Walter A Carnielli's Books

Paraconsistency

The Logical Way to the Inconsistent

By: Walter Alexandr Carnielli

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Paraconsistency

The Logical Way to the Inconsistent

By: Walter Alexandr Carnielli

This book presents a study on the foundations of a large class of paraconsistent logics from the point of view of the logics of formal inconsistency. It also presents several systems of non-standard logics with paraconsistent features.

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Page Count

582

Publisher

CRC Press

Published Date

ISBN 10

0203910133

ISBN 13

9780203910139

Computability

Computable Functions, Logic, and the Foundations of Mathematics

By: Richard L Epstein,Walter A Carnielli

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Computability

Computable Functions, Logic, and the Foundations of Mathematics

By: Richard L Epstein,Walter A Carnielli

Now in a new edition!--the classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal logic to give a full development of Gödel's incompleteness theorems. Part IV considers the significance of the technical work with a discussion of Church's Thesis and readings on the foundations of mathematics. This new edition contains the timeline "Computability and Undecidability" as well as the essay "On mathematics".

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Page Count

382

Publisher

Advanced Reasoning Forum

Published Date

ISBN 10

0981550738

ISBN 13

9780981550732

Paraconsistent Logic: Consistency, Contradiction and Negation

By: Walter Carnielli,Marcelo Esteban Coniglio

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Paraconsistent Logic: Consistency, Contradiction and Negation

By: Walter Carnielli,Marcelo Esteban Coniglio

This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical theory and offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative achievements in contemporary logic, with deep roots in philosophical questions involving negation and consistency This book offers an invaluable introduction to a topic of central importance in logic and philosophy. It discusses (i) the history of paraconsistent logic; (ii) language, negation, contradiction, consistency and inconsistency; (iii) logics of formal inconsistency (LFIs) and the main paraconsistent propositional systems; (iv) many-valued companions, possible-translations semantics and non-deterministic semantics; (v) paraconsistent modal logics; (vi) first-order paraconsistent logics; (vii) applications to information processing, databases and quantum computation; and (viii) applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning.

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Page Count

417

Publisher

Springer

Published Date

ISBN 10

3319332058

ISBN 13

9783319332055

Modalities and Multimodalities

By: Walter Carnielli,Claudio Pizzi

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Modalities and Multimodalities

By: Walter Carnielli,Claudio Pizzi

In the last two decades modal logic has undergone an explosive growth, to thepointthatacompletebibliographyofthisbranchoflogic,supposingthat someone were capable to compile it, would ?ll itself a ponderous volume. What is impressive in the growth of modal logic has not been so much the quick accumulation of results but the richness of its thematic dev- opments. In the 1960s, when Kripke semantics gave new credibility to the logic of modalities? which was already known and appreciated in the Ancient and Medieval times? no one could have foreseen that in a short time modal logic would become a lively source of ideas and methods for analytical philosophers,historians of philosophy,linguists, epistemologists and computer scientists. The aim which oriented the composition of this book was not to write a new manual of modal logic (there are a lot of excellent textbooks on the market, and the expert reader will realize how much we bene?ted from manyofthem)buttoo?ertoeveryreader,evenwithnospeci?cbackground in logic, a conceptually linear path in the labyrinth of the current panorama of modal logic. The notion which in our opinion looked suitable to work as a compass in this enterprise was the notion of multimodality, or, more speci?cally, the basic idea of grounding systems on languages admitting more than one primitive modal operator.

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Page Count

304

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402085907

ISBN 13

9781402085901

Analysis and Synthesis of Logics

How to Cut and Paste Reasoning Systems

By: Walter Carnielli,Marcelo Coniglio,Dov M. Gabbay,Paula Gouveia,Cristina Sernadas

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Analysis and Synthesis of Logics

How to Cut and Paste Reasoning Systems

By: Walter Carnielli,Marcelo Coniglio,Dov M. Gabbay,Paula Gouveia,Cristina Sernadas

Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature. The issue of preservation of properties is addressed.

