Download or read book Neutrality and Many Valued Logics written by Andrew Schumann and published by Infinite Study. This book was released on 2007 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Many Valued and Nonmonotonic Turn in Logic written by Dov M. Gabbay and published by Elsevier. This book was released on 2007-08-13 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20th century non-classical logic. These are many-valuedness and non-monotonicity. On the one approach, in deference to vagueness, temporal or quantum indeterminacy or reference-failure, sentences that are classically non-bivalent are allowed as inputs and outputs to consequence relations. Many-valued, dialetheic, fuzzy and quantum logics are, among other things, principled attempts to regulate the flow-through of sentences that are neither true nor false. On the second, or non-monotonic, approach, constraints are placed on inputs (and sometimes on outputs) of a classical consequence relation, with a view to producing a notion of consequence that serves in a more realistic way the requirements of real-life inference. 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.The chief preoccupation of non-monotonic (and default) logicians is how to constrain inputs and outputs of the consequence relation. In what is called "left non-monotonicity, it is forbidden to add new sentences to the inputs of true consequence-statements. The restriction takes notice of the fact that new information will sometimes override an antecedently (and reasonably) derived consequence. In what is called "right non-monotonicity, limitations are imposed on outputs of the consequence relation. Most notably, perhaps, is the requirement that the rule of or-introduction not be given free sway on outputs. Also prominent is the effort of paraconsistent logicians, both preservationist and dialetheic, to limit the outputs of inconsistent inputs, which in classical contexts are wholly unconstrained.In some instances, our two themes coincide. Dialetheic logics are a case in point. Dialetheic logics allow certain selected sentences to have, as a third truth value, the classical values of truth and falsity together. So such logics also admit classically inconsistent inputs. A central task is to construct a right non-monotonic consequence relation that allows for these many-valued, and inconsistent, inputs.The Many Valued and Non-Monotonic Turn in Logic is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science, AI, linguistics, cognitive science, argumentation theory, and the history of ideas. - Detailed and comprehensive chapters covering the entire range of modal logic. - Contains the latest scholarly discoveries and interprative insights that answers many questions in the field of logic.

Download or read book Topics in Philosophical Logic written by N. Rescher and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to introduce the reader to some new areas oflogic which have yet to find their way into the bulk of modern logic books written from the more orthodox direction of the mainstream of develop ments. Such a work seems to me much needed, both because of the in trinsic value and increasing prominence of the nonstandard sector of logic, and because this particular sector is of the greatest interest from the standpoint of philosophical implications and applications. This book unites a series of studies in philosophical logic, drawing for the most part on material which I have contributed to the journal liter ature of the subject over the past ten years. Despite the fact that some of these essays have been published in various journals at different times, they possess a high degree of thematic and methodological unity. All of these studies deal with material of substantial current interest in philo sophical logic and embody a fusion of the modern techniques of logical and linguistic-philosophical analysis for the exploration of areas of logic that are of substantial philosophical relevance.

Download or read book Computer Science and Multiple Valued Logic written by David C. Rine and published by Elsevier. This book was released on 2014-05-12 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer Science and Multiple-Valued Logic: Theory and Applications focuses on the processes, methodologies, and approaches involved in multiple-valued logic and its relationship to computer science. The selection first tackles an introduction to multiple-valued logic, lattice theory of post algebras, multiple-valued logic design and applications in binary computers, smallest many-valued logic for the treatment of complemented and uncomplemented error signals, and chain based lattices. Discussions focus on formulation, representation theory, theory and circuit design, logical tables, and unary operations. The text then examines multiple-valued signal processing with limiting, development of multiple-valued logic as related to computer science, p-algebras, and an algorithm for axiomatizing every finite logic. The book takes a look at completeness properties of multiple-valued logic algebras, computer simplification of multi-valued switching functions, and minimization of multivalued functions. Topics include generation of prime implicants, realizations, minimization algorithms, decomposition algorithm for multi-valued switching functions, and relation between the sum-of-products form and array of cubes. The selection is aimed at computer engineers, computer scientists, applied mathematicians, and physicists interested in multiple-valued logic as the discipline relates to computer engineering and computer science.

