of the Truth Structure on 0 107 Elements of Fuzzy Propositional Logic 131
 The Formal Language of Predicate Logic 197 The Semantic Truth Structure on the Language С 205 The Syntactic Truth Structure on the Language 233 Elements of Fuzzy Predicate Logic 259 Further Applications of Logic in Computer Science 273 Exercises Part II 315 A Boolean Algebras 321 B MVAlgebras 339

 Applications of Propositional Logic in Computer Science 153 Exercises Part I 178 Introductory Considerations 187