First Order Logic And Automated Theorem Proving
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Logic For Computer Science
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Author : Jean H. Gallier
language : en
Publisher: Courier Dover Publications
Release Date : 2015-06-18
Logic For Computer Science written by Jean H. Gallier and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-18 with Mathematics categories.
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.
First Order Logic And Automated Theorem Proving
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Author : Melvin Fitting
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
First Order Logic And Automated Theorem Proving written by Melvin Fitting and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
There are many kinds of books on formal logic. Some have philosophers as their intended audience, some mathematicians, some computer scien tists. Although there is a common core to all such books, they will be very different in emphasis, methods, and even appearance. This book is intended for computer scientists. But even this is not precise. Within computer science formal logic turns up in a number of areas, from pro gram verification to logic programming to artificial intelligence. This book is intended for computer scientists interested in automated theo rem 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.
First Order Logic And Automated Theorem Proving
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Author : Department of Mathematics and Computer Science Lehman College Melvin Fitting
language : en
Publisher:
Release Date : 2012
First Order Logic And Automated Theorem Proving written by Department of Mathematics and Computer Science Lehman College Melvin Fitting and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Artificial intelligence categories.
This monograph on classical logic presents fundamental concepts and results in a rigorous mathematical style. Applications to automated theorem proving are considered and usable programs in Prolog are provided. This material can be used both as a first text in formal logic and as an introduction to automation issues, and is intended for those interested in computer science and mathematics at the beginning graduate level. The book begins with propositional logic, then treats first-order logic, and finally, first-order logic with equality. In each case the initial presentation is semantic: Boolean valuations for propositional logic, models for first-order logic, and normal models when equality is added. This defines the intended subjects independently of a particular choice of proof mechanism. Then many kinds of proof procedures are introduced: tableau, resolution, natural deduction, Gentzen sequent and axiom systems. Completeness issues are centered in a model existence theorem, which permits the coverage of a variety of proof procedures without repetition of detail. In addition, results such as compactness, interpolation, and the Beth definability theorem are easily established.Implementations of tableau theorem provers are given in Prolog, and resolution is left as a project for the student.
Concrete Semantics
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Author : Tobias Nipkow
language : en
Publisher: Springer
Release Date : 2014-12-03
Concrete Semantics written by Tobias Nipkow and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-03 with Computers categories.
Part I of this book is a practical introduction to working with the Isabelle proof assistant. It teaches you how to write functional programs and inductive definitions and how to prove properties about them in Isabelle’s structured proof language. Part II is an introduction to the semantics of imperative languages with an emphasis on applications like compilers and program analysers. The distinguishing feature is that all the mathematics has been formalised in Isabelle and much of it is executable. Part I focusses on the details of proofs in Isabelle; Part II can be read even without familiarity with Isabelle’s proof language, all proofs are described in detail but informally. The book teaches the reader the art of precise logical reasoning and the practical use of a proof assistant as a surgical tool for formal proofs about computer science artefacts. In this sense it represents a formal approach to computer science, not just semantics. The Isabelle formalisation, including the proofs and accompanying slides, are freely available online, and the book is suitable for graduate students, advanced undergraduate students, and researchers in theoretical computer science and logic.
Extensions Of First Order Logic
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Author : Maria Manzano
language : en
Publisher: Cambridge University Press
Release Date : 1996-03-29
Extensions Of First Order Logic written by Maria Manzano and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-03-29 with Computers categories.
An introduction to many-sorted logic as an extension of first-order logic.
Handbook Of Practical Logic And Automated Reasoning
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Author : John Harrison
language : en
Publisher: Cambridge University Press
Release Date : 2009-03-12
Handbook Of Practical Logic And Automated Reasoning written by John Harrison and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-12 with Computers categories.
A one-stop reference, self-contained, with theoretical topics presented in conjunction with implementations for which code is supplied.
Modelling Puzzles In First Order Logic
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Author : Adrian Groza
language : en
Publisher: Springer Nature
Release Date : 2021-10-26
Modelling Puzzles In First Order Logic written by Adrian Groza and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-26 with Mathematics categories.
Keeping students involved and actively learning is challenging. Instructors in computer science are aware of the cognitive value of modelling puzzles and often use logical puzzles as an efficient pedagogical instrument to engage students and develop problem-solving skills. This unique book is a comprehensive resource that offers teachers and students fun activities to teach and learn logic. It provides new, complete, and running formalisation in Propositional and First Order Logic for over 130 logical puzzles, including Sudoku-like puzzles, zebra-like puzzles, island of truth, lady and tigers, grid puzzles, strange numbers, or self-reference puzzles. Solving puzzles with theorem provers can be an effective cognitive incentive to motivate students to learn logic. They will find a ready-to-use format which illustrates how to model each puzzle, provides running implementations, and explains each solution. This concise and easy-to-follow textbook is a much-needed support tool for students willing to explore beyond the introductory level of learning logic and lecturers looking for examples to heighten student engagement in their computer science courses.
Proof Theory And Automated Deduction
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Author : Jean Goubault-Larrecq
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-30
Proof Theory And Automated Deduction written by Jean Goubault-Larrecq and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-30 with Computers categories.
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
Automated Theorem Proving In Software Engineering
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Author : Johann M. Schumann
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Automated Theorem Proving In Software Engineering written by Johann M. Schumann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Computers categories.
Growing demands for the quality, safety, and security of software can only be satisfied by the rigorous application of formal methods during software design. This book methodically investigates the potential of first-order logic automated theorem provers for applications in software engineering. Illustrated by complete case studies on protocol verification, verification of security protocols, and logic-based software reuse, this book provides techniques for assessing the prover's capabilities and for selecting and developing an appropriate interface architecture.
Automated Theorem Proving
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Author : Wolfgang Bibel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Automated Theorem Proving written by Wolfgang Bibel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Computers categories.
Since both the coments and the structure of the book appeared to be successful, only minor changes were made. In particular, some recent work in ATP has been incorporated so that the book continues to reflect the state of the art in the field. The most significant change is in the quality of the layout including the removal of a number of inaccuracies and typing errors. R. Caferra, E. Eder, F. van der Linden, and J. Muller have caught vanous minor errors. P. Haddawy and S.T. Pope have provided many stilistic improvements of the English text. Last not least, A. Bentrup and W. Fischer have produced the beautiful layout. The extensive work of typesetting was financally supported within ESPRIT pro ject 415. Munchen, September 1986 W. Bibel PREFACE Among the dreams of mankind is the one dealing with the mechanization of human thought. As the world today has become so complex that humans apparently fail to manage it properly with their intellectual gifts, the realization of this dream might be regarded even as something like a necessity. On the other hand, the incredi ble advances in computer technology let it appear as a real possibility.