A Treatise On Many Valued Logics
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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.
An Introduction to Many valued Logics
![An Introduction to Many valued Logics](https://youbookinc.com/wp-content/uploads/2024/06/cover.jpg)
Author | : Robert Ackermann |
Publsiher | : Unknown |
Total Pages | : 0 |
Release | : 2005 |
Genre | : Electronic Book |
ISBN | : OCLC:1335579062 |
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Many valued Logics
Author | : John Barkley Rosser,Atwell Rufus Turquette |
Publsiher | : Greenwood |
Total Pages | : 146 |
Release | : 1977 |
Genre | : Philosophy |
ISBN | : STANFORD:36105032786738 |
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Many valued Logics
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Author | : Anonim |
Publsiher | : Unknown |
Total Pages | : 124 |
Release | : 1952 |
Genre | : Electronic Book |
ISBN | : OCLC:867443849 |
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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.
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.
Many valued Logics
Author | : Grzegorz Malinowski |
Publsiher | : Oxford University Press on Demand |
Total Pages | : 131 |
Release | : 1993 |
Genre | : Mathematics |
ISBN | : 0198537875 |
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The book attempts an elementary exposition of the topics connected with many-valued logics. It gives an account of the constructions being "many-valued" at their origin, i.e. those obtained through intended introduction of logical values next to truth and falsity. To this aim, the matrixmethod has been chosen as a prevailing manner of presenting the subject. The inquiry throws light upon the profound problem of the criteria of many-valuedness and its classical characterizations. Besides, the reader can find information concerning the main systems of many-valued logic, related axiomatic constructions, and conceptions inspired by many valuedness. The examples of various applications to philosophical logic and some practical domains, as switching theory or Computer Science, helps to see many-valuedness in a wider perspective. Together with a selective bibliography and historical references it makes the work especially useful as a survey andguide in this field of logic.