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An Introduction to Many-Valued and Fuzzy Logic by Merrie Bergmann Pdf
Professor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical systems - Lukasiewicz, Gödel, and product logics - are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems.
A Treatise on Many-valued Logics by Siegfried Gottwald Pdf
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.
Fuzzy Logic and Mathematics by Radim Bělohlávek,Joseph W. Dauben,George J. Klir Pdf
The main part of the book is a comprehensive overview of the development of fuzzy logic and its applications in various areas of human affair since its genesis in the mid 1960s. This overview is then employed for assessing the significance of fuzzy logic and mathematics based on fuzzy logic.
An Introduction to Many-valued Logics by Robert Ackermann Pdf
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.
Fuzzy Logic of Quasi-Truth: An Algebraic Treatment by Antonio Di Nola,Revaz Grigolia,Esko Turunen Pdf
This book presents the first algebraic treatment of quasi-truth fuzzy logic and covers the algebraic foundations of many-valued logic. It offers a comprehensive account of basic techniques and reports on important results showing the pivotal role played by perfect many-valued algebras (MV-algebras). It is well known that the first-order predicate Łukasiewicz logic is not complete with respect to the canonical set of truth values. However, it is complete with respect to all linearly ordered MV –algebras. As there are no simple linearly ordered MV-algebras in this case, infinitesimal elements of an MV-algebra are allowed to be truth values. The book presents perfect algebras as an interesting subclass of local MV-algebras and provides readers with the necessary knowledge and tools for formalizing the fuzzy concept of quasi true and quasi false. All basic concepts are introduced in detail to promote a better understanding of the more complex ones. It is an advanced and inspiring reference-guide for graduate students and researchers in the field of non-classical many-valued logics.
The Many Valued and Nonmonotonic Turn in Logic by Dov M. Gabbay,John Woods Pdf
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.
Fuzzy Logic: Theory and Applications by Lukas Brooks Pdf
Fuzzy logic refers to a mathematical many-valued logic which considers truth value to be more of one range of values than the other. The main use of fuzzy logic is in fields like artificial intelligence and control theory. This book provides comprehensive insights into this field. It is a compilation of chapters that discuss the most vital concepts in the field of fuzzy logic. The topics included in this text are of utmost significance and are bound to provide incredible insights to readers. This textbook, with its detailed analyses and data, will prove immensely beneficial to students involved in this area at various levels. It will be of great help to those studying artificial intelligence, computer science and probability.
This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. It aims to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named ‘fuzzy inference’ can be naturally understood as logical deduction. It is for mathematicians, logicians, computer scientists, specialists in artificial intelligence and knowledge engineering, and developers of fuzzy logic.
Lattice-Valued Logic by Yang Xu,Da Ruan,Keyun Qin,Jun Liu Pdf
Lattice-valued Logic aims at establishing the logical foundation for uncertain information processing routinely performed by humans and artificial intelligence systems. In this textbook for the first time a general introduction on lattice-valued logic is given. It systematically summarizes research from the basic notions up to recent results on lattice implication algebras, lattice-valued logic systems based on lattice implication algebras, as well as the corresponding reasoning theories and methods. The book provides the suitable theoretical logical background of lattice-valued logic systems and supports newly designed intelligent uncertain-information-processing systems and a wide spectrum of intelligent learning tasks.
Proof Theory for Fuzzy Logics by George Metcalfe,Nicola Olivetti,Dov M. Gabbay Pdf
Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems (including key standard completeness results) and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations.
Routledge Companion to Philosophy of Language by Gillian Russell,Delia Graff Fara Pdf
Philosophy of language is the branch of philosophy that examines the nature of meaning, the relationship of language to reality, and the ways in which we use, learn, and understand language. The Routledge Companion to Philosophy of Language provides a comprehensive and up-to-date survey of the field, charting its key ideas and movements, and addressing contemporary research and enduring questions in the philosophy of language. Unique to this Companion is clear coverage of research from the related disciplines of formal logic and linguistics, and discussion of the applications in metaphysics, epistemology, ethics and philosophy of mind. Organized thematically, the Companion is divided into seven sections: Core Topics; Foundations of Semantics; Parts of Speech; Methodology; Logic for Philosophers of Language; Philosophy of Language for the Rest of Philosophy; and Historical Perspectives. Comprised of 70 never-before-published essays from leading scholars--including Sally Haslanger, Jeffrey King, Sally McConnell-Ginet, Rae Langton, Kit Fine, John MacFarlane, Jeff Pelletier, Scott Soames, Jason Stanley, Stephen Stich and Zoltan Gendler Szabo--the Routledge Companion to Philosophy of Language promises to be the most comprehensive and authoritative resource for students and scholars alike.
Fuzzy Logic: A Practical Approach by Jacob Lopez Pdf
Fuzzy logic is a type of many-valued logic which is used to handle the concept of partial truth. The truth value within this field can range from completely true to completely false. In fuzzy logic, the truth values of variables can be any real number between 0 and 1, where both extremes are inclusive. It depends on the observation that people make decisions on the basis of constant and non-numerical information. Fuzzy models are mathematical means for recognizing, representing, interpreting, manipulating and utilizing data and information that are vague and uncertain. It is applied in many fields such as control theory and artificial intelligence. The topics covered in this extensive book deal with the core aspects of fuzzy logic. It covers in detail some existent theories and innovative concepts revolving around this field. Those in search of information to further their knowledge will be greatly assisted by this book.
Fuzzy Logic is becoming an essential method of solving problems in all domains. It gives tremendous impact on the design of autonomous intelligent systems. The purpose of this book is to introduce Hybrid Algorithms, Techniques, and Implementations of Fuzzy Logic. The book consists of thirteen chapters highlighting models and principles of fuzzy logic and issues on its techniques and implementations. The intended readers of this book are engineers, researchers, and graduate students interested in fuzzy logic systems.
Presents the use of fuzzy logic as a logic and as an uncertainty theory in the decision-making context Discusses the development of the TOPSIS method in classical and fuzzy context Justifies the use of fuzzy logic as an uncertainty theory Provides illustrative examples for each fuzzy TOPSIS extension Includes related MATLAB codes and case studies
Handbook of Mathematical Fuzzy Logic by Petr Cintula,Christian G Fermueller,Carles Noguera Pdf
Originating as an attempt to provide solid logical foundations for fuzzy set theory, and motivated also by philosophical and computational problems of vagueness and imprecision, Mathematical Fuzzy Logic (MFL) has become a significant subfield of mathematical logic. Research in this area focuses on many-valued logics with linearly ordered truth values and has yielded elegant and deep mathematical theories and challenging problems, thus continuing to attract an ever increasing number of researchers. This handbook provides, through its several volumes, an up-to-date systematic presentation of the best-developed areas of MFL. Its intended audience is researchers working on MFL or related fields, that may use the text as a reference book, and anyone looking for a comprehensive introduction to MFL. This handbook will be useful not only for readers interested in pure mathematical logic, but also for those interested in logical foundations of fuzzy set theory or in a mathematical apparatus suitable for dealing with some philosophical and linguistic issues related to vagueness. This third volume starts with three chapters on semantics of fuzzy logics, namely, on the structure of linearly ordered algebras, on semantic games, and on Ulam-Renyi games; it continues with an introduction to fuzzy logics with evaluated syntax, a survey of fuzzy description logics, and a study of probability on MV-algebras; and it ends with a philosophical chapter on the role of fuzzy logics in theories of vagueness."
