Proof Theory And Automated Deduction

Author : Jean Goubault-Larrecq
Publisher : Springer Science & Business Media
ISBN 13 : 9781402003684
Total Pages : 448 pages
Book Rating : 4.84/5 ( download)

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Download or read book Proof Theory and Automated Deduction written by Jean Goubault-Larrecq and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Jean Goubault-Larrecq
Publisher : Springer
ISBN 13 : 9789401139816
Total Pages : 0 pages
Book Rating : 4.14/5 ( download)

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Download or read book Proof Theory and Automated Deduction written by Jean Goubault-Larrecq and published by Springer. This book was released on 2001-12-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last twenty years have witnessed an accelerated development of pure and ap plied logic, particularly in response to the urgent needs of computer science. Many traditional logicians have developed interest in applications and in parallel a new generation of researchers in logic has arisen from the computer science community. A new attitude to applied logic has evolved, where researchers tailor a logic for their own use in the same way they define a computer language, and where auto mated deduction for the logic and its fragments is as important as the logic itself. In such a climate there is a need to emphasise algorithmic logic methodologies alongside any individual logics. Thus the tableaux method or the resolution method are as central to todays discipline of logic as classical logic or intuitionistic logic are. From this point of view, J. Goubault and I. Mackie's book on Proof Theory and Automated Deduction is most welcome. It covers major algorithmic methodolo gies as well as a variety of logical systems. It gives a wide overview for the ap plied consumer of logic while at the same time remains relatively elementary for the beginning student. A decade ago I put forward my view that a logical system should be presented as a point in a grid. One coordinate is its philosphy, motivation, its accepted theorems and its required non-theorems. The other coordinate is the algorithmic methodol ogy and execution chosen for its effective presentation. Together these two aspects constitute a 'logic'.

Author : Heinrich Wansing
Publisher : Springer Science & Business Media
ISBN 13 : 9401727988
Total Pages : 317 pages
Book Rating : 4.83/5 ( download)

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Download or read book Proof Theory of Modal Logic written by Heinrich Wansing and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.

Author : Dov M. Gabbay
Publisher : Springer Science & Business Media
ISBN 13 : 9780792364733
Total Pages : 282 pages
Book Rating : 4.32/5 ( download)

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Download or read book Goal-Directed Proof Theory written by Dov M. Gabbay and published by Springer Science & Business Media. This book was released on 2000-08-31 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : S.R. Buss
Publisher : Elsevier
ISBN 13 : 0080533183
Total Pages : 823 pages
Book Rating : 4.86/5 ( download)

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Download or read book Handbook of Proof Theory written by S.R. Buss and published by Elsevier. This book was released on 1998-07-09 with total page 823 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Dov M. Gabbay
Publisher : Springer Science & Business Media
ISBN 13 : 9401717133
Total Pages : 273 pages
Book Rating : 4.37/5 ( download)

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Download or read book Goal-Directed Proof Theory written by Dov M. Gabbay and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : George Metcalfe
Publisher : Springer Science & Business Media
ISBN 13 : 1402094094
Total Pages : 279 pages
Book Rating : 4.95/5 ( download)

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Download or read book Proof Theory for Fuzzy Logics written by George Metcalfe and published by Springer Science & Business Media. This book was released on 2008-11-27 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : David Delahaye
Publisher :
ISBN 13 : 9781848901667
Total Pages : 250 pages
Book Rating : 4.66/5 ( download)

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Download or read book All about Proofs, Proofs for All written by David Delahaye and published by . This book was released on 2015-01-22 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of new and improved proof systems, proof formats and proof search methods is one of the most essential goals of Logic. But what is a proof? What makes a proof better than another? How can a proof be found efficiently? How can a proof be used? Logicians from different communities usually provide radically different answers to such questions. Their principles may be folklore within their own communities but are often unknown to outsiders. This book provides a snapshot of the current state of the art in proof search and proof production as implemented in contemporary automated reasoning tools such as SAT-solvers, SMT-solvers, first-order and higher-order automated theorem provers and proof assistants. Furthermore, various trends in proof theory, such as the calculus of inductive constructions, deduction modulo, deep inference, foundational proof certificates and cut-elimination, are surveyed; and applications of formal proofs are illustrated in the areas of cryptography, verification and mathematical proof mining. Experts in these topics were invited to present tutorials about proofs during the Vienna Summer of Logic and the chapters in this book reflect their tutorials. Therefore, each chapter is intended to be accessible not only to experts but also to novice researchers from all fields of Logic.

Author : A. S. Troelstra
Publisher : Cambridge University Press
ISBN 13 : 9780521779111
Total Pages : 436 pages
Book Rating : 4.11/5 ( download)

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Download or read book Basic Proof Theory written by A. S. Troelstra and published by Cambridge University Press. This book was released on 2000-07-27 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jean H. Gallier
Publisher : Courier Dover Publications
ISBN 13 : 0486780821
Total Pages : 532 pages
Book Rating : 4.25/5 ( download)

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Download or read book Logic for Computer Science written by Jean H. Gallier and published by Courier Dover Publications. This book was released on 2015-06-18 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.