[PDF] First Order Logic And Automated Theorem Proving eBook

Author : Melvin Fitting
Publisher : Springer Science & Business Media
Page : 258 pages
File Size : 29,90 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1468403575

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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.

Author : Melvin Fitting
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 36,26 MB
Release : 1996
Category : Computers
ISBN : 9780387945934

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Propositional logic - Semantic tableaux and resolution - Other propositional proof procedures - First-order logic - First-order proof procedures - Implementing tableaux and resolution - Further first-order features - Equality.

Author : Department of Mathematics and Computer Science Lehman College Melvin Fitting
Publisher :
Page : 0 pages
File Size : 28,5 MB
Release : 2012
Category : Artificial intelligence
ISBN : 9781468403596

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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.

Author : D.W. Loveland
Publisher : Elsevier
Page : 419 pages
File Size : 26,90 MB
Release : 2016-08-19
Category : Computers
ISBN : 1483296776

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Automated Theorem Proving: A Logical Basis

Author : John Harrison
Publisher : Cambridge University Press
Page : 703 pages
File Size : 34,42 MB
Release : 2009-03-12
Category : Computers
ISBN : 0521899575

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A one-stop reference, self-contained, with theoretical topics presented in conjunction with implementations for which code is supplied.

Author : Jean H. Gallier
Publisher : Courier Dover Publications
Page : 532 pages
File Size : 49,77 MB
Release : 2015-06-18
Category : Mathematics
ISBN : 0486780821

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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.

Author : Johann M. Schumann
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 32,69 MB
Release : 2013-06-29
Category : Computers
ISBN : 3662226464

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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.

Author : Arnaldo Pérez Castaño
Publisher : Apress
Page : 701 pages
File Size : 38,75 MB
Release : 2018-05-23
Category : Computers
ISBN : 1484233573

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Discover how all levels Artificial Intelligence (AI) can be present in the most unimaginable scenarios of ordinary lives. This book explores subjects such as neural networks, agents, multi agent systems, supervised learning, and unsupervised learning. These and other topics will be addressed with real world examples, so you can learn fundamental concepts with AI solutions and apply them to your own projects. People tend to talk about AI as something mystical and unrelated to their ordinary life. Practical Artificial Intelligence provides simple explanations and hands on instructions. Rather than focusing on theory and overly scientific language, this book will enable practitioners of all levels to not only learn about AI but implement its practical uses. What You’ll Learn Understand agents and multi agents and how they are incorporated Relate machine learning to real-world problems and see what it means to you Apply supervised and unsupervised learning techniques and methods in the real world Implement reinforcement learning, game programming, simulation, and neural networks Who This Book Is For Computer science students, professionals, and hobbyists interested in AI and its applications.

Author : David A. Duffy
Publisher :
Page : 272 pages
File Size : 36,60 MB
Release : 1991-09-09
Category : Computers
ISBN :

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An overview of ATP techniques for the non-specialist, it discusses all the main approaches to proof: resolution, natural deduction, sequentzen, and the connection calculi. Also discusses strategies for their application and three major implemented systems. Looks in detail at the new field of ``inductionless induction'' and brings out its relationship to the classical approach to proof by induction.

Author : Monty Newborn
Publisher : Springer Science & Business Media
Page : 250 pages
File Size : 39,98 MB
Release : 2000-12-15
Category : Mathematics
ISBN : 9780387950754

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This text and software package introduces readers to automated theorem proving, while providing two approaches implemented as easy-to-use programs. These are semantic-tree theorem proving and resolution-refutation theorem proving. The early chapters introduce first-order predicate calculus, well-formed formulae, and their transformation to clauses. Then the author goes on to show how the two methods work and provides numerous examples for readers to try their hand at theorem-proving experiments. Each chapter comes with exercises designed to familiarise the readers with the ideas and with the software, and answers to many of the problems.