The Resolution Calculus

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Publisher : Springer Science & Business Media
ISBN 13 : 3642606059
Total Pages : 307 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis The Resolution Calculus by : Alexander Leitsch

Download or read book The Resolution Calculus written by Alexander Leitsch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: The History of the Book In August 1992 the author had the opportunity to give a course on resolution theorem proving at the Summer School for Logic, Language, and Information in Essex. The challenge of this course (a total of five two-hour lectures) con sisted in the selection of the topics to be presented. Clearly the first selection has already been made by calling the course "resolution theorem proving" instead of "automated deduction" . In the latter discipline a remarkable body of knowledge has been created during the last 35 years, which hardly can be presented exhaustively, deeply and uniformly at the same time. In this situ ation one has to make a choice between a survey and a detailed presentation with a more limited scope. The author decided for the second alternative, but does not suggest that the other is less valuable. Today resolution is only one among several calculi in computational logic and automated reasoning. How ever, this does not imply that resolution is no longer up to date or its potential exhausted. Indeed the loss of the "monopoly" is compensated by new appli cations and new points of view. It was the purpose of the course mentioned above to present such new developments of resolution theory. Thus besides the traditional topics of completeness of refinements and redundancy, aspects of termination (resolution decision procedures) and of complexity are treated on an equal basis.

A Resolution Principle for a Logic with Restricted Quantifiers

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Publisher : Springer Science & Business Media
ISBN 13 : 9783540550341
Total Pages : 132 pages
Book Rating : 4.5/5 (53 download)

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Book Synopsis A Resolution Principle for a Logic with Restricted Quantifiers by : Hans-Jürgen Bürckert

Download or read book A Resolution Principle for a Logic with Restricted Quantifiers written by Hans-Jürgen Bürckert and published by Springer Science & Business Media. This book was released on 1991-12-11 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents foundations for a constrained logic scheme treating constraints as a very general form of restricted quantifiers. The constraints - or quantifier restrictions - are taken from a general constraint system consisting of constraint theory and a set of distinguished constraints. The book provides a calculus for this constrained logic based on a generalization of Robinson's resolution principle. Technically, the unification procedure of the resolution rule is replaced by suitable constraint-solving methods. The calculus is proven sound and complete for the refutation of sets of constrained clauses. Using a new and elegant generalization of the notion ofa ground instance, the proof technique is a straightforward adaptation of the classical proof technique. The author demonstrates that the constrained logic scheme can be instantiated by well-known sorted logics or equational theories and also by extensions of predicate logics with general equational constraints or concept description languages.

A Many-Sorted Calculus Based on Resolution and Paramodulation

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Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis A Many-Sorted Calculus Based on Resolution and Paramodulation by : Christoph Walther

Download or read book A Many-Sorted Calculus Based on Resolution and Paramodulation written by Christoph Walther and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Many-Sorted Calculus Based on Resolution and Paramodulation emphasizes the utilization of advantages and concepts of many-sorted logic for resolution and paramodulation based automated theorem proving. This book considers some first-order calculus that defines how theorems from given hypotheses by pure syntactic reasoning are obtained, shifting all the semantic and implicit argumentation to the syntactic and explicit level of formal first-order reasoning. This text discusses the efficiency of many-sorted reasoning, formal preliminaries for the RP- and ?RP-calculus, and many-sorted term rewriting and unification. The completeness and soundness of the ?RP-calculus, sort theorem, and automated theorem prover for the ?RP-calculus are also elaborated. This publication is a good source for students and researchers interested in many-sorted calculus.

A comparison of the resolution calculus and the connection method, and a new calculus generalizing both methods

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Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (633 download)

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Book Synopsis A comparison of the resolution calculus and the connection method, and a new calculus generalizing both methods by : Elmar Eder

Download or read book A comparison of the resolution calculus and the connection method, and a new calculus generalizing both methods written by Elmar Eder and published by . This book was released on 1989 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Language in Action

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Publisher : MIT Press
ISBN 13 : 9780262720243
Total Pages : 390 pages
Book Rating : 4.7/5 (22 download)

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Book Synopsis Language in Action by : Johan van Benthem

Download or read book Language in Action written by Johan van Benthem and published by MIT Press. This book was released on 1995 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Language in Action demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. Since its initial publication it has become the classic work in the foundations of categorial grammar. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature. Van Benthem presents the categorial processing of syntax and semantics as a central component in a more general dynamic logic of information flow, in tune with computational developments in artificial intelligence and cognitive science. Using the paradigm of categorial grammar, he describes the substructural logics driving the dynamics of natural language syntax and semantics. This is a general type-theoretic approach that lends itself easily to proof-theoretic and semantic studies in tandem with standard logic. The emphasis is on a broad landscape of substructural categorial logics and their proof-theoretical and semantic peculiarities. This provides a systematic theory for natural language understanding, admitting of significant mathematical results. Moreover, the theory makes possible dynamic interpretations that view natural languages as programming formalisms for various cognitive activities.

