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: oPropositional and predicate logic oLogic networks oLogic programming oProof of correctness oSemantics oSyntax oCompletenesss oNon-contradiction oTheorems 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.

There are many good AI books. Usually they consecrate at most one or two chapters to the imprecision knowledge processing. To our knowledge this is among the few books to be entirely dedicated to the treatment of knowledge imperfection when bui- ing intelligent systems. We consider that an entire book should be focused on this important aspect of knowledge processing. The expected audience for this book - cludes undergraduate students in computer science, IT&C, mathematics, business, medicine, etc. , graduates, specialists and researchers in these fields. The subjects treated in the book include expert systems, knowledge representation, reasoning under knowledge Imperfection (Probability Theory, Possibility Theory, Belief Theory, and Approximate Reasoning). Most of the examples discussed in details throughout the book are from the medical domain. Each chapter ends with a set of carefully pe- gogically chosen exercises, which complete solution provided. Their understanding will trigger the comprehension of the theoretical notions, concepts and results. Chapter 1 is dedicated to the review of expert systems. Hence are briefly discussed production rules, structure of ES, reasoning in an ES, and conflict resolution. Chapter 2 treats knowledge representation. That includes the study of the differences between data, information and knowledge, logical systems with focus on predicate calculus, inference rules in classical logic, semantic nets and frames.