A proof theoretical approach to default reasoning I: Tableaux for default logic

Journal of Logic and Computation

Volumn 6, Issue 2, 1996, Pages 205-231

  Amati, Gianni ^a   Aiello, Luigia Carlucci ^b   Gabbay, Dov ^c   Pirri, Fiora ^b  

^a FONDAZIONE UGO BORDONI   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

^c IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Default systems; Modal logic; Tableau systems

Indexed keywords

EID: 0043128785     PISSN: 0955792X     EISSN: None     Source Type: Journal    
DOI: 10.1093/logcom/6.2.205     Document Type: Article

References (47)

1. G. Amati, L. Carlucci-Aiello and F. Pirri. Defaults as restrictions on Classical Hilbert-style proofs. Journal of Logic Language and Information, to appear.
2. P. Besnard. Deafult Logic. Springer-Verlag, Berlin, 1989.
3. P. Besnard, R. Quiniou and P. Quinton. A theorem-prover for a decidable subset of default logic. In Proceedings of the Fifth National Conference on Artificial Intelligence (AAAI-83), pp. 27-30. Morgan Kaufmann, San Mateo, CA, 1983.
4. G. Brewka. Cumulative default logic: in defence of nonmonotonic inference rules. Artificial Intelligence Journal, 50, 183-206, 1991.
5. M. R. B. Clarke and D. M. Gabbay. An intuitionistic basis for nonmonotonic reasoning. In Non-standard logics for automated reasoning, P. Smets, E. H. Mandami, D. Dubois, and H. Prade, eds, pp. 164-174. Academic Press, London, 1988.
6. M. Cadoli and M. Schaerf. A survey of complexity results for non-monotonie logics. Journal of Logic Programming, 17, 127-160, 1993.
7. J. P. Delgrande and W. K. Jackson. Default logic revisited. In Proceedings of the Second International Conference on the Principles of Knowledge Representation and Reasoning (KR-91), pp. 118-127. Morgan Kaufmann, San Mateo, CA, 1991.
8. P. Doherty and W. Lukaszewicz. Nm13, a non-monotonic logic with explicit default. Journal of Applied Non-Classical Logics, 2, 9-48, 1992.
9. D. Etherington. Formalizing nonmonotonic reasoning. Artificial Intelligence Journal, 31, 41-87, 1987.
10. D. Etherington. Reasoning with incomplete information. Morgan Kaufman, 1988.
11. M. Fitting. Proof Methods for Modal and Intuitionistic Logics. Reidel Publishing Company, Dordrecht, 1983.
12. M. Fitting. First Order Logic and Automated Theorem Proving. Springer-Verlag, New York, 1989.
13. C. Froidevaux and J. Mengin. Default logics: a unified view. Computational Intelligence, 1994, to appear.
14. D. M. Gabbay. Classical vs non classical logic. In Handbook of Logic in AI, vol. 2, D. M. Gabbay and C. Hogger, eds, Oxford University Press, 1993.
15. R. A. Guerreiro, M. A. Casanova and A. S. Hemerly. Contribution to a proof theory for generic defaults. In Proceedings of the Ninth European Conference on Artificial Intelligence (ECAI-90), pp. 213-218. Pitman, London, 1990.
16. M. Gelfond, V. Lifschitz, H. Przimusinska, and M. Truszczynski. Disjunctive defaults. In Proceedings of the Second International Conference on the Principles of Knowledge Representation and Reasoning (KR-91), pp. 230-237. Morgan Kaufmann, San Mateo, CA, 1991.
17. P. Gärdenfors and D. Makinson. Nonmonotonic inference based on expectations. Artificial Intelligence Journal, 65, 197-246, 1994.
18. L. Giordano and A. Martelli. On cumulative default reasoning. Artificial Intelligence Journal, 66, 161-180, 1994.
19. G. Gottlob and Z. Mingyi. Cumulative default logic: finite characterization, algorithms and complexity. Artificial Intelligence Journal, 69, 329-345, 1994.
20. G. Gottlob. Complexity results for non-monotonic logics. Journal of Logic and Computation, 2, 397-425, 1992.
21. U. Junker and G. Brewka. Handling partially ordered defaults in TMS. In Symbolic and Quantitative Approaches for Uncertainty, European Conference (ECSQAU), pp. 211-218. Springer-Verlag, Berlin, 1991.