Download or read book Neutrosophic logics on Non Archimedean Structures written by Andrew Schumann and published by Infinite Study. This book was released on with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Many valued Logic written by Nicholas Rescher and published by McGraw-Hill Companies. This book was released on 1969 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Introduction to Non Classical Logic written by Graham Priest and published by Cambridge University Press. This book was released on 2008-04-10 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

Download or read book The Cosmopolitan State written by H Patrick Glenn and published by OUP Oxford. This book was released on 2013-05-23 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of the 'nation-state' has failed, Glenn argues, and a major shift in our understanding of the state is needed. He provides an original approach by situating cosmopolitanism in its historical context and demonstrating that the state is necessarily cosmopolitan in character, and has always been subject to transnational law-making.

Download or read book Non commutative Multiple Valued Logic Algebras written by Lavinia Corina Ciungu and published by Springer Science & Business Media. This book was released on 2013-08-23 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects. A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing. Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.

Download or read book Innovations and Advanced Techniques in Computer and Information Sciences and Engineering written by Tarek Sobh and published by Springer Science & Business Media. This book was released on 2007-09-04 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes a set of rigorously reviewed world-class manuscripts addressing and detailing state-of-the-art research projects in the areas of Computer Science, Computer Engineering and Information Sciences. The book presents selected papers from the conference proceedings of the International Conference on Systems, Computing Sciences and Software Engineering (SCSS 2006). All aspects of the conference were managed on-line.

Download or read book Rough Sets written by Sheela Ramanna and published by Springer Nature. This book was released on 2021-09-17 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume LNAI 12872 constitutes the proceedings of the International Joint Conference on Rough Sets, IJCRS 2021, Bratislava, Slovak Republic, in September 2021. The conference was held as a hybrid event due to the COVID-19 pandemic. The 13 full paper and 7 short papers presented were carefully reviewed and selected from 26 submissions, along with 5 invited papers. The papers are grouped in the following topical sections: core rough set models and methods, related methods and hybridization, and areas of applications.

Download or read book Individuals Essence and Identity written by A. Bottani and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Andrea Bottani Massimiliano Carrara Pierdaniele Giaretta What do we do when we do metaphysics? The aim of this introduction is to give a provisional answer to this question, and then to explain the subtitle of the volume. It is easy to observe that when we do meta physics we engage in a linguistic activity, mainly consisting of uttering declarative sentences that are not very clear to most people. That is true, but, of course, it is not very informative. What do we speak of when we do metaphysics? A traditional answer could be: we speak of what things really are, so suggesting that things can appear in a way that is different from the way they really are. So understood, meta physics is about the sense, or the senses, of "real being". A question that immediately arises is whether the sense of being is unique or is different for different types of things. Another question is whether it is possible that something could appear to be, but really not be. Modem analytic metaphysicians usually answer that the sense of being is unique, while acknowledging that there are different kinds of things, and that to say that something could appear to be but really not be is a plain contradiction, unless what is understood is that it could appear to us that there is something having such and such features, but viii Individuals, Essence, and Identity really there is no such a thing.

Download or read book Indian Philosophy written by Jonardon Ganeri and published by Routledge. This book was released on 2019-11-14 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: The selection of essays in this volume aims to present Indian philosophy as an autonomous intellectual tradition, with its own internal dynamics, rhythms, techniques, problematics and approaches, and to show how the richness of this tradition has a vital role in a newly emerging global and international discipline of philosophy, one in which a diversity of traditions exchange ideas and grow through their interaction with one another. This new volume is an abridgement of the four-volume set, Indian Philosophy, published by Routledge in 2016. The selection of chapters was made in collaboration with the editors at Routledge. The purpose of this volume is to reintroduce the heritage of ‘Indian Philosophy’ to a contemporary readership by acquainting the reader with some of the core themes of Indian philosophy, such as the concept of philosophy, philosophy as a search for the self, Buddhist philosophy of mind, metaphysics, epistemology, language and logic.