Symbolic Logic and Mechanical Theorem Proving

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Publisher : Academic Press
ISBN 13 : 0080917283
Total Pages : 349 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Symbolic Logic and Mechanical Theorem Proving by : Chin-Liang Chang

Download or read book Symbolic Logic and Mechanical Theorem Proving written by Chin-Liang Chang and published by Academic Press. This book was released on 2014-06-28 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.

The Calculus of Computation

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Publisher : Springer Science & Business Media
ISBN 13 : 3540741135
Total Pages : 375 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis The Calculus of Computation by : Aaron R. Bradley

Download or read book The Calculus of Computation written by Aaron R. Bradley and published by Springer Science & Business Media. This book was released on 2007-09-18 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written with graduate and advanced undergraduate students in mind, this textbook introduces computational logic from the foundations of first-order logic to state-of-the-art decision procedures for arithmetic, data structures, and combination theories. The textbook also presents a logical approach to engineering correct software. Verification exercises are given to develop the reader's facility in specifying and verifying software using logic. The treatment of verification concludes with an introduction to the static analysis of software, an important component of modern verification systems. The final chapter outlines courses of further study.

Automated Deduction - CADE 28

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Publisher : Springer Nature
ISBN 13 : 3030798763
Total Pages : 655 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Automated Deduction - CADE 28 by : André Platzer

Download or read book Automated Deduction - CADE 28 written by André Platzer and published by Springer Nature. This book was released on 2021 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Logic for Computer Science

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Publisher : Courier Dover Publications
ISBN 13 : 0486780821
Total Pages : 532 pages
Book Rating : 4.4/5 (867 download)

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Book Synopsis Logic for Computer Science by : Jean H. Gallier

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.

Mathematical Logic for Computer Science

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Publisher : Springer Science & Business Media
ISBN 13 : 1447103351
Total Pages : 311 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Mathematical Logic for Computer Science by : Mordechai Ben-Ari

Download or read book Mathematical Logic for Computer Science written by Mordechai Ben-Ari and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a mathematics textbook with theorems and proofs. The choice of topics has been guided by the needs of computer science students. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and yet sufficiently elementary for undergraduates. In order to provide a balanced treatment of logic, tableaux are related to deductive proof systems. The book presents various logical systems and contains exercises. Still further, Prolog source code is available on an accompanying Web site. The author is an Associate Professor at the Department of Science Teaching, Weizmann Institute of Science.

Resolution of Curve and Surface Singularities in Characteristic Zero

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Publisher : Springer Science & Business Media
ISBN 13 : 1402020295
Total Pages : 506 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Resolution of Curve and Surface Singularities in Characteristic Zero by : K. Kiyek

Download or read book Resolution of Curve and Surface Singularities in Characteristic Zero written by K. Kiyek and published by Springer Science & Business Media. This book was released on 2012-09-11 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. •• . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it • To solve the problem, it is enough to consider a special kind of Cremona trans formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.

The Complexity of Resolution Procedures for Theorem Proving in the Propositional Calculus

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Publisher :
ISBN 13 :
Total Pages : 250 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis The Complexity of Resolution Procedures for Theorem Proving in the Propositional Calculus by : Zvi Galil

Download or read book The Complexity of Resolution Procedures for Theorem Proving in the Propositional Calculus written by Zvi Galil and published by . This book was released on 1975 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comparative study on the complexity of various procedures for proving that a set of clauses is contradictory is described. All the procedures either use the resolution rule in some form or are closely related to procedures which do. Among the precedures considered are resolution, regular resolution, Davis Putnam procedure, resolution with extension, bounded (and iterated bounded) resolution, enumeration procedures, and semantic trees. The results include exponential lower bounds for the run-time of most of the procedures, relations between the various procedures, and implications to the complexity of integer programming routines.

