On computing belief change operations using quantified boolean formulas

Journal of Logic and Computation

Volumn 14, Issue 6, 2004, Pages 801-826

  Delgrande, James P ^a   Schaub, Torsten ^b   Tompits, Hans ^c   Woltran, Stefan ^c  

^a SIMON FRASER UNIVERSITY   (Canada)

^b UNIVERSITY OF POTSDAM   (Germany)

^c VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Belief change; Quantified boolean formulas

Indexed keywords

COMPUTATIONAL COMPLEXITY; FORMAL LOGIC; KNOWLEDGE BASED SYSTEMS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; SET THEORY;

BELIEF CHANGE EXTENSION; BELIEF CONTRACTION; CHOICE REVISION; QUANTIFIED BOOLEAN FORMULAS;

BOOLEAN FUNCTIONS;

EID: 10944270245     PISSN: 0955792X     EISSN: None     Source Type: Journal    
DOI: 10.1093/logcom/14.6.801     Document Type: Article

References (59)

1. C. Alchourrón, P. Gärdenfors, and D. Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50, 510-530, 1985.
2. S. Benferhat, D. Dubois, and H. Prade. A computational model for belief change and fusing ordered belief bases. In Frontiers in Belief Revision, volume 22 of Applied Logic Series, M.-A. Williams and H. Rott, eds., pp. 109-134. Kluwer Academic Publishers, 2001.
3. A. Borgida. Language features for flexible handling of exceptions in information systems. ACM Transactions on Database Systems, 10, 565-603, 1985.
4. M. Cadoli, A. Giovanardi, and M. Schaerf. An algorithm to evaluate quantified Boolean formulae. In Proceedings of the 15th National Conference on Artificial Intelligence (AAAI '98), pp. 262-267, Madison, Wisconsin, 1998.
5. T. Chou and M. Winslett. A model-based belief revision system. Journal of Automated Reasoning, 12, 157-208, 1994.
6. A. Church. Introduction to Mathematical Logic, Volume I. Princeton University Press, 1956.
7. M. Dalal. Investigations into theory of knowledge base revision. In Proceedings of the Seventh National Conference on Artificial Intelligence (AAAI '88), pp. 449-479, St. Paul, Minnesota, 1988.
8. J. de Kleer. An assumption-based TMS. Artificial Intelligence, 28, 127-162, 1986.
9. A. del Val. Syntactic characterizations of belief change operators. In Proceedings of the 13th International Joint Conference on Artificial Intelligence (IJCAI '93), pp. 540-545, Chambéry, France, 1993.
10. J. Delgrande, A. Hunter, and T. Schaub. COBA: A consistency-based belief revision system. In Proceedings of the Eighth European Conference on Logics in Artificial Intelligence (JELIA 2002), S. Greco and N. Leone, eds, volume 2424 of Lecture Notes in Artificial Intelligence, pp. 509-512. Springer-Verlag, 2002.
11. J. Delgrande and T. Schaub. A consistency-based model for belief change: Preliminary report. In Proceedings of the 17th National Conference on Artificial Intelligence (AAAI 2000), pp. 392-398, Austin, Texas, 2000.
12. J. Delgrande and T. Schaub. A consistency-based approach for belief change. Artificial Intelligence, 151, 1-41, 2003.
13. E. Eder. Relative Complexities of First-Order Calculi. W. Bibel and W. vom Hahm, eds. Artificial Intelligence. Vieweg Wiesbadem, 1992.
14. U. Egly, T. Eiter, V. Klotz, H. Tompits, and S. Woltran. Computing stable models with quantified Boolean formulas: Some experimental results. In Proceedings of the 2001 AAAI Spring Symposium on Answer Set Programming, pp. 53-59, 2001.
15. U. Egly, T. Eiter, H. Tompits, and S. Woltran. Solving advanced reasoning tasks using quantified Boolean formulas. In Proceedings of the 17th National Conference on Artificial Intelligence (AAAI 2000), pp. 417-422, Austin, Texas, 2000.
