A Proof Procedure Using Connection Graphs

Journal of the ACM (JACM)

Volumn 22, Issue 4, 1975, Pages 572-595

  Kowalski, Robert ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

connection graph; logic; programaning; theorem proving

Indexed keywords

MATHEMATICAL TECHNIQUES - GRAPH THEORY;

MATHEMATICAL PROGRAMMING;

EID: 0016565757     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/321906.321919     Document Type: Article

References (38)

1. Andrews, P B. Resolution with merging. J ACM 15, 3 (July 1968), 367-381.
2. Bledsoe, W. W. Splitting and reduction heuristics in automatic theorem-proving Artif. Intel 2 (1971), 55-77.
3. Bledsoe, W. W., Boyer, R. S., and Henneman, W H Computer proofs of limit theorems. Artif. Intel 3 (1972), 27-60.
4. Bledsoe, W. W., and Bruell, P. A man-machine theorem-proving system. Third International Joint Conf on Artificial Intelligence, 1973, pp. 36-65.
5. Boyer, R. S., and Moore, J S. The sharing of structure in theorem-proving programs. In Machine Intelligence 7, B. Meltzer and D Michie, Eds., Edinburgh U. Press, Edinburgh, Scotland, 1972, pp. 101-116.
6. Colmerauer, A. Les systemes-Q ou un formalisme pour analyser et synthetiser des phrases sur ordinateur Pub. interne No 43, Dep d'informatique, Université de Montréal, Montréal, Canada, 1970.
7. Colmerauer, A Cancellation systems Personal communication, 1972.
8. Colmerauer, A., Kanoui, H., Pasero, R, and Roussel, P. Un systeme de communication homme-machine en Francais. Rapport préliminaire, Groupe de Researche en Intelligence Artificielle, Université d'Aix Marseille, Luminy, 1972.
9. van Emden, M H. First-order predicate logic as a high-level program language. Memo No. MIP-R-106, U. of Edinburgh, Edinburgh, Scotland, 1974.
10. Gelperin, D Deletion-directed search in resolution-based proof procedures Advance Papers of the Third International Joint Conf on Artificial Intelligence, Stanford U., Stanford, Calif., 1973, pp 47-50.
11. Geoffrion, A. M., and Marsten, R. E. Integer programming algorithms. A framework and state-of-the-art survey. Manag. Sci. 18 (1972), 465-491.
12. Hayes, P. J. Computation and deduction. Proc. 2nd MFCS Symposium, Czechoslovak Academy of Sciences, 1973, pp. 105-118.
13. Hewitt, C. PLANNER A language for proving theorems in robots. Proc of the International Joint Conf. on Artificial Intelligence, Washington D. C, 1969, pp 295-301.
14. Kowalski, R, and Hayes, P. J. Semantic trees in automatic theorem-proving. In Machine Intelligence 4, B. Meltzer and D. Michie, Eds, Edinburgh U. Press, Edinburgh, Scotland, 1968, pp. 87-101.
15. Kowalski, R. The case for using equality axioms in automatic demonstration. Proc. IRIA Symposium on Automatic Demonstration (Lecture Notes in Mathematics, No. 125), Springer-Verlag, Berlin, Heidelberg, New York, 1968, pp. 112-127.
16. Kowalski, R. Studies in the completeness and efficiency of theorem-proving by resolution. Ph.D Th., U. of Edinburgh, Edinburgh, Scotland, 1970.
17. Kowalski, R. And-or graphs, theorem-proving graphs and bi-directional search In Machine Intelligence 7, B Meltzer and D Michie, Eds., Edinburgh U Press, Edinburgh, Scotland, 1972, pp 167-194.
18. Kowalski, R An improved theorem-proving system for first-order logic D C.L. Memo No. 65, U of Edinburgh, Edinburgh, Scotland, 1973.
19. Kowalski, R Predicate logic as programming language. Proc IFIP Cong. 1974, Stockholm, North-Holland Pub. Co, Amsterdam, pp. 569-574.
20. Kowalski, R Logic for problem-solving D.C.L. Memo No. 75, U. of Edinburgh, Edinburgh, Scotland, 1974.
21. Kowalski, R., and Kuehner, D. Linear resolution with selection function. Artif. Intel 2 (1971), 227-260.
22. Loveland, D. A linear format for resolution Proc. IRIA Symp on Automatic Demonstration, Versailles, France, Springer-Verlag, Berlin, Heidelberg, New York, 1970, pp. 147-162.
23. Luckham, D. Some tree-paring strategies for theorem-proving. In Machine Intelligence 3, D Michie, Ed, Edinburgh U Press, Edinburgh, Scotland, 1968, pp. 95-112.
24. Luckham, D. Refinement theorems in resolution theory. Proc. IRIA Symp on Automatic Demonstration, Versailles, France, Springer-Verlag, Berlin, Heidelberg, New York, 1970, pp. 162-190.
25. Meltzer, B. Some notes on resolution strategies. In Machine Intelligence 3, D. Michie, Ed, Edinburgh U. Press, Edinburgh, Scotland, 1968, pp 71-75.
26. Minker, J., and Van Der Brug, G. J. Representations of the language recognition problem for a theorem-prover. Tech. Rep. TR-199, Computer Science Center, U of Maryland, College Park, Md., 1972.
27. Nilsson, N. J. Problem solving methods in artificial intelligence. McGraw-Hill, New York, 1971.
28. Pohl, I. Bi-directional search. In Machine Intelligence 7, B. Meltzer and D. Michie, Eds., Edinburgh U. Press, Edinburgh, Scotland, 1972, pp 127-140.
29. Reiter, R. The predicate elimination strategy in theorem-proving Proc. 2nd ACM Symp on the Theory of Computing, Northampton, Mass, 1970, pp 180-183.
30. Robinson, J. A. A machine-oriented logic based on the resolution principle J. ACM 12, 1 (Jan 1965), 23-41.
31. Robinson, J. A. Automatic deduction with hyper-resolution. Int. J. of Computer Math. 1 (1965), 227-234.
32. Robinson, J A A review of automatic theorem-proving Proc. of Symposia in Applied Mathematics, Vol 19, Amer. Math. Soc, Providence, R. I., 1967, pp. 1-18.
33. Stillman, R. B. The concept of weak substitution in theorem-proving. J ACM 20, 4 (Oct. 1973), 648-667.
34. Wilkins, D E. QUEST. A non-clausal theorem-proving system. M.Sc. Th, U of Essex, Col-ehester, Essex, England, 1973.
35. Winston, P. H. The MIT Robot. In Machine Intelligence 7, B. Meltzer and D. Michie, Eds., Edinburgh U. Press, Edinburgh, Scotland, 1972, pp 431-463.
36. Wos, L., Carson, D. F., and Robinson, G A The unit preference strategy in theorem-proving Proc. AFIPS 1964 FJCC, Vol 26, Spartan Books, New York, pp 616-621.
37. Wos, L., Robinson, G. A., and Carson, D. F. Efficiency and completeness of the set of support strategy in theorem proving J ACM 12, 4 (Oct 1965), 536-541.
38. Zamov, N K, and Sharonov, V I. On a class of strategies which can be used to establish decidability by the resolution principle (In Russian). Issled po konstruktivnoye matematikye i matematicheskoie logikye III 16 (1969), 54-64 (National Lending Library, Russian Translating Program 5857, Boston Spa, Yorkshire), England).