Clause trees: A tool for understanding and implementing resolution in automated reasoning

Artificial Intelligence

Volumn 92, Issue 1-2, 1997, Pages 25-89

  Horton, J D ^a   Spencer, Bruce ^a  

^a UNIVERSITY OF NEW BRUNSWICK   (Canada)

Author keywords

Automated theorem proving; Minimality; Proof procedures; Redundancy

Indexed keywords

DATA STRUCTURES; FORMAL LOGIC; SET THEORY; THEOREM PROVING; TREES (MATHEMATICS);

CLAUSE TREES;

ARTIFICIAL INTELLIGENCE;

EID: 0031142303     PISSN: 00043702     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0004-3702(96)00046-x     Document Type: Article

References (40)

1. P.B. Andrews, Refutations by matings, IEEE Trans. Comput. 25 (1976) 801-807.
2. O.L. Astrachan and D.W. Loveland, METEORs: high performance theorem provers using model elimination, in: R.S. Boyer, ed., Automated Reasoning: Essays in Honor of Woody Bledsoe (Kluwer Academic Publishers, Dordrecht, 1991).
3. O.L. Astrachan and M. Stickel, Caching and lemmaizing in model elimination theorem provers, in: D. Kapur, ed., Automated Deduction - CADE-11, Saratoga Springs, Lecture Notes in Artificial Intelligence. 607 (Springer, Berlin, 1992) 224-238.
4. W. Bibel, Short proof of the pigeonhole formulas based on the connection method, J. Autom. Reasoning 6 (1990) 287-297.
5. C.-L. Chang and R.C.-T. Lee, Symbolic Logic and Mechanical Theorem Proving (Academic Press, New York, 1973).
6. V. Chvátal and E. Szemerédi, Many hard examples for resolution, J. ACM 35 (1988) 759-768.
7. S.A. Cook and R.A. Reckhow, The relative efficiency of prepositional proof systems, J. Symbolic Logic 44 (1979) 36-50.
8. N. Eisinger, Completeness, Confluence and Related Properties of Clause Graph Resolution, Research Notes in Artificial Intelligence (Pittman, London/Morgan Kaufmann, San Mateo, CA, 1991).
9. A. Haken, The intractability of resolution, Theoret. Comput. Sci. 39 (1985) 297-308.
10. F. Harary, Graph Theory (Addison-Wesley, Reading, MA, 1969).
11. J.D. Horton and D. Sharpe, private communication.
12. J.D. Horton and B. Spencer, A top down algorithm to find only minimal clause trees, in: L. Dreschler-Fischer and S. Pribbenow, eds., KI-95 Activities: Workshops, Posters, Demos, Bielefeld (Gesellschaft für Informatik, Bonn, 1995) 79-80.
13. J.D. Horton and B. Spencer, Reducing search with minimal clause trees, Tech. Rept. TR95-099, Faculty of Computer Science, University of New Brunswick, Fredericton, NB, Canada (1995).
14. J.D. Horton and B. Spencer, Bottom-up procedures for minimal clause trees, Tech. Rept. TR96-101, Faculty of Computer Science, University of New Brunswick, Fredericton, NB, Canada (1996).
15. R. Hynes, The disequality strategy in theorem proving, undergraduate thesis, Faculty of Computer Science, University of New Brunswick, Fredericton, NB, Canada (1995).
16. R. Kowalski and D. Kuehner, Linear resolution with selection function, Artif. Intell. 2 (1971) 227-260.
17. R. Letz, K. Mayr and C. Goller, Controlled integration of the cut rule into connection tableau calculi, J. Autom. Reasoning 13 (1994) 297-337.
18. R. Letz, J. Shumann, S. Bayerl and W. Bibel, SETHEO: a high-performance theorem prover, J. Autom. Reasoning 8 (1992) 183-212.
19. J. Lobo, J. Miner and A. Rajasekar, Fundamentals of Disjunctive Logic Programming (MIT Press, Boston, 1992).
20. D.W. Loveland, Mechanical theorem proving by model elimination, J. ACM 15 (1968) 236-251.
21. D.W. Loveland, Automated Theorem Proving: A Logical Basis (North-Holland, Amsterdam, 1978).
22. W.W. McCune, OTTER 2.0 users guide, Tech. Rept. ANL-90/9, Mathematics and Computer Science Division, Argonne National Laboratories, Argonne, IL (1990).
23. J. Minker and G. Zanon, An extension to linear resolution with selection function, Inform. Process. Lett. 14 (1982) 191-194.
24. N.V. Murray and E. Rosenthal, Dissolution: making paths vanish, J. ACM 40 (1993) 504-535.
25. R. Reiter, Two results on ordering for resolution with merging and linear format, J. ACM 18 (1971) 630-646.
26. J.A. Robinson, A machine-oriented logic based on the resolution principle, J. ACM 12 (1965) 23-41.
27. D. Sharpe, AllPaths theorem prover, Undergraduate thesis, Faculty of Computer Science, University of New Brunswick, Fredericton, NB, Canada (1995).
28. D. Sharpe, Backwards basic factoring: a pessimistic analog of basic factoring, in: J. Stewman, ed., Proceedings of the Ninth Florida Artificial Intelligence Research Symposium, Key West, FL (1996) 459-462.
29. R.E. Shostak, Refutation graphs, Artif. Intell. 7 (1976) 51-64.
30. B. Spencer, Linear resolution with ordered clauses, in: J. Lobo, D. Loveland and A. Rajasekar, eds., Proceedings ILPS Workshop - Disjunctive Logic Programming, San Diego, CA (1991).
31. B. Spencer, The ordered clause restriction of model elimination and SLI resolution, in: D. Miller, ed., Proceedings International Symposium of Logic Programming, Vancouver, BC (1993) 678.
32. B. Spencer, Avoiding duplicate proofs with the foothold refinement, Ann. Math. Artif. Intell. 12 (1994) 117-140.
33. B. Spencer, J.D. Horton and K. Francis, Experiments with the ALPOC theorem prover, Tech. Rept. TR95-094, Faculty of Computer Science, University of New Brunswick, Fredericton, NB, Canada (1995).
34. M. Stickel, A Prolog technology theorem prover: implementation by an extended Prolog compiler. J. Autom. Reasoning 1 (1988) 353-380.
35. M. Stickel, A Prolog technology theorem prover: a new exposition and implementation in Prolog, Theor. Comput. Sci. 104 (1992) 109-128.
36. M. Stickel, personal communication.
37. M. Stickel, Upside-down meta-interpretation of the model elimination theorem-proving procedure for deduction and abduction, J. Autom. Reasoning 13 (1994) 189-210.
38. G. Sutcliffe, C. Suttner and T. Yemenis, The TPTP problem library, in: D. Kapur, ed., Automated Deduction - CADE-12, Nancy, Lecture Notes in Artificial Intelligence 814 (Springer, Berlin, 1994) 252-266.
39. G.S. Tseitin, On the complexity of derivations in prepositional calculus, in: A.O. Stisenko, ed., Studies in Mathematics and Mathematical Logic Part II (Consultants Bureau, New York, 1970) 115-125.
40. L. Wos, Automated Reasoning: 33 Basic Research Problems (Prentice-Hall, Englewood Cliffs, NJ, 1988).