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 VI Finite Injury Priority Method written by Wei Li and published by Springer Nature. This book was released on with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Fuzzy Systems and Data Mining VII written by C. Shen and published by IOS Press. This book was released on 2021-11-04 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy systems and data mining are indispensible aspects of the computer systems and algorithms on which the world has come to depend. This book presents papers from FSDM 2021, the 7th International Conference on Fuzzy Systems and Data Mining. The conference, originally due to take place in Seoul, South Korea, was held online on 26-29 October 2021, due to ongoing restrictions connected with the COVID-19 pandemic. The annual FSDM conference provides a platform for knowledge exchange between international experts, researchers, academics and delegates from industry. This year, the committee received 266 submissions, and this book contains 52 papers, including keynotes and invited presentations, oral and poster contributions. The papers cover four main areas: 1) fuzzy theory, algorithms and systems – including topics like stability; 2) fuzzy applications – which are widely used and cover various types of processing as well as hardware and architecture for big data and time series; 3) the interdisciplinary field of fuzzy logic and data mining; and 4) data mining itself. The topic most frequently addressed this year is fuzzy systems. The book offers an overview of research and developments in fuzzy logic and data mining, and will be of interest to all those working in the field of data science.
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 R Calculus III Post Three Valued Logic written by Wei Li and published by . This book was released on 2022 with total page 0 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 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 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 A First Course in Mathematical Logic and Set Theory written by Michael L. O'Leary and published by John Wiley & Sons. This book was released on 2015-09-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.
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 The Lvov Warsaw School Past and Present written by Ángel Garrido and published by Birkhäuser. This book was released on 2018-06-12 with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of new investigations and discoveries on the history of a great tradition, the Lvov-Warsaw School of logic and mathematics, by the best specialists from all over the world. The papers range from historical considerations to new philosophical, logical and mathematical developments of this impressive School, including applications to Computer Science, Mathematics, Metalogic, Scientific and Analytic Philosophy, Theory of Models and Linguistics.
Download or read book Universal Algebra and Lattice Theory written by R.S. Freese and published by Springer. This book was released on 2006-11-15 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Logico Philosophical Studies written by A. Menne and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Logic Language Information and Computation written by Luke Ong and published by Springer. This book was released on 2012-08-18 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 19th Workshop on Logic, Language, Information and Communication, WoLLIC 2012, held in Buenos Aires, Argentina, in September 2012. The papers accompanying 8 invited lectures are presented together with 16 contributed papers; the latter were carefully reviewed and selected from 46 submissions. The papers report advances in inter-disciplinary research involving formal logic, theory of computation, foundations of mathematics, and computational linguistics.
Download or read book Encyclopedia of Microcomputers written by Allen Kent and published by CRC Press. This book was released on 2000-12-05 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the 26th volume in the Encyclopedia of Microcomputers series. It covers topics such as volume graphics and an automatic fuzzy rule generation method for handwriting recognition.
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.