16. T. Eiter and G. Gottlob. On the complexity of propositional knowledge base revision, updates, and counterfactuals. Artificial Intelligence, 57, 227-270, 1992.
17. T. Eiter, V. Klotz, H. Tompits, and S. Woltran. Modal nonmonotonic logics revisited: Efficient encodings for the basic reasoning tasks. In Proceedings of the Eleventh Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2002), volume 2381 of Lecture Notes in Computer Science, pp. 100-114. Springer-Verlag, 2002.
18. R. Fagin, J. Ullman, and M. Vardi. On the semantics of updates in databases. Preliminary report. In Proceedings of the Second ACM Symposium on Principles of Database Systems SIGACT-SIGMOD, pp. 352-365, 1983.
19. R. Feldmann, B. Monien, and S. Schamberger. A distributed algorithm to evaluate quantified Boolean formulas. In Proceedings of the 17th National Conference on Artificial Intelligence (AAAI 2000), pp. 285-290, Austin, Texas, 2000.
20. K. Forbus. Introducing actions into qualitative simulation. In Proceedings of the Eleventh International Joint Conference on Artificial Intelligence (IJCAI '89), pp. 1273-1278, Los Angeles, California, 1989.
21. P. Gärdenfors. Knowledge in Flux: Modelling the Dynamics of Epistemic States. The MIT Press, Cambridge, MA, 1988.
22. M. R. Garey and D. S. Johnson. Computers and Intractability. W. H. Freeman, 1979.
23. M. Ginsberg. Counterfactuals. Artificial Intelligence, 30, 35-79, 1986.
24. E. Giunchiglia, M. Narizzano, and A. Tacchella. QUBE: A system for deciding quantified Boolean formulas satisfiability. In Proceedings of the First International Joint Conference on Automated Reasoning (IJCAR 2001), volume 2083 of Lecture Notes in Artificial Intelligence, pp. 364-369. Springer-Verlag, 2001.
25. H. Katsuno and A. Mendelzon. On the difference between updating a knowledge base and revising it. In Belief Revision, P. Gärdenfors, ed., pp. 183-203. Cambridge University Press, 1992.
26. H. Kautz and B. Selman. Planning as satisfiability. In Proceedings of the Tenth European Conference on Artificial Intelligence (ECAI '92), pp. 359-363, Vienna, Austria, 1992.
27. H. Kleine-Büning, M. Karpinski, and A. Flögel. Resolution for quantified Boolean formulas. Information and Computation, 117, 12-18, 1995.
28. S. Konieczny and R. Pino Pérez. Merging information under constraints: a logical framework. Journal of Logic and Computation, 12, 773-808, 2002.
29. S. Leśniewski. Grundzüge eines neuen Systems der Grundlagen der Mathematik. Fundamenta Mathematica, 14, 1-81, 1929.
30. R. Letz. Lemma and model caching in decision procedures for quantified Boolean formulas. In Proceedings of the Eleventh Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2002), volume 2381 of Lecture Notes in Computer Science, pp. 160-175. Springer-Verlag, 2002.
31. P. Liberatore and M. Schaerf. Relating belief revision and circumscription. In Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI '95), pp. 1557-1563, Montréal, Canada, 1995. Morgan Kaufmann.
32. P. Liberatore and M. Schaerf. Reducing belief revision to circumscription (and vice versa). Artificial Intelligence, 93, 261-296, 1997.
33. P. Liberatore and M. Schaerf. Arbitration (or how to merge knowledge bases). IEEE Transactions on Knowledge and Data Engineering, 10, 76-90, 1998.
34. V. Lifschitz. Circumscription. In Handbook of Logic in Artificial Intelligence and Logic Programming, D. M. Gabbay, C. J. Hogger, and J. A. Robinson, eds, pp. 297-352. Clarendon Press, 1994.
