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Proof Theory and Automated Deduction

Author : Jean Goubault-Larrecq

Publisher : Springer Science & Business Media

Page : 448 pages

File Size : 19,44 MB

Release : 2001-11-30

Category : Computers

ISBN : 9781402003684

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Book Description

Interest in computer applications has led to a new attitude to applied logic in which researchers tailor a logic in the same way they define a computer language. In response to this attitude, this text for undergraduate and graduate students discusses major algorithmic methodologies, and tableaux and resolution methods. The authors focus on first-order logic, the use of proof theory, and the computer application of automated searches for proofs of mathematical propositions. Annotation copyrighted by Book News, Inc., Portland, OR



Goal-Directed Proof Theory

Author : Dov M. Gabbay

Publisher : Springer Science & Business Media

Page : 282 pages

File Size : 35,45 MB

Release : 2000-08-31

Category : Philosophy

ISBN : 9780792364733

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Book Description

Goal Directed Proof Theory presents a uniform and coherent methodology for automated deduction in non-classical logics, the relevance of which to computer science is now widely acknowledged. The methodology is based on goal-directed provability. It is a generalization of the logic programming style of deduction, and it is particularly favourable for proof search. The methodology is applied for the first time in a uniform way to a wide range of non-classical systems, covering intuitionistic, intermediate, modal and substructural logics. The book can also be used as an introduction to these logical systems form a procedural perspective. Readership: Computer scientists, mathematicians and philosophers, and anyone interested in the automation of reasoning based on non-classical logics. The book is suitable for self study, its only prerequisite being some elementary knowledge of logic and proof theory.



Proof Theory of Modal Logic

Author : Heinrich Wansing

Publisher : Springer Science & Business Media

Page : 334 pages

File Size : 45,45 MB

Release : 1996-10-31

Category : Computers

ISBN : 9780792341208

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Book Description

This volume deals with formal, mechanizable reasoning in modal logics, that is, logics of necessity, possibility, belief, time computations etc. It is therefore of immense interest for various interrelated disciplines such as philosophy, AI, computer science, logic, cognitive science and linguistics. The book consists of 15 original research papers, divided into three parts. The first part contains papers which give a profound description of powerful proof-theoretic methods as applied to the normal modal logic S4. Part II is concerned with a number of generalizations of the standard proof-theoretic formats, while the third part presents new and important results on semantics-based proof systems for modal logic.



Proof Theory for Fuzzy Logics

Author : George Metcalfe

Publisher : Springer Science & Business Media

Page : 279 pages

File Size : 15,74 MB

Release : 2008-11-27

Category : Mathematics

ISBN : 1402094094

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Book Description

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.



Handbook of Proof Theory

Author : S.R. Buss

Publisher : Elsevier

Page : 823 pages

File Size : 37,29 MB

Release : 1998-07-09

Category : Mathematics

ISBN : 0080533183

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Book Description

This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth.The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.



Logic for Computer Science

Author : Jean H. Gallier

Publisher : Courier Dover Publications

Page : 532 pages

File Size : 49,16 MB

Release : 2015-06-18

Category : Mathematics

ISBN : 0486780821

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Book Description

This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.



Deduction

Author : W. Bibel

Publisher :

Page : 264 pages

File Size : 25,70 MB

Release : 1993

Category : Computers

ISBN :

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Book Description

Deduction: Automated Logic presents the broad topic of automated deductive reasoning in a concise and comprehensive manner. This book features broad coverage of deductive methods on the level of propositional and first-order logic, the strategic aspects of automated deduction, the applications of deduction mechanisms to a range of different areas, and their realization in concrete systems. This book can be used both by readers seeking a broad survey of the area, and by those requiring a reference for more detailed analysis on individual topics. It is an invaluable text for students of artificial intelligence, cognitive science, and theorum- proving at the advanced undergraduate and graduate level. Intended for readers who wish to become familiar with the area as a whole, or with selected topics, in a relatively short time Serves as a reference book for consultation on individual topics Contains one of the most comprehensive collections of different deduction mechanisms which has ever appeared in a single book, all presented in a uniform framework Contains extensive references and exercises Thoroughly cross-referenced



Basic Proof Theory

Author : A. S. Troelstra

Publisher : Cambridge University Press

Page : 436 pages

File Size : 26,2 MB

Release : 2000-07-27

Category : Computers

ISBN : 9780521779111

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Book Description

This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.



Automated Deduction - CADE 28

Author : André Platzer

Publisher : Springer Nature

Page : 655 pages

File Size : 21,57 MB

Release : 2021

Category : Artificial intelligence

ISBN : 3030798763

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Book Description

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions.



Structural Proof Theory

Author : Sara Negri

Publisher : Cambridge University Press

Page : 279 pages

File Size : 48,40 MB

Release : 2008-07-10

Category : Mathematics

ISBN : 9780521068420

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Book Description

A concise introduction to structural proof theory, a branch of logic studying the general structure of logical and mathematical proofs.