Restricting backtracking in connection calculi

AI Communications

Volumn 23, Issue 2-3, 2010, Pages 159-182

  Otten, Jens ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

Author keywords

Automated theorem proving; Connection calculus; LeanCoP; Restricted backtracking

Indexed keywords

AUTOMATED THEOREM PROVER; AUTOMATED THEOREM PROVING; COMPACT PROGRAMS; GOAL-ORIENTED; PROOF SEARCH; THEOREM PROVERS; TIME COMPLEXITY;

AUTOMATA THEORY; AUTOMATION; BIOMINERALIZATION; CALCULATIONS; OPEN SYSTEMS; PATHOLOGY; PROBLEM SOLVING; PROLOG (PROGRAMMING LANGUAGE);

THEOREM PROVING;

EID: 77950216905     PISSN: 09217126     EISSN: None     Source Type: Journal    
DOI: 10.3233/AIC-2010-0464     Document Type: Conference Paper

References (45)

1. P. Baumgartner, N. Eisinger and U. Furbach, A confluent connection calculus, in: 16th CADE, H. Ganzinger, ed., LNAI, Vol.1632, Springer, Heidelberg, 1999, pp. 329-343.
2. B. Beckert and J. Posegga, leanTAP: lean, tableau-based theorem proving, in: 12th CADE, A. Bundy, ed., LNAI, Vol.814, Springer, Heidelberg, 1994, pp. 793-797.
3. W. Bibel, Matings in matrices, Communications of the ACM 26 (1983), 844-852.
4. W. Bibel, Automated Theorem Proving, Vieweg, Wiesbaden, 1987.
5. W. Clocksin and C. Mellish, Programming in Prolog, Springer, Heidelberg, 1981.
6. S.A. Cook, The complexity of theorem-proving procedures, in: Proceedings of 3rd Annual ACM Symposium on the Theory of Computing, Shaker Heights, OH, USA, 1971, pp. 151-158.
7. E. Eder, Relative Complexities of First Order Calculi, Vieweg, Wiesbaden, 1992.
8. M.C. Fitting, First-order Logic and Automated Theorem Proving, Springer, Heidelberg, 1990.
9. G. Gentzen, Untersuchungen über das logische Schließen, Mathematische Zeitschrift 39 (1935), 176-210, 405-431.
10. R. Hähnle, Tableaux and related methods, in: Handbook of Automated Reasoning, A. Robinson and A. Voronkov, eds, Elsevier, Amsterdam, 2001, pp. 100-178.
11. R. Hähnle and P. Schmitt, The liberalized -rule in free variable semantic tableaux, Journal of Automated Reasoning 13 (1994), 211-221.
12. K. Korovin, iProver - An instantiation-based theorem prover for first-order logic (system description), in: IJCAR'2008, A. Armando, P. Baumgartner and G. Dowek, eds, LNCS, Vol.5195, Springer, Heidelberg, 2008, pp. 292-298.
13. C. Kreitz and J. Otten, Connection-based theorem proving in classical and non-classical logics, Journal of Universal Computer Science 5 (1999), 88-112.
14. S.-J. Lee and D. Plaisted, Eliminating duplicates with the hyper-linking strategy, Journal of Automated Reasoning 9 (1992), 25-42.
15. R. Letz, Properties and relations of tableau and connection calculi, in: Intellectics and Computational Logic, S. Hölldobler, ed., Kluwer, Amsterdam, 2000, pp. 245-261.
16. R. Letz, J. Schumann, S. Bayerl and W. Bibel, SETHEO: a high-performance theorem prover, Journal of Automated Reasoning 8 (1992), 183-212.
17. R. Letz, K. Mayr and C. Goller, Controlled integration of the cut rule into connection tableaux calculi, Journal of Automated Reasoning 13 (1994), 297-337.
18. R. Letz and G. Stenz, Model elimination and connection tableau procedures, in: Handbook of Automated Reasoning, A. Robinson and A. Voronkov, eds, Elsevier, Amsterdam, 2001, pp. 2015-2114.
19. D. Loveland, Mechanical theorem proving by model elimination, Journal of the ACM 15 (1968), 236-251.
20. A. Martelli and U. Montanari, An efficient unification algorithm, ACM Transactions on Programming Languages and Systems (TOPLAS) 4 (1982), 258-282.
21. W. McCune, OTTER 2.0. in: CADE-10, M.E. Stickel, ed., LNCS, Vol.449, Springer, Heidelberg, 1990, pp. 663-664.