35. J. Łukasiewicz and A. Tarski. Untersuchungen über den Aussagenkalkül. Comptes Rendus Séances Société des Sciences et Lettres Varsovie, 23, 30-50, 1930.
36. D. Makinson. How to give it up: a survey of some formal aspects of the logic of theory change. Synthese, 62, 347-363, 1985.
37. J. McCarthy. Circumscription - a form of nonmonotonic reasoning. Artificial Intelligence, 13, 27-39, 1980.
38. A. R. Meyer and L. J. Stockmeyer. Word problems requiring exponential time. In ACM Symposium on Theory of Computing (STOC '73), pp. 1-9. ACM Press, 1973.
39. B. Nebel. Syntax based approaches to belief revision. In Belief Revision, P. Gärdenfors, ed., pp. 52-88. Cambridge University Press, 1992.
40. C. Papadimitriou. Computational Complexity. Addison-Wesley, Reading, MA, 1994.
41. D. Pearce, H. Tompits, and S. Woltran. Encodings for equilibrium logic and logic programs with nested expressions. In Proceedings of the Tenth Portuguese Conference on Artificial Intelligence (EPIA 2001), volume 2258 of Lecture Notes in Artificial Intelligence, pp. 306-320. Springer-Verlag, 2001.
42. D. A. Plaisted and S. Greenbaum. A structure preserving clause form translation. Journal of Symbolic Computation, 2, 293-304, 1986.
43. D. Poole. A logical framework for default reasoning. Artificial Intelligence, 36, 27-48, 1988.
44. R. Reiter. A theory of diagnosis from first principles. Artificial Intelligence, 32, 57-96, 1987.
45. J. Rintanen. Constructing conditional plans by a theorem prover. Journal of Artificial Intelligence Research, 10, 323-352, 1999.
46. J. Rintanen. Improvements to the evaluation of quantified Boolean formulae. In Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI '99), pp. 1192-1197, Stockholm, Sweden, 1999.
47. B. Russell. The theory of implication. American Journal of Mathematics, 28, 159-202, 1906.
48. K. Satoh. Nonmonotonic reasoning by minimal belief revision. In Proceedings of the International Conference on Fifth Generation Computer Systems, pp. 455-462, Tokyo, 1988.
49. J. Srzednicki and Z. Stachniak, editors. Lesniewski's Systems Protothetic. Dordrecht, 1998.
50. L. J. Stockmeyer. The polynomial-time hierarchy. Theoretical Computer Science, 3, 1-22, 1976.
51. H. Tompits. Expressing default abduction problems as quantified Boolean formulas. AI Communications, 16, 89-105, 2003.
52. R. Wassermann. Resource-Bounded Belief Revision. PhD thesis, Institute for Logic, Language, and Computation, University of Amsterdam, 1999.
53. A. Weber. Updating prepositional formulas, In Proceedings of the First Conference on Expert Database Systems, pp. 487-500, 1986.
54. A. N. Whitehead and B. Russell. Principia Mathematica, Volume 1-3. Cambridge University Press, 1910-13.
55. M.-A. Williams. Theory base change: a computational model. In Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI '95), pp. 1541-1547, Montréal, Canada, 1995.
56. M. Winslett. Reasoning about action using a possible models approach. In Proceedings of the Seventh National Conference on Artificial Intelligence (AAAI '88), pp. 89-93, St. Paul, Minnesota, 1988.
57. M. Winslett. Sometimes updates are circumscription. In Proceedings of the Eleventh International Joint Conference on Artificial Intelligence (IJCAI '89), N. S. Sridharan, ed., pp. 859-863, Detroit, Michigan, 1989. Morgan Kaufmann.
58. M. Winslett. Updating Logical Databases. Cambridge University Press, 1990.
59. C. Wrathall. Complete sets and the polynomial-time hierarchy. Theoretical Computer Science, 3, 23-33, 1976.