Download or read book Vagueness written by Timothy Williamson and published by Routledge. This book was released on 2002-01-04 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: If you keep removing single grains of sand from a heap, when is it no longer a heap? From discussions of the heap paradox in classical Greece, to modern formal approaches like fuzzy logic, Timothy Williamson traces the history of the problem of vagueness. He argues that standard logic and formal semantics apply even to vague languages and defends the controversial, realist view that vagueness is a form of ignorance - there really is a grain of sand whose removal turns a heap into a non-heap, but we can never know exactly which one it is.

Download or read book Advances and Applications of DSmT for Information Fusion Collected works second volume written by Florentin Smarandache and published by Infinite Study. This book was released on 2006-01-01 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume dedicated to Dezert-Smarandache Theory (DSmT) in Information Fusion brings in new fusion quantitative rules (such as the PCR1-6, where PCR5 for two sources does the most mathematically exact redistribution of conflicting masses to the non-empty sets in the fusion literature), qualitative fusion rules, and the Belief Conditioning Rule (BCR) which is different from the classical conditioning rule used by the fusion community working with the Mathematical Theory of Evidence. Other fusion rules are constructed based on T-norm and T-conorm (hence using fuzzy logic and fuzzy set in information fusion), or more general fusion rules based on N-norm and N-conorm (hence using neutrosophic logic and neutrosophic set in information fusion), and an attempt to unify the fusion rules and fusion theories. The known fusion rules are extended from the power set to the hyper-power set and comparison between rules are made on many examples. One defines the degree of intersection of two sets, degree of union of two sets, and degree of inclusion of two sets which all help in improving the all existing fusion rules as well as the credibility, plausibility, and communality functions. The book chapters are written by Frederic Dambreville, Milan Daniel, Jean Dezert, Pascal Djiknavorian, Dominic Grenier, Xinhan Huang, Pavlina Dimitrova Konstantinova, Xinde Li, Arnaud Martin, Christophe Osswald, Andrew Schumann, Tzvetan Atanasov Semerdjiev, Florentin Smarandache, Albena Tchamova, and Min Wang.

Download or read book Philosophical Topics written by and published by . This book was released on 2000 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vols. for 1981- include the proceedings of the Southwestern Philosophical Society.

Download or read book Representations of Multiple Valued Logic Functions written by Radomir S. Stankovic and published by Springer Nature. This book was released on 2022-06-01 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compared to binary switching functions, the multiple-valued functions (MV) offer more compact representations of the information content of signals modeled by logic functions and, therefore, their use fits very well in the general settings of data compression attempts and approaches. The first task in dealing with such signals is to provide mathematical methods for their representation in a way that will make their application in practice feasible. Representation of Multiple-Valued Logic Functions is aimed at providing an accessible introduction to these mathematical techniques that are necessary for application of related implementation methods and tools. This book presents in a uniform way different representations of multiple-valued logic functions, including functional expressions, spectral representations on finite Abelian groups, and their graphical counterparts (various related decision diagrams). Three-valued, or ternary functions, are traditionally used as the first extension from the binary case. They have a good feature that the ratio between the number of bits and the number of different values that can be encoded with the specified number of bits is favourable for ternary functions. Four-valued functions, also called quaternary functions, are particularly attractive, since in practical realization within today prevalent binary circuits environment, they may be easy coded by binary values and realized with two-stable state circuits. At the same time, there is much more considerable advent in design of four-valued logic circuits than for other $p$-valued functions. Therefore, this book is written using a hands-on approach such that after introducing the general and necessarily abstract background theory, the presentation is based on a large number of examples for ternary and quaternary functions that should provide an intuitive understanding of various representation methods and the interconnections among them. Table of Contents: Multiple-Valued Logic Functions / Functional Expressions for Multiple-Valued Functions / Spectral Representations of Multiple-Valued Functions / Decision Diagrams for Multiple-Valued Functions / Fast Calculation Algorithms