Many-valued logics

  • 124 Pages
  • 0.94 MB
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  • English
by
North-Holland Pub. Co. , Amsterdam
Many-valued
Statement[by] J. Barkley Rosser [and] Atwell R. Turquette.
SeriesStudies in logic and the foundations of mathematics
ContributionsTurquette, Atwell R. 1914- joint author.
Classifications
LC ClassificationsBC135 .R59 1952
The Physical Object
Pagination124 p.
ID Numbers
Open LibraryOL6116311M
LC Control Number52014912

The book contains information about several many-valued logics (the 3-valued systems of Lukasiewicz, Kleene, and Bochvar; and other systems having more than 3 values), as well as a more general, abstract discussion of many-valued by: This book provides an incisive, basic introduction to many-valued logics and to the constructions Many-valued logics book are "many-valued" at their origin.

Using the matrix method, the author sheds light on the profound problems of many-valuedness criteria and its classical by:   Many-Valued Logics: A Mathematical and Computational Introduction Paperback – J by Luis M Augusto (Author)Cited by: 2. Many-valued logics Paperback – January 1, by J.

Barkley Rosser (Author)Author: J. Barkley Rosser. Her major focus is on the use of many-valued and fuzzy logics to deal with vagueness. She understands a fuzzy logic as an infinite valued logic, rather than a probabilistic logic that assigns a probability weight to propositions. One cannot do better than this work on this topicCited by: This indifference toward the meaning of many-valued statements indicates that we have no prejudices regarding the possible interpretations of our systems of many-valued logic.

As far as our treatment is concerned, the meaning of a many-valued statement could be a linguistic entity such as a many-valued proposition or a physical entity such as one of many positional contacts. Many-valued logic Nicholas Rescher Snippet view - About the author () Born in Germany, Nicholas Rescher moved to the United States with his parents in and became a naturalized.

Many-valued logics treat their truth degrees as technical tools, and intend to choose them suitably for particular applications. It is a rather difficult philosophical problem to discuss the (possible, non-technical) nature of such “truth degrees” or “truth values”. Many-valued Logics as Logics without the Contraction Rule Logics lacking some or all of structural rules, when they are formulated in sequent calculi, are called substructural logics.

The class of substructural logics. Many-valued logic is a vast field with hundreds of published papers and over ten monographs devoted to it.

I have attempted to keep this survey to manageable length by focussing on many-valued Author: Siegfried Gottwald. This book provides an incisive, basic introduction to many-valued logics and to the constructions that are "many-valued" at their origin.

Using the matrix method, the author sheds light on the profound problems of many-valuedness criteria and its classical : Many-valued logics were developed as an attempt to handle philosophical doubts about the "law of excluded middle" in classical logic.

The first many-valued formal systems were developed by J. Lukasiewicz in Poland and in the U.S.A. in the s, and since then the field has expanded dramatically as the applicability of the systems to other philosophical and semantic problems was.

In logic, an infinite-valued logic (or real-valued logic or infinitely many-valued logic) is a many-valued logic in which truth values comprise a continuous range.

Description Many-valued logics FB2

Traditionally, in Aristotle's logic, logic other than bivalent logic was the norm, as the law of the excluded middle precluded more.

Prior, Arthur Norman () Many-Valued Logics: The Last of Three Talks on “The Logic Game”, The Listener 57 () – Google Scholar Prior, Arthur Norman () Notes on the Axiomatics of Propositional Calculus (with C. Meredith), Notre Dame Journal of Formal Logic 4 () –Cited by: Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values.

This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic, as well as other non-classical logics, is.

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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 by: The second paper, “The Development of Multiple-valued Logic as Related to Computer Science,” shows that the development of multiple-valued logic is contemporaneous with the computer age and is related to computer science, where there is a well established connection of 2-valued logic to computer structures and programs.

Many-valued logics were developed as an attempt to handle philosophical doubts about the "law of excluded middle" in classical logic. The first many-valued formal systems were developed by J. Lukasiew. Description This book provides an incisive, basic introduction to many-valued logics and to the constructions that are "many-valued" at their origin.

Using the matrix method, the author sheds light on the profound problems of many-valuedness criteria and its classical characterizations.

Read the latest chapters of Studies in Logic and the Foundations of Mathematics atElsevier’s leading platform of peer-reviewed scholarly literature. 'Many-valued Logics' attempts an elementary exposition of the topics connected with logical many-valueness. It provides readers with a stimulating discussion which focuses on the constructions being "many-valued" at their origin, i.e.

those obtained through. Abstract. Many-valued logic is a vast field with hundreds of published papers and numerous monographs devoted to it. I have attempted to keep this survey to manageable length by focusing on many-valued logic as an independent by: Even decidable propositional logics can be computationally complex (e.g., already intuitionistic logic is PSPACE-complete).

On the other hand, finite-valued logics are computationally relatively Author: Siegfried Gottwald. Additional Physical Format: Online version: Rosser, J. Barkley (John Barkley), Many-valued logics.

Westport, Conn.: Greenwood Press,© Many-valued logics are becoming increasingly important in all areas of computer science. 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.

In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value.

Details Many-valued logics FB2

This is contrasted with the more commonly known bivalent logics (such as classical sentential or Boolean logic) which provide only for true and. Additional Physical Format: Online version: Rosser, J.

Barkley (John Barkley), Many-valued logics. Amsterdam, North-Holland Pub. Co., (OCoLC)   Originally published in An introduction to the literature of nonstandard logic, in particular to those nonstandard logics known as many-valued logics.

Part I expounds and discusses implicational calculi, modal logics and many-valued logics and their associated by: Abstract. I shall endeavour to cover as many branches of many-valued logic and as much of the work done in these branches as space permits. Much must, of course, be omitted, and I should therefore like to refer to an excellent bibliography of many-valued logics by Nicholas Rescher in his book (Many-Valued Logic, McGraw Hill ,).This only covers publications toso I have given a Cited by: 2.

This chapter provides an overview of the many-valued logics. From a philosophical, especially epistemological point of view, the semantic aspect of (classical) logic is more basic than the syntactic one, because it is mainly the semantic ideas that determine what are suitable syntactic versions of the corresponding (system of) logic.

Many-valued logics produce an interesting problem. Non-bivalent inputs produce classically valid consequence statements, for any choice of outputs. A major task of many-valued logics of all stripes is to fashion an appropriately non-classical relation of consequence.In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc.Many-valued logics | J.

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