Automated Theorem Proving

by Wolfgang Bibel

Overview

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 project 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.

Product Details

ISBN-13:	9783528085209
Publisher:	Vieweg+Teubner Verlag
Publication date:	01/01/1982
Edition description:	1982
Pages:	292
Product dimensions:	6.69(w) x 9.61(h) x 0.03(d)
Language:	German

Table of Contents

I. Natural and formal logic.- 1. Logic abstracted from natural reasoning.- 2. Logical rules.- II. The connection method in propositional logic.- 1. The language of propositional logic.- 2. The semantics of propositional logic.- 3. A basic syntactic characterization of validity.- 4. The connection calculus.- 5. Consistency, completeness, and confluence.- 6. Algorithmic aspects.- 7. Exercises.- 8. Bibliographical and historical remarks.- III. The connection method in first-order logic.- 1. The language of first-order logic.- 2. The semantics of first-order logic.- 3. A basic syntactic characterization of validity.- 4. Transformation to normal form.- 5. Unification.- 6. The connection calculus.- 7. Algorithmic aspects.- 8. Exercises.- 9. Bibliographical and historical remarks.- IV. Variants and improvements.- 1. Resolution.- 2. Linear resolution and the connection method.- 3. On performance evaluation.- 4. Connection graph resolution and the connection method.- 5. A connection procedure for arbitrary matrices.- 6. Reduction, factorization, and tautological circuits.- 7. Logical calculi of natural deduction.- 8. An alternative for skolemization.- 9. Linear unification.- 10. Splitting by need.- 11. Summary and prospectus.- 12. Exercises.- 13. Bibliographical and historical remarks.- V. Applications and extensions.- 1. Structuring and processing knowledge.- 2. Programming and problem solving.- 3. The connection method with equality.- 4. Rewrite rules and generalized unification.- 5. The connection method with induction.- 6. The connection method in higher-order logic.- 7. Aspects of actual implementations.- 8. Omissions.- 9. Exercises.- 10. Bibliographical and historical remarks.- References.- List of Symbols.