Principles Of Automated Theorem Proving
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| Author | : David A. Duffy |
| Publisher | : |
| Total Pages | : 272 |
| Release | : 1991-09-09 |
| Genre | : Computers |
| ISBN | : |
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 | : Wen-tsün Wu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 308 |
| Release | : 1994-04-14 |
| Genre | : Computers |
| ISBN | : 9783211825068 |
This book is a translation of Professor Wu’s seminal Chinese book of 1984 on Automated Geometric Theorem Proving. The translation was done by his former student Dongming Wang jointly with Xiaofan Jin so that authenticity is guaranteed. Meanwhile, automated geometric theorem proving based on Wu’s method of characteristic sets has become one of the fundamental, practically successful, methods in this area that has drastically enhanced the scope of what is computationally tractable in automated theorem proving. This book is a source book for students and researchers who want to study both the intuitive first ideas behind the method and the formal details together with many examples.
| Author | : Johann M. Schumann |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 252 |
| Release | : 2013-06-29 |
| Genre | : Computers |
| ISBN | : 3662226464 |
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 | : Monty Newborn |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 250 |
| Release | : 2000-12-15 |
| Genre | : Mathematics |
| ISBN | : 9780387950754 |
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.
| Author | : Melvin Fitting |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 258 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1468403575 |
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 | : Monty Newborn |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 244 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461300894 |
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.
| Author | : D.W. Loveland |
| Publisher | : Elsevier |
| Total Pages | : 419 |
| Release | : 2016-08-19 |
| Genre | : Computers |
| ISBN | : 1483296776 |
Automated Theorem Proving: A Logical Basis
| Author | : Jean H. Gallier |
| Publisher | : Courier Dover Publications |
| Total Pages | : 532 |
| Release | : 2015-06-18 |
| Genre | : Mathematics |
| ISBN | : 0486780821 |
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 | : W. W. Bledsoe |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 372 |
| Release | : 1984 |
| Genre | : Mathematics |
| ISBN | : 082185027X |
| Author | : Wolfgang Bibel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 434 |
| Release | : 2013-03-09 |
| Genre | : Philosophy |
| ISBN | : 940170435X |
1. BASIC CONCEPTS OF INTERACTIVE THEOREM PROVING Interactive Theorem Proving ultimately aims at the construction of powerful reasoning tools that let us (computer scientists) prove things we cannot prove without the tools, and the tools cannot prove without us. Interaction typi cally is needed, for example, to direct and control the reasoning, to speculate or generalize strategic lemmas, and sometimes simply because the conjec ture to be proved does not hold. In software verification, for example, correct versions of specifications and programs typically are obtained only after a number of failed proof attempts and subsequent error corrections. Different interactive theorem provers may actually look quite different: They may support different logics (first-or higher-order, logics of programs, type theory etc.), may be generic or special-purpose tools, or may be tar geted to different applications. Nevertheless, they share common concepts and paradigms (e.g. architectural design, tactics, tactical reasoning etc.). The aim of this chapter is to describe the common concepts, design principles, and basic requirements of interactive theorem provers, and to explore the band width of variations. Having a 'person in the loop', strongly influences the design of the proof tool: proofs must remain comprehensible, - proof rules must be high-level and human-oriented, - persistent proof presentation and visualization becomes very important.
