Representing paraconsistent reasoning via quantified propositional logic

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3300 LNCS, Issue , 2004, Pages 84-118

  Besnard, Philippe ^a   Schaub, Torsten ^b,d   Tompits, Hans ^c   Woltran, Stefan ^c  

^a CNRS   (France)

^b UNIVERSITY OF POTSDAM   (Germany)

^c VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^d SIMON FRASER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC FORMULAS; PARACONSISTENT REASONING; QUANTIFIED BOOLEAN FORMULAS (QBF); CLASSICAL PROPOSITIONAL LOGIC; COMPLEXITY RESULTS; EFFICIENT SOLVERS; POLYNOMIAL-TIME; PROPOSITIONAL LOGIC; QUANTIFIED BOOLEAN FORMULAS; SECOND-ORDER LOGIC;

POLYNOMIAL APPROXIMATION; RAPID PROTOTYPING; BOOLEAN ALGEBRA; BOOLEAN FUNCTIONS; FORMAL LOGIC;

FORMAL LOGIC; COMPUTER CIRCUITS;

EID: 27144457597     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: None     Document Type: Conference Paper

References (73)

1. M. Arenas, L. Bertossi, and J. Chomicki. Consistent query answers in inconsistent databases. In Proceedings of the Eighteenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS '99), pages 68-79. ACM Press, 1999.
2. O. Arieli. Paraconsistent preferential reasoning by signed quantified Boolean formulae. In Proceedings of the 16th European Conference on Artificial Intelligence (ECAI 2004), 2004. To appear.
3. O. Arieli and M. Denecker. Reducing preferential paraconsistent reasoning to classical entailment. Journal of Logic and Computation, 13(4):557-580, 2003.
4. O. Arieli, M. Denecker, B. V. Nuffelen, and M. Bruynooghe. Database repair by signed formulae. In Proceedings of the Third Conference on Foundations of Information and Knowledge Systems (FoIKS '04), volume 2942 of Lecture Notes in Computer Science, pages 14-30. Springer-Verlag, 2004.
5. A. Avron. Simple consequence relations. Information and Computation, 92:105139, 1991.
6. A. Ayari and D. Basin. QUBOS: Deciding quantified Boolean logic using propositional satisfiability solvers. In M. Aagaard and J. O'Leary, editors, Proceedings of the Fourth International Conference on Formal Methods in Computer-Aided Design (FMCAD 2002), volume 2517 of Lecture Notes in Computer Science, pages 187-201. Springer-Verlag, 2002.
7. S. Benferhat, D. Dubois, and H. Prade. Argumentative inference in uncertain and inconsistent knowledge bases. In Proceedings of the Ninth Conference on Uncertainty in Artificial Intelligence (UAI '93), pages 411-419, 1993.
8. S. Benferhat, D. Dubois, and H. Prade. Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 1: The flat case. Studia Logica, 58(1):17-45, 1997.
9. P. Besnard. An Introduction to Default Logic. Springer-Verlag, 1989.
10. P. Besnard and T. Schaub. Circumscribing inconsistency. In Proceedings of the 15th International Joint Conference on Artificial Intelligence (IJCAI '97), pages 150-155. Morgan Kaufmann Publishers, 1997.
11. P. Besnard and T. Schaub. Signed systems for paraconsistent reasoning. Journal of Automated Reasoning, 20:191-213, 1998.
12. P. Besnard, T. Schaub, H. Tompits, and S. Woltran. Paraconsistent reasoning via quantified Boolean formulas, I: Axiomatising signed systems. In S. Flesca, S. Greco, N. Leone, and G. Ianni, editors, Proceedings of the Eighth European Conference on Logics in Artificial Intelligence (JELIA '02), volume