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

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CRC Press, May 20, 1998 - Mathematics - 384 pages
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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
  • Non-contradiction
  • 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
    General Considerations about Fuzzy Sets
    351
    References
    359
    Copyright

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    About the author (1998)

    Reghis, Department of Mathematics, University of Timisoara, Romania.

    Reventa, Departmentof Computer Science, Glendon College, York University, Toronto, Ontario, Canada.

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