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Page Count

612

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402067828

ISBN 13

9781402067822

New Trends in Hopf Algebra Theory

Proceedings of the Colloquium on Quantum Groups and Hopf Algebras, La Falda, Sierras de Córdoba, Argentina, August 9-13, 1999

By: Nicolás Andruskiewitsch,Walter Ricardo Ferrer Santos,Hans-Jürgen Schneider

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New Trends in Hopf Algebra Theory

Proceedings of the Colloquium on Quantum Groups and Hopf Algebras, La Falda, Sierras de Córdoba, Argentina, August 9-13, 1999

By: Nicolás Andruskiewitsch,Walter Ricardo Ferrer Santos,Hans-Jürgen Schneider

This volume presents the proceedings from the Colloquium on Quantum Groups and Hopf Algebras held in Cordoba (Argentina) in 1999. The meeting brought together researchers who discussed recent developments in Hopf algebras, one of the most important being the influence of quantum groups. Articles offer introductory expositions and surveys on topics of current interest that, to date, have not been available in the current literature. Surveys are included on characteristics of Hopf algebras and their generalizations, biFrobenius algebras, braided Hopf algebras, inner actions and Galois theory, face algebras, and infinitesimal Hopf algebras. The following topics are also covered: existence of integrals, classification of semisimple and pointed Hopf algebras, *-Hopf algebras, dendriform algebras, etc. Non-classical topics are also included, reflecting its applications both inside and outside the theory.

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Page Count

376

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821821261

ISBN 13

9780821821268

Computability

Computable Functions, Logic, and the Foundations of Mathematics

By: Richard L Epstein,Walter A Carnielli

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Computability

Computable Functions, Logic, and the Foundations of Mathematics

By: Richard L Epstein,Walter A Carnielli

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Page Count

382

Publisher

Advanced Reasoning Forum

Published Date

ISBN 10

0981550738

ISBN 13

9780981550732

Analysis and Synthesis of Logics

How to Cut and Paste Reasoning Systems

By: Walter Carnielli,Marcelo Coniglio,Dov M. Gabbay,Paula Gouveia,Cristina Sernadas

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Analysis and Synthesis of Logics

How to Cut and Paste Reasoning Systems

By: Walter Carnielli,Marcelo Coniglio,Dov M. Gabbay,Paula Gouveia,Cristina Sernadas

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Page Count

612

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402067828

ISBN 13

9781402067822

Paraconsistent Logic: Consistency, Contradiction and Negation

By: Walter Carnielli,Marcelo Esteban Coniglio

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Paraconsistent Logic: Consistency, Contradiction and Negation

By: Walter Carnielli,Marcelo Esteban Coniglio

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Page Count

417

Publisher

Springer

Published Date

ISBN 10

3319332058

ISBN 13

9783319332055

Methods and Applications of Mathematical Logic

Proceedings of the VII Latin American Symposium on Mathematical Logic Held July 29-August 2, 1985

By: Walter Alexandre Carnielli,Luiz Paulo de Alcantara,Sociedade Brasileira Matemtica

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Methods and Applications of Mathematical Logic

Proceedings of the VII Latin American Symposium on Mathematical Logic Held July 29-August 2, 1985

By: Walter Alexandre Carnielli,Luiz Paulo de Alcantara,Sociedade Brasileira Matemtica

This volume constitutes the proceedings of the Seventh Latin American Symposium on Mathematical Logic, held July 29-August 2, 1985, at the University of Campinas in Brazil. Striking a balance between breadth of scope and depth of results, the papers in this collection range over a variety of topics in classical and non-classical logics. The book provides readers with an introduction to the active lines of research in mathematical logic and particularly emphasizes the connections to other fields, especially philosophy, computer science, and probability theory. The potential applicability of the mathematical methods studied in logic has become important because various areas--such as software engineering, mathematical biology, physics, and linguistics--now appear to need mathematical methods of the kind studied in logic.

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Page Count

268

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821854089

ISBN 13

9780821854082

Book's by Walter A Carnielli

Paraconsistency

Paraconsistency

Computability

Computability

Paraconsistent Logic: Consistency, Contradiction and Negation

Paraconsistent Logic: Consistency, Contradiction and Negation

Modalities and Multimodalities

Modalities and Multimodalities

Analysis and Synthesis of Logics

Analysis and Synthesis of Logics

New Trends in Hopf Algebra Theory

New Trends in Hopf Algebra Theory

Computability

Computability

Analysis and Synthesis of Logics

Analysis and Synthesis of Logics

Paraconsistent Logic: Consistency, Contradiction and Negation

Paraconsistent Logic: Consistency, Contradiction and Negation

Methods and Applications of Mathematical Logic

Methods and Applications of Mathematical Logic

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