Many Valued Logics 2
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A Treatise on Many valued Logics
Author | : Siegfried Gottwald |
Publsiher | : Unknown |
Total Pages | : 624 |
Release | : 2001 |
Genre | : Many-valued logic |
ISBN | : UCSC:32106015740118 |
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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.
Many Valued Logics 2
Author | : Leonard Bolc,Piotr Borowik |
Publsiher | : Springer Science & Business Media |
Total Pages | : 328 |
Release | : 2003-10-23 |
Genre | : Mathematics |
ISBN | : 3540645071 |
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Many-valued logics are becoming increasingly important in all areas of computer science. This is the second volume of an authoritative two-volume handbook on many valued logics by two leading figures in the field. 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. Among the applications presented are those in software specification and electronic circuit verification.
R Calculus II Many Valued Logics
Author | : Wei Li,Yuefei Sui |
Publsiher | : Springer Nature |
Total Pages | : 281 |
Release | : 2022-04-12 |
Genre | : Mathematics |
ISBN | : 9789811692949 |
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This second volume of the book series shows R-calculus is a combination of one monotonic tableau proof system and one non-monotonic one. The R-calculus is a Gentzen-type deduction system which is non-monotonic, and is a concrete belief revision operator which is proved to satisfy the AGM postulates and the DP postulates. It discusses the algebraical and logical properties of tableau proof systems and R-calculi in many-valued logics. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic. Also it is very useful for all those who are interested in data, digitization and correctness and consistency of information, in modal logics, non monotonic logics, decidable/undecidable logics, logic programming, description logics, default logics and semantic inheritance networks.
Neutrality and Many Valued Logics
Author | : Andrew Schumann,Florentin Smarandache |
Publsiher | : Infinite Study |
Total Pages | : 123 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 9781599730264 |
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In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert's style, sequent, and hypersequent. Recall that hypersequents are a natural generalization of Gentzen's style sequents that was introduced independently by Avron and Pottinger. In particular, we consider Hilbert's style, sequent, and hypersequent calculi for infinite-valued logics based on the three fundamental continuous t-norms: Lukasiewicz's, Godel?s, and Product logics. We present a general way that allows to construct systematically analytic calculi for a large family of non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and p-adic valued logics characterized by a special format of semantics with an appropriate rejection of Archimedes' axiom. These logics are built as different extensions of standard many-valued logics (namely, Lukasiewicz's, Godel?s, Product, and Post's logics). The informal sense of Archimedes' axiom is that anything can be measured by a ruler. Also logical multiple-validity without Archimedes' axiom consists in that the set of truth values is infinite and it is not well-founded and well-ordered. We consider two cases of non-Archimedean multi-valued logics: the first with many-validity in the interval [0,1] of hypernumbers and the second with many-validity in the ring of p-adic integers. Notice that in the second case we set discrete infinite-valued logics. Logics investigated: 1. hyperrational valued Lukasiewicz's, Godel?s, and Product logics, 2. hyperreal valued Lukasiewicz's, Godel?s, and Product logics, 3. p-adic valued Lukasiewicz's, Godel?s, and Post's logics.
Beyond Two Theory and Applications of Multiple Valued Logic
Author | : Melvin Fitting,Ewa Orlowska |
Publsiher | : Physica |
Total Pages | : 374 |
Release | : 2013-06-05 |
Genre | : Mathematics |
ISBN | : 9783790817690 |
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This volume represents the state of the art for much current research in many-valued logics. Primary researchers in the field are among the authors. Major methodological issues of many-valued logics are treated, as well as applications of many-valued logics to reasoning with fuzzy information. Areas covered include: Algebras of multiple valued logics and their applications, proof theory and automated deduction in multiple valued logics, fuzzy logics and their applications, and multiple valued logics for control theory and rational belief.
An Introduction to Many valued Logics
Author | : Robert Ackermann |
Publsiher | : Routledge |
Total Pages | : 83 |
Release | : 2019-10-30 |
Genre | : Philosophy |
ISBN | : 9781000735475 |
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Originally published in 1967. 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 calculi. Part II considers the detailed development of various many-valued calculi, and some of the important metathereoms which have been proved for them. Applications of the calculi to problems in the philosophy are also surveyed. This work combines criticism with exposition to form a comprehensive but concise survey of the field.
Many valued Logic
Author | : Nicholas Rescher |
Publsiher | : McGraw-Hill Companies |
Total Pages | : 392 |
Release | : 1969 |
Genre | : Philosophy |
ISBN | : MINN:31951001799821P |
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Many valued Logics
Author | : John Barkley Rosser |
Publsiher | : Unknown |
Total Pages | : 8 |
Release | : 1957 |
Genre | : Many-valued logic |
ISBN | : UOM:39015095251958 |
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This is a summary of a talk given at the Logic Institute on July 2. The talk reviewed the existing literature on the subject and expounded new results, as yet unpublished.