22. U. Junker. A correct nonmonotonic ATMS. In Proceedings of the Eleventh International Joint Conference on Artificial Intelligence (IJCAI-89), pp. 1049-1053. Morgan Kaufmann, San Mateo, CA, 1989.
23. S. Kraus, D. Lehmann, and M. Magidor. Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence Journal, 44, 167-208, 1990.
24. H. Kautz and B. Selman. Hard problems for simple default logics. Artificial Intelligence Journal, 49, 243-279, 1991.
25. F. Levy. Computing extensions of default theories. In Symbolic and Quantitative Approaches for Uncertainty, European Conference (ECSQAU), pp. 219-226. Springer-Verlag, Berlin, 1991.
26. W. Lukaszewicz. Considerations on default logic. In Proceedings of the Nonmonotonic Reasoning Workshop, pp. 165-193. New Paltz, NY, 1984.
27. W. Lukaszewicz. Considerations on default logic: an alternative approach. Computational Intelligence, 4, 1-16, 1988.
28. W. Lukaszewicz. Nonmonotonic Reasoning: Formalization of Commonsense Reasoning. Ellis Horwood, New York, 1990.
29. C. MacNish. Hierarchical default logic. In Symbolic and Quantitative Approaches for Uncertainty, European Conference (ECSQAU), pp. 247-254, 1991.
30. D. Makinson. General theory of cumulative inference. In Proceedings of the 2nd International Workshop on Non-monotonic reasoning, pp. 1-18, 1988.
31. D. Makinson. General patterns in nonmonotonic reasoning. In Handbook of Logic in AI and Logic Programming: Nonmonotonic and Uncertain Reasoning, vol. 2, D. M. Gabbay, ed, Oxford University Press, Oxford, 1993.
32. D. Poole, R. Goebel, and R. Aleliunas. Theorist: a logical reasoning system for default and diagnosis. In The Knowledge Frontier, N. Cercone and G. Mc Calla, eds, pp. 331-352. Springer Verlag, 1987.
33. D. Poole. A logical system for default reasoning. In Proceedings of the Nonmonotonic Reasoning Workshop, pp. 373-384, 1984.
34. D. Poole. Representing knowledge for logic-based diagnosis. In Proceedings of the International Conference on Fifth Generation Computer Systems, pp. 1282-1289, 1988.
35. D. Poole. Explanation and prediction: an architecture for default and abductive reasoning. Computational Intelligence, 5, 97-110, 1989.
36. D. Poole. Normality and faults in logic-based diagnosis. In Proceedings of the Eleventh International Joint Conference on Artificial Intelligence (IJCAI-89), pp. 1304-1310, 1989.
37. D. Poole. What the lottery paradox tells us about default reasoning. In Proceedings of the 1st International Conference on Principles of Knowledge Representation and Reasoning (KR'89), pp. 333-340, 1989.
38. D. Poole. Compiling a default reasoning system into prolog. New Generation Computing, 9, 3-38, 1991.
39. C.H. Papadimitriou and M Sideri. Default theories that always have extensions. Artificial Intelligence Journal, 69, 348-357, 1994.
40. R. Reiter. A logic for default reasoning. Artificial Intelligence Journal, 13, 81-132, 1980.
41. R. Reiter. A theory of diagnosis from first principles. Artificial Intelligence Journal, 32, 57-96, 1987.
42. R. Rychlik. Some variations on default logic. In Proceedings of the Ninth National Conference on Artificial Intelligence (AAAI-91), pp. 183-188, 1991.
43. E. Sandewall. A functional approach to non-monotonic logic. Computational Intelligence, 1, 80-87, 1985.
44. C. Schwind. A tableau-based theorem prover for a decidable subset of default logic. In Proceedings of the Tenth Conference on Automated Deduction (CADE-90), pp. 541-546, 1990.
45. T. Shaub. On commitment and cumulativity in default logic. In Symbolic and Quantitative Approaches for Uncertainty. European conference (ECSQAU), pp. 305-309, 1991.
46. R. M. Smullyan. First Order Logic. Springer-Verlag, Berlin, 1968.
47. C. Schwind and V. Risch. A tableau-based characterization for default logic. In Symbolic and Quantitative Approaches for Uncertainty, European Conference (ECSQAU), pp. 310-317, 1991.