Algebraic Foundations Of Many Valued Reasoning
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Algebraic Foundations Of Many Valued Reasoning
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Author : R.L. Cignoli
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Algebraic Foundations Of Many Valued Reasoning written by R.L. Cignoli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
This unique textbook states and proves all the major theorems of many-valued propositional logic and provides the reader with the most recent developments and trends, including applications to adaptive error-correcting binary search. The book is suitable for self-study, making the basic tools of many-valued logic accessible to students and scientists with a basic mathematical knowledge who are interested in the mathematical treatment of uncertain information. Stressing the interplay between algebra and logic, the book contains material never before published, such as a simple proof of the completeness theorem and of the equivalence between Chang's MV algebras and Abelian lattice-ordered groups with unit - a necessary prerequisite for the incorporation of a genuine addition operation into fuzzy logic. Readers interested in fuzzy control are provided with a rich deductive system in which one can define fuzzy partitions, just as Boolean partitions can be defined and computed in classical logic. Detailed bibliographic remarks at the end of each chapter and an extensive bibliography lead the reader on to further specialised topics.
Algebraic And Proof Theoretic Aspects Of Non Classical Logics
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Author : S. Aguzzoli
language : en
Publisher: Springer
Release Date : 2007-10-28
Algebraic And Proof Theoretic Aspects Of Non Classical Logics written by S. Aguzzoli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-28 with Computers categories.
Published in honor of Daniele Mundici on the occasion of his 60th birthday, the 17 revised papers of this Festschrift volume include invited extended versions of the most interesting contributions to the International Conference on the Algebraic and Logical Foundations of Many-Valued Reasoning, held in Gargnano, Italy, in March 2006. Edited in collaboration with FoLLI, the Association of Logic, Language and Information, it is the third volume of the FoLLI LNAI subline.
Fuzzy Sets Logics And Reasoning About Knowledge
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Author : Didier Dubois
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Fuzzy Sets Logics And Reasoning About Knowledge written by Didier Dubois and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Philosophy categories.
Fuzzy Sets, Logics and Reasoning about Knowledge reports recent results concerning the genuinely logical aspects of fuzzy sets in relation to algebraic considerations, knowledge representation and commonsense reasoning. It takes a state-of-the-art look at multiple-valued and fuzzy set-based logics, in an artificial intelligence perspective. The papers, all of which are written by leading contributors in their respective fields, are grouped into four sections. The first section presents a panorama of many-valued logics in connection with fuzzy sets. The second explores algebraic foundations, with an emphasis on MV algebras. The third is devoted to approximate reasoning methods and similarity-based reasoning. The fourth explores connections between fuzzy knowledge representation, especially possibilistic logic and prioritized knowledge bases. Readership: Scholars and graduate students in logic, algebra, knowledge representation, and formal aspects of artificial intelligence.
Many Valued Logics 1
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Author : Leonard Bolc
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Many Valued Logics 1 written by Leonard Bolc and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.
The Many Valued And Nonmonotonic Turn In Logic
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Author : Dov M. Gabbay
language : en
Publisher: Elsevier
Release Date : 2007-08-13
The Many Valued And Nonmonotonic Turn In Logic written by Dov M. Gabbay and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-13 with Mathematics categories.
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.
Mathematics Behind Fuzzy Logic
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Author : Esko Turunen
language : en
Publisher: Physica
Release Date : 1999-09-24
Mathematics Behind Fuzzy Logic written by Esko Turunen and has been published by Physica this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-24 with Business & Economics categories.
Many results in fuzzy logic depend on the mathematical structure the truth value set obeys. In this textbook the algebraic foundations of many-valued and fuzzy reasoning are introduced. The book is self-contained, thus no previous knowledge in algebra or in logic is required. It contains 134 exercises with complete answers, and can therefore be used as teaching material at universities for both undergraduated and post-graduated courses. Chapter 1 starts from such basic concepts as order, lattice, equivalence and residuated lattice. It contains a full section on BL-algebras. Chapter 2 concerns MV-algebra and its basic properties. Chapter 3 applies these mathematical results on Lukasiewicz-Pavelka style fuzzy logic, which is studied in details; besides semantics, syntax and completeness of this logic, a lot of examples are given. Chapter 4 shows the connection between fuzzy relations, approximate reasoning and fuzzy IF-THEN rules to residuated lattices.
Beyond Two Theory And Applications Of Multiple Valued Logic
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Author : Melvin Fitting
language : en
Publisher: Physica
Release Date : 2013-06-05
Beyond Two Theory And Applications Of Multiple Valued Logic written by Melvin Fitting and has been published by Physica this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-05 with Mathematics categories.
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.
Reasoning In Quantum Theory
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Author : Maria Luisa Dalla Chiara
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Reasoning In Quantum Theory written by Maria Luisa Dalla Chiara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
"Is quantum logic really logic?" This book argues for a positive answer to this question once and for all. There are many quantum logics and their structures are delightfully varied. The most radical aspect of quantum reasoning is reflected in unsharp quantum logics, a special heterodox branch of fuzzy thinking. For the first time, the whole story of Quantum Logic is told; from its beginnings to the most recent logical investigations of various types of quantum phenomena, including quantum computation. Reasoning in Quantum Theory is designed for logicians, yet amenable to advanced graduate students and researchers of other disciplines.
Formal Methods Foundations And Applications
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Author : Leila Ribeiro
language : en
Publisher: Springer
Release Date : 2016-11-12
Formal Methods Foundations And Applications written by Leila Ribeiro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-12 with Computers categories.
This book constitutes the refereed proceedings of the 19th Brazilian Symposium on Formal Methods, SBMF 2016, which took place in Natal, Brazil, in November 2016. The 12 papers presented together with two invited talks were carefully reviewed and selected from 22 submissions. They are organized in the following topical sections: analysis and verification; modeling and logic; and model checking.
Symbolic And Quantitative Approaches To Reasoning With Uncertainty
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Author : Lluis Godo
language : en
Publisher: Springer
Release Date : 2005-08-25
Symbolic And Quantitative Approaches To Reasoning With Uncertainty written by Lluis Godo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-25 with Computers categories.
These are the proceedings of the 8th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2005, held in Barcelona (Spain), July 6–8, 2005. The ECSQARU conferences are biennial and have become a major forum for advances in the theory and practice of r- soning under uncertainty. The ?rst ECSQARU conference was held in Marseille (1991), and after in Granada (1993), Fribourg (1995), Bonn (1997), London (1999), Toulouse (2001) and Aalborg (2003). The papers gathered in this volume were selected out of 130 submissions, after a strict review process by the members of the Program Committee, to be presented at ECSQARU 2005. In addition, the conference included invited lectures by three outstanding researchers in the area, Seraf ́ ?n Moral (Imprecise Probabilities), Rudolf Kruse (Graphical Models in Planning) and J ́ erˆ ome Lang (Social Choice). Moreover, the application of uncertainty models to real-world problems was addressed at ECSQARU 2005 by a special session devoted to s- cessful industrial applications, organized by Rudolf Kruse. Both invited lectures and papers of the special session contribute to this volume. On the whole, the programme of the conference provided a broad, rich and up-to-date perspective of the current high-level research in the area which is re?ected in the contents of this volume. IwouldliketowarmlythankthemembersoftheProgramCommitteeandthe additional referees for their valuable work, the invited speakers and the invited session organizer.