A Many-Sorted Calculus Based on Resolution and Paramodulation

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Publisher : Morgan Kaufmann
ISBN 13 : 1483258939
Total Pages : 169 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis A Many-Sorted Calculus Based on Resolution and Paramodulation by : Christoph Walther

Download or read book A Many-Sorted Calculus Based on Resolution and Paramodulation written by Christoph Walther and published by Morgan Kaufmann. This book was released on 2014-07-10 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Many-Sorted Calculus Based on Resolution and Paramodulation emphasizes the utilization of advantages and concepts of many-sorted logic for resolution and paramodulation based automated theorem proving. This book considers some first-order calculus that defines how theorems from given hypotheses by pure syntactic reasoning are obtained, shifting all the semantic and implicit argumentation to the syntactic and explicit level of formal first-order reasoning. This text discusses the efficiency of many-sorted reasoning, formal preliminaries for the RP- and ?RP-calculus, and many-sorted term rewriting and unification. The completeness and soundness of the ?RP-calculus, sort theorem, and automated theorem prover for the ?RP-calculus are also elaborated. This publication is a good source for students and researchers interested in many-sorted calculus.

A Resolution Calculus Giving Definite Answers

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Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (17 download)

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Book Synopsis A Resolution Calculus Giving Definite Answers by : Ulf R. Schmerl

Download or read book A Resolution Calculus Giving Definite Answers written by Ulf R. Schmerl and published by . This book was released on 1991 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

First-Order Logic and Automated Theorem Proving

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Publisher : Springer Science & Business Media
ISBN 13 : 1468403575
Total Pages : 258 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis First-Order Logic and Automated Theorem Proving by : Melvin Fitting

Download or read book First-Order Logic and Automated Theorem Proving written by Melvin Fitting and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many kinds of books on formal logic. Some have philosophers as their intended audience, some mathematicians, some computer scientists. Although there is a common core to all such books they will be very dif ferent in emphasis, methods, and even appearance. This book is intended for computer scientists. But even this is not precise. Within computer sci ence formal logic turns up in a number of areas, from program verification to logic programming to artificial intelligence. This book is intended for computer scientists interested in automated theorem proving in classical logic. To be more precise yet, it is essentially a theoretical treatment, not a how-to book, although how-to issues are not neglected. This does not mean, of course, that the book will be of no interest to philosophers or mathematicians. It does contain a thorough presentation of formal logic and many proof techniques, and as such it contains all the material one would expect to find in a course in formal logic covering completeness but not incompleteness issues. The first item to be addressed is, what are we talking about and why are we interested in it. We are primarily talking about truth as used in mathematical discourse, and our interest in it is, or should be, self-evident. Truth is a semantic concept, so we begin with models and their properties. These are used to define our subject.

Introduction to Mathematical Logic and Resolution Principle

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Publisher : Alpha Science International, Limited
ISBN 13 : 9781842655665
Total Pages : 0 pages
Book Rating : 4.6/5 (556 download)

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Book Synopsis Introduction to Mathematical Logic and Resolution Principle by : Guo-Jun Wang

Download or read book Introduction to Mathematical Logic and Resolution Principle written by Guo-Jun Wang and published by Alpha Science International, Limited. This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Mathematical Logic Resolution Principle, Second Edition, in nine chapters, discusses Boolean algebra theory, propositional calculus and predicated calculus theory, resolution principle theory and the latest theory of multivalue logic. The book also includes supplement or alternations on the proof of the completion of K in first-order system, concerning Quantitative Logic.

From Logic to Logic Programming

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Publisher : MIT Press
ISBN 13 : 9780262041423
Total Pages : 240 pages
Book Rating : 4.0/5 (414 download)

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Book Synopsis From Logic to Logic Programming by : Kees Doets

Download or read book From Logic to Logic Programming written by Kees Doets and published by MIT Press. This book was released on 1994 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This mathematically oriented introduction to the theory of logic programming presents a systematic exposition of the resolution method for propositional, first-order, and Horn- clause logics, together with an analysis of the semantic aspects of the method. It is through the inference rule of resolution that both proofs and computations can be manipulated on computers, and this book contains elegant versions and proofs of the fundamental theorems and lemmas in the proof theory of logic programming. Advanced topics such as recursive complexity and negation as failure and its semantics are covered, and streamlined setups for SLD- and SLDNF-resolution are described. No other book treats this material in such detail and with such sophistication. Doets provides a novel approach to resolution that is applied to the first-order case and the case of (positive) logic programs. In contrast to the usual approach, the concept of a resolvent is defined nonconstructively, without recourse to the concept of unification, allowing the soundness and completeness proofs to be carried out in a more economic way. Other new material includes computability results dealing with analytical hierarchy, results on infinite derivations and an exposition on general logic programs using 3-valued logic.