Abstract

A Prolog technology theorem prover (PTTP) is an extension of Prolog that is complete for the full first-order predicate calculus. It differs from Prolog in its use of unification with the occurs check for soundness, the model-elimination reduction rule that is added to Prolog inferences to make the inference system complete, and depth-first iterative-deepening search instead of unbounded depth-first search to make the search strategy complete. A Prolog technology theorem prover has been implemented by an extended Prolog-to-LISP compiler that supports these additional features. It is capable of proving theorems in the full first-order predicate calculus at a rate of thousands of inferences per second. 1 This is a revised and expanded version of a paper presented at the 8th International Conference on Automated Deduction, Oxford, England, July 1986, and is to appear in Journal of Automated Reasoning. This research was supported by the Defense Advanced Research Projects Agency under Co...

Citations

503	Principles of Artificial Intelligence - Nilsson - 1982
473	An Abstract Prolog instruction set - Warren - 1983
327	Depth-first iterative-deepening: An optimal admissible tree search - Korf - 1985
261	Symbolic Logic and Mechanical Theorem Proving - Chang, Lee - 1973
211	Automated Theorem Proving: A Logical Basis - Loveland - 1987
102	Theorem proving via general matings - Andrews - 1981
90	Linear resolution with selection function - Kowaiski, Kuehner - 1971
75	Prolog and infinite trees - Colmerauer - 1982
37	A prolog technology theorem prover - Stickel - 1988
30	The sharing of structures in theorem-proving programs - Boyer, Moore - 1972
30	Refutation graphs - Shostak - 1976
27	Non-Horn Clause Logic Programming Without Contrapositives - Plaisted - 1988
27	A Parallel Implementation of Iterative-Deepening-A - Rao, Kumar, et al.
26	A simplified format for the model elimination procedure - Loveland - 1969
19	An implementation of the model elimination proof procedure - Fleisig, Loveland, et al. - 1974
13	An analysis of consecutively bounded depth-first search with applications in automated deduction - Stickel, Tyson - 1985
12	A simplified problem reduction format - Plaisted - 1982
11	Resolution, Refinements, and Search Strategies: A Comparative Study - Wilson, Minker - 1976
10	Describing Prolog by Its Interpretation and Compilation - Cohen - 1985
10	Logic machine architecture: kernel functions - Lusk, McCune, et al. - 1982
10	The linked inference principle, II: The user’s viewpoint - Wos, Veroff, et al. - 1984
5	Automated Theorem Proving. Friedr. Vieweg - Bibel - 1982
5	Paths to high-performance automated theorem proving - Butler, Lusk, et al. - 1986
5	The Markgraf Karl Refutation Procedure - Raph - 1984
4	A hole in goal trees: Some guidance from resolution theory - Loveland, Stickel - 1973
3	Logic machine architecture: inference mechanisms - Lusk, McCune, et al. - 1982
3	A portable environment for research in automated reasoning - Lusk, Overbeek - 1984
2	A Prolog-like interpreter for non-Horn clauses - Eder - 1976
2	Experimental tests of resolution based theorem-proving strategies - Lawrence, Starkey - 1974
2	Study of automatic theorem-proving programs - Reboh, Raphael, et al. - 1972
2	An experiment in programming with full first-order logic - Umrigar, Pitchumani - 1985
1	PROTHEO/2: sequential PROLOGlike theorem prover based on the connection method - Bayerl, Kurfess, et al. - 1986
1	MKRP: a performance test by working mathematicians - Burckert, Wang, et al. - 1983
1	Automated theorem proving: Mapping logic into AI - Loveland - 1986
1	Nonclausal Logic Programming - Malachi - 1986
1	Chess 4.5---the Northwestern University University chess program - Slate, Atkin - 1977
1	QUEST: a non-clausal theorem proving system - Wilkins - 1973