Download or read book R Calculus II Many Valued Logics written by Wei Li and published by Springer Nature. This book was released on 2022-04-12 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book R Calculus III Post Three Valued Logic written by Wei Li and published by Springer Nature. This book was released on 2022-11-19 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third volume of the book series shows R-calculus is a Gentzen-typed 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. In this book, R-calculus is taken as Tableau-based/sequent-based/multisequent-based to preserve the satisfiability of the Theory/sequent/multisequent to revise, or sequent-based, to preserve the satisfiability of the sequent to revise. The R-calculi for Post and three-valued logic is given. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic.
Download or read book R Calculus IV Propositional Logic written by Wei Li and published by Springer Nature. This book was released on 2023-03-27 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fourth volume of the book series combines propositional logic and R-calculus for a new point of view to consider belief revision. It gives the R-calculi for propositional logic, description logics, propositional modal logic, logic programming, ⇝-propositional logic, semantic networks, and three-valued logic, etc.. Applications of R-calculus in logic of supersequents are also given. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic.
Download or read book R Calculus V Description Logics written by Wei Li and published by Springer Nature. This book was released on 2024-01-05 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book series consists of two parts, decidable description logics and undecidable description logics. It gives the R-calculi for description logics. This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic.
Download or read book Many Valued Logics 2 written by Leonard Bolc and published by Springer Science & Business Media. This book was released on 2003-10-23 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Many Valued Logics 1 written by Leonard Bolc and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 E.Post in the U.S.A. in the 1920s, and since then the field has expanded dramatically as the applicability of the systems to other philosophical and semantic problems was recognized. Intuitionisticlogic, for example, arose from deep problems in the foundations of mathematics. Fuzzy logics, approximation logics, and probability logics all address questions that classical logic alone cannot answer. All these interpretations of many-valued calculi motivate specific formal systems thatallow detailed mathematical treatment. In this volume, the authors are concerned with finite-valued logics, and especially with three-valued logical calculi. Matrix constructions, axiomatizations of propositional and predicate calculi, syntax, semantic structures, and methodology are discussed. Separate chapters deal with intuitionistic logic, fuzzy logics, approximation logics, and probability logics. These systems all find application in practice, in automatic inference processes, which have been decisive for the intensive development of these logics. This volume acquaints the reader with theoretical fundamentals of many-valued logics. It is intended to be the first of a two-volume work. The second volume will deal with practical applications and methods of automated reasoning using many-valued 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 Temporal Logic written by Nicholas Rescher and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to temporal logic, a now flourishing branch of philosophical logic whose origin is of recent date, its main impetus having been provided by the publication in the late 1950s of A. N. PRIOR'S pioneering book, Time and Modality (Oxford, The Clarendon Press, 1957). Virtually all work in the field to around 1966 is surveyed in PRIOR'S elegant treatise Past, Present and Future (Oxford, The Clarendon Press, 1967). In consequence, it is no simple matter to write a comprehensive book on the subject with out merely rehearsing material already dealt with in PRIOR'S works. We believe, however, that the present book succeeds in this difficult endeavor because it approaches established materials from wholly novel points of departure, and is thus able to attain new perspectives and achieve new results. Its introductory character notwithstanding, the present work is consequently in substantial measure devoted to an exposition of new findings and a demonstration of new results. Parts of the book have been published previously. Chapter II is a modified version of an article of the same title by N. RESCHER and JAMES GARSON in The Journal of Symbolic Logic (vol. 33 [1968], pp.537-548). And Chapter XIII is a modified version of the article "Temporally Conditioned Descriptions" by N. RESCHER and JOHN ROBISON in Ratio, vol. 8 (1966), pp. 46-54. The authors are grateful to Professors GARSON and ROBISON, and to the editors of the jounal involved, for their permission to use this materials here.
Download or read book Beyond Two Theory and Applications of Multiple Valued Logic written by Melvin Fitting and published by Physica. This book was released on 2013-06-05 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantified Representation of Uncertainty and Imprecision written by Dov M. Gabbay and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: We are happy to present the first volume of the Handbook of Defeasible Reasoning and Uncertainty Management Systems. Uncertainty pervades the real world and must therefore be addressed by every system that attempts to represent reality. The representation of uncertainty is a ma jor concern of philosophers, logicians, artificial intelligence researchers and com puter sciencists, psychologists, statisticians, economists and engineers. The present Handbook volumes provide frontline coverage of this area. This Handbook was produced in the style of previous handbook series like the Handbook of Philosoph ical Logic, the Handbook of Logic in Computer Science, the Handbook of Logic in Artificial Intelligence and Logic Programming, and can be seen as a companion to them in covering the wide applications of logic and reasoning. We hope it will answer the needs for adequate representations of uncertainty. This Handbook series grew out of the ESPRIT Basic Research Project DRUMS II, where the acronym is made out of the Handbook series title. This project was financially supported by the European Union and regroups 20 major European research teams working in the general domain of uncertainty. As a fringe benefit of the DRUMS project, the research community was able to create this Hand book series, relying on the DRUMS participants as the core of the authors for the Handbook together with external international experts.
Download or read book A Treatise on Many valued Logics written by Siegfried Gottwald and published by . This book was released on 2001 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Modern Uses of Multiple Valued Logic written by M. Dunn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of invited papers from the 1975 International Sym posium on Multiple-valued Logic. Also included is an extensive bib liography of works in the field of multiple-valued logic prior to 1975 - this supplements and extends an earlier bibliography of works prior to 1965, by Nicholas Rescher in his book Many-Valued Logic, McGraw-Hill, 1969. There are a number of possible reasons for interest in the present volume. First, the range of various uses covered in this collection of papers may be taken as indicative of a breadth which occurs in the field of multiple-valued logic as a whole - the papers here can do no more than cover a small sample: question-answering systems, analysis of computer hazards, algebraic structures relating to multiple-valued logic, algebra of computer programs, fuzzy sets. Second, a large part of the interest in such uses and applications has occurred in the last twenty, even ten years. It would be too much to expect this to be reflected in Rescher's 1969 book. Third, in the 1970's a series of annual symposia have been held on multiple-valued logic, which have brought much of this into a sharp focus. * The 1971 and 1972 symposia were held at the SUNY at Buffalo, the 1973 symposium at the Uni versity of Toronto, and the 1974 symposium at West Virginia Uni versity. Papers from these symposia are included in the bibliography which may be found in an appendix of this book.
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 Deductive Systems in Traditional and Modern Logic written by Alex Citkin and published by MDPI. This book was released on 2020-11-18 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a contemporary view on different aspects of the deductive systems in various types of logics including term logics, propositional logics, logics of refutation, non-Fregean logics, higher order logics and arithmetic.
Download or read book Multiple Conclusion Logic written by D. J. Shoesmith and published by CUP Archive. This book was released on 1978-07-06 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a sustained study of the subject and is certain to stimulate further research.
Download or read book Handbook of Tableau Methods written by M. D'Agostino and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent years have been blessed with an abundance of logical systems, arising from a multitude of applications. A logic can be characterised in many different ways. Traditionally, a logic is presented via the following three components: 1. an intuitive non-formal motivation, perhaps tie it in to some application area 2. a semantical interpretation 3. a proof theoretical formulation. There are several types of proof theoretical methodologies, Hilbert style, Gentzen style, goal directed style, labelled deductive system style, and so on. The tableau methodology, invented in the 1950s by Beth and Hintikka and later per fected by Smullyan and Fitting, is today one of the most popular, since it appears to bring together the proof-theoretical and the semantical approaches to the pre of a logical system and is also very intuitive. In many universities it is sentation the style first taught to students. Recently interest in tableaux has become more widespread and a community crystallised around the subject. An annual tableaux conference is being held and proceedings are published. The present volume is a Handbook a/Tableaux pre senting to the community a wide coverage of tableaux systems for a variety of logics. It is written by active members of the community and brings the reader up to frontline research. It will be of interest to any formal logician from any area.
Download or read book Computer Science Logic written by Jerzy Marcinkowski and published by Springer. This book was released on 2004-09-09 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thisvolumecontainspapersselectedforpresentationatthe2004AnnualConf- enceoftheEuropeanAssociationforComputerScienceLogic, heldonSeptember 20-24, 2004 in Karpacz, Poland. The CSL conference series started as the International Workshops on C- puterScienceLogic, andthen, after?vemeetings, becametheAnnualConference of the European Association for Computer Science Logic. This conference was the 18th meeting, and the 13th EACSL conference. Altogether 99 abstracts were submitted, followed by 88 papers. Each of these paperswasrefereedbyatleastthreereviewers. Then, afteratwo-weekelectronic discussion, the Programme Committee selected 33 papers for presentation at the conference. Apart from the contributed papers, the Committee invited lectures from Albert Atserias, Martin Hyland, Dale Miller, Ken McMillan and Pawel Urzyczyn. WewouldliketothankallPCmembersandthesubrefereesfortheirexcellent work. The electronic PC meeting would not be possible without good software support. We decided to use the GNU CyberChair system, created by Richard van de Stadt, and we are happy with this decision. We also would like to thank Micha l Moskal who installed and ran CyberChair for us. Finally, we would like to thank ToMasz Wierzbicki, who helped with the preparation of this volume. We gratefully acknowledge?nancial support for the conference received from the Polish Committee for Scienti?c Research, and Wroc law University. July 2004 Jerzy Marcinkowski and Andrzej Tarlecki Organization CSL 2004 was organized by the Institute of Computer Science, Wrocla w University.