22. W. McCune, OTTER 3.0 reference manual and guide, Technical Report ANL-94/6, Argonne National Laboratory, 1994.
23. W. McCune, Release of Prover9, in: Mile High Conference on Quasigroups, Loops and Nonassociative Systems, Denver, 2005.
24. A. Nonnengart and C. Weidenbach, Computing small clause normal forms, in: Handbook of Automated Reasoning, A. Robinson and A. Voronkov, eds, Elsevier, Amsterdam, 2001, pp. 335-367.
25. J. Otten, ileanTAP: an intuitionistic theorem prover, in: TABLEAUX'97, D. Galmiche, ed., LNAI, Vol.1227, Springer, Heidelberg, 1997, pp. 307-312.
26. J. Otten, Clausal connection-based theorem proving in intuitionistic first-order logic, in: TABLEAUX'2005, B. Beckert, ed., LNAI, Vol.3702, Springer, Heidelberg, 2005, pp. 245-261.
27. J. Otten, leanCoP 2.0 and ileanCoP 1.2: high performance lean theorem proving in classical and intuitionistic logic, in: IJCAR'2008, A. Armando, P. Baumgartner and G. Dowek, eds, LNCS, Vol.5195, Springer, Heidelberg, 2008, pp. 283-291.
28. J. Otten and W. Bibel, leanCoP: lean connection-based theorem proving, Journal of Symbolic Computation 36 (2003), 139-161.
29. J. Otten and C. Kreitz, T-string-unification: unifying prefixes in non-classical proof methods, in: TABLEAUX'96, P. Miglioli, U. Moscato, D. Mundici and M. Ornaghi, eds, LNAI, Vol.1071, Springer, Heidelberg, 1996, pp. 244-260.
30. J. Otten and C. Kreitz, A uniform proof procedure for classical and non-classical logics, in: KI-96: Advances in Artificial Intelligence, G. Görz and S. Hölldobler, eds, LNAI, Vol.1137, Springer, Heidelberg, 1996, pp. 307-319.
31. D. Plaisted and S. Greenbaum, A structure-preserving clause form translation, Journal of Symbolic Computation 2 (1986), 293-304.
32. T. Raths and J. Otten, randoCoP: randomizing the proof search order in the connection calculus, in: IJCAR'08 Workshop on Practical Aspects of Automated Reasoning (PAAR-2008), Sydney, Australia, B. Konev, R. Schmidt and S. Schulz, eds, CEUR Workshop Proceedings, 2008, pp. 94-102.
33. T. Raths, J. Otten and C. Kreitz, The ILTP problem library for intuitionistic logic, Journal of Automated Reasoning 38 (2007), 261-271.
34. J.A. Robinson, A machine-oriented logic based on the resolution principle, Journal of the ACM 12(1) (1965), 23-41.
35. S. Schulz, E - a Brainiac theorem prover, AI Communications 15(2) (2002), 111-126.
36. R. Statman, Intuitionistic propositional logic is polynomialspace complete, Theoretical Computer Science 9 (1979), 67-72.
37. M. Stickel, A Prolog technology theorem prover: implementation by an extended Prolog compiler, Journal of Automated Reasoning 4 (1988), 353-380.
38. M. Stickel, A Prolog technology theorem prover: a new exposition and implementation in Prolog, Theoretical Computer Science 104 (1992), 109-128.
39. G. Sutcliffe, The 4th IJCAR automated theorem proving system competition, AI Communications 22 (2009), 59-72.
40. G. Sutcliffe and C. Suttner, The TPTP problem library - CNF release v1.2.1, Journal of Automated Reasoning 21 (1998), 177-203.
41. G. Sutcliffe and C. Suttner, Evaluating general purpose automated theorem proving systems, Artificial Intelligence 131(1,2) (2001), 39-54.
42. A. Riazanov and A. Voronkov, The design and implementation of Vampire, AI Communications 15(2,3) (2002), 91-110.
43. C. Weidenbach, R. Schmidt, T. Hillenbrand, R. Rusev and D. Topic, System description: SPASS version 3.0, in: CADE- 21, F. Pfenning, ed., LNCS, Vol.4603, Springer, Heidelberg, 2007, pp. 514-520.
44. A. Waaler, Connections in nonclassical logics, in: Handbook of Automated Reasoning, A. Robinson and A. Voronkov, eds, Elsevier, Amsterdam, 2001, pp. 1487-1578.
45. L. Wallen, Automated Deduction in Nonclassical Logic, MIT Press, Cambridge, 1990.