Multiple-Valued Logic Design: An Introduction explains the theory and applications of this increasingly important subject. Written in a clear and understandable style, the author develops the material in a skillful way. Without using a huge mathematical apparatus, he introduces the subject in a general form that includes the well-known binary logic as a special case. The book is further enhanced by more 200 explanatory diagrams and circuits, hardware and software applications with supporting PASCAL programming, and comprehensive exercises with even-numbered answers (...) for every chapter. Requiring introductory knowledge in Boolean algebra, 2-valued logic, or 2-valued switching theory, Multiple-Valued Logic Design: An Introduction is an ideal book for courses not only in logic design, but also in switching theory, nonclassical logic, and computer arithmetic. Computer scientists, mathematicians, and electronic engineers can also use the book as a basis for research into multiple-valued logic design. (shrink)

Motivated by aspects of reasoning in theories of physics, Robin Giles defined a characterization of infinite valued Łukasiewicz logic in terms of a game that combines Lorenzen-style dialogue rules for logical connectives with a scheme for betting on results of dispersive experiments for evaluating atomic propositions. We analyze this game and provide conditions on payoff functions that allow us to extract many-valued truth functions from dialogue rules of a quite general form. Besides finite and infinite valued Łukasiewicz logics, also Meyer (...) and Slaney’s Abelian logic and Cancellative Hoop Logic turn out to be characterizable in this manner. (shrink)

A notation called sets-as-signs is developed, and then it is demonstrated how it can be used to modify any known inference method to handle many-valued logics. Applications are discussed, both in pure mathematics, and in hardware verification and interval arithmetic. Concludes with a historical overview of activities in many-valued theorem proving. Annotation copyright by Book News, Inc., Portland, OR.

This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. It aims to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named ‘fuzzy inference’ can be naturally understood as logical deduction. It is for mathematicians, logicians, computer scientists, specialists in artificial intelligence and knowledge engineering, and developers of fuzzy logic.

Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers (...) in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations. (shrink)

The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, (...) a trilattice of truth values – a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi. (shrink)

The most natural and straightforward step beyond two‐valued logic is to introduce more logical values, thereby rejecting the principle of bivalence. Another, indirect, way consists in challenging the classical laws concerning the sentence connectives and introducing other non‐two‐valued connectives into the language. Either way, prepositional logic seems fundamental to many‐valuedness, rather than its first‐order extension. Hence, although there has been interesting research into first‐order many‐valued logics, we shall confine our discussion here to the 0‐order case.

A growing interest in many-valued logic has developed which to a large extent is based on applications, intended as well as already realised ones. These applications range from the field of computer science, e.g. in the areas of automated theorem proving, approximate reasoning, multi-agent systems, switching theory, and program verification, through the field of pure mathematics, e.g. in independence of consistency proofs, in generalized set theories, or in the theory of particular algebraic structures, into the fields of humanities, linguistics and (...) philosophy. (shrink)