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Algebraic Foundations of Many-Valued Reasoning

Algebraic Foundations of Many-Valued Reasoning PDF Author: R.L. Cignoli
Publisher: Springer Science & Business Media
ISBN: 9401594805
Category : Mathematics
Languages : en
Pages : 238

Book Description
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 Foundations of Many-Valued Reasoning

Algebraic Foundations of Many-Valued Reasoning PDF Author: R.L. Cignoli
Publisher: Springer Science & Business Media
ISBN: 9401594805
Category : Mathematics
Languages : en
Pages : 238

Book Description
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

Algebraic and Proof-theoretic Aspects of Non-classical Logics PDF Author: S. Aguzzoli
Publisher: Springer
ISBN: 3540759395
Category : Computers
Languages : en
Pages : 317

Book Description
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

Fuzzy Sets, Logics and Reasoning about Knowledge PDF Author: Didier Dubois
Publisher: Springer Science & Business Media
ISBN: 9401716528
Category : Philosophy
Languages : en
Pages : 421

Book Description
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.

The Many Valued and Nonmonotonic Turn in Logic

The Many Valued and Nonmonotonic Turn in Logic PDF Author: Dov M. Gabbay
Publisher: Elsevier
ISBN: 008054939X
Category : Mathematics
Languages : en
Pages : 691

Book Description
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.

Beyond Two: Theory and Applications of Multiple-Valued Logic

Beyond Two: Theory and Applications of Multiple-Valued Logic PDF Author: Melvin Fitting
Publisher: Physica
ISBN: 3790817694
Category : Mathematics
Languages : en
Pages : 374

Book Description
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.

Formal Methods: Foundations and Applications

Formal Methods: Foundations and Applications PDF Author: Leila Ribeiro
Publisher: Springer
ISBN: 3319498150
Category : Computers
Languages : en
Pages : 253

Book Description
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.

Reasoning in Quantum Theory

Reasoning in Quantum Theory PDF Author: Maria Luisa Dalla Chiara
Publisher: Springer Science & Business Media
ISBN: 9781402019784
Category : Mathematics
Languages : en
Pages : 326

Book Description
"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.

Paraconsistent semantics for Pavelka style fuzzy sentential logic

Paraconsistent semantics for Pavelka style fuzzy sentential logic PDF Author: E. Turunen
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 15

Book Description
The root of this work is on the one hand in Belnap’s four valued paraconsistent logic, and on the other hand on Pavelka’s papers further developed by Turunen.

Handbook of Philosophical Logic

Handbook of Philosophical Logic PDF Author: Dov M. Gabbay
Publisher: Springer Science & Business Media
ISBN: 940170452X
Category : Philosophy
Languages : en
Pages : 417

Book Description
It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as weIl as to consumers of logic in many applied areas. The main logic artiele in the Encyelopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good. ! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook 0/ Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook 0/ Philosophical Logic, published 1983-1989 came at a fortunate at the evolution of logic. This was the time when logic temporal junction was gaining ground in computer science and artificial intelligence cireles. These areas were under increasing commercial pressure to provide devices which help andjor replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.

On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory

On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory PDF Author: Susanne Saminger-Platz
Publisher: Springer
ISBN: 3319288083
Category : Technology & Engineering
Languages : en
Pages : 275

Book Description
The book is a collection of contributions by leading experts, developed around traditional themes discussed at the annual Linz Seminars on Fuzzy Set Theory. The different chapters have been written by former PhD students, colleagues, co-authors and friends of Peter Klement, a leading researcher and the organizer of the Linz Seminars on Fuzzy Set Theory. The book also includes advanced findings on topics inspired by Klement’s research activities, concerning copulas, measures and integrals, as well as aggregation problems. Some of the chapters reflect personal views and controversial aspects of traditional topics, while others deal with deep mathematical theories, such as the algebraic and logical foundations of fuzzy set theory and fuzzy logic. Originally thought as an homage to Peter Klement, the book also represents an advanced reference guide to the mathematical theories related to fuzzy logic and fuzzy set theory with the potential to stimulate important discussions on new research directions in the field.