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First-Order Logic and Automated Theorem Proving
This graduate-level text presents fundamental concepts and results of classical logic in a rigorous mathematical style. Applications to automated theorem proving are considered and usable Prolog programs provided. It will serve both as a first text in formal logic and an introduction to automation issues for students in computer science or mathematics.
The book treats propositional logic, first-order logic, and first-order logic with equality. In each case the initial presentation is semantic, to define the intended subjects independently of the choice of proof mechanism. Then many kinds of proof procedure are introduced. Results such as completeness, compactness, and interpolation are established, and theorem provers are implemented in Prolog. This new edition includes material on AE calculus, Herbrand's Theorem, Gentzen's Theorem, and related topics.
The book treats propositional logic, first-order logic, and first-order logic with equality. In each case the initial presentation is semantic, to define the intended subjects independently of the choice of proof mechanism. Then many kinds of proof procedure are introduced. Results such as completeness, compactness, and interpolation are established, and theorem provers are implemented in Prolog. This new edition includes material on AE calculus, Herbrand's Theorem, Gentzen's Theorem, and related topics.
- GenresLogicPhilosophy
242 pages, Hardcover
First published April 28, 1990
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About the author
Melvin Fitting
23 books3 followersMelvin "Mel" Fitting (born January 24, 1942) is a logician with special interests in philosophical logic and tableau proof systems. He was a Professor at City University of New York, Lehman College and the Graduate Center from 1968 to 2013. At the Graduate Center he was in the departments of Computer Science, Philosophy, and Mathematics, and at Lehman College he was in the department of Mathematics and Computer Science. He is now Professor emeritus.
Fitting was born in Troy, New York. His undergraduate degree is from Rensselaer Polytechnic Institute, and his doctorate is from Yeshiva University, both in mathematics. His thesis advisor was Raymond Smullyan.
In June 2012 Melvin Fitting was given the Herbrand Award by CADE, for distinguished contributions to automated deduction.
A loose motivation for much of Melvin Fitting's work can be formulated succinctly as follows. There are many logics. Our principles of reasoning vary with context and subject matter. Multiplicity is one of the glories of modern formal logic. The common thread tying logics together is a concern for what can be said (syntax), what that means (semantics), and relationships between the two. A philosophical position that can be embodied in a formal logic has been shown to be coherent, not correct. Logic is a tool, not a master, but it is an enjoyable tool to use
Fitting was born in Troy, New York. His undergraduate degree is from Rensselaer Polytechnic Institute, and his doctorate is from Yeshiva University, both in mathematics. His thesis advisor was Raymond Smullyan.
In June 2012 Melvin Fitting was given the Herbrand Award by CADE, for distinguished contributions to automated deduction.
A loose motivation for much of Melvin Fitting's work can be formulated succinctly as follows. There are many logics. Our principles of reasoning vary with context and subject matter. Multiplicity is one of the glories of modern formal logic. The common thread tying logics together is a concern for what can be said (syntax), what that means (semantics), and relationships between the two. A philosophical position that can be embodied in a formal logic has been shown to be coherent, not correct. Logic is a tool, not a master, but it is an enjoyable tool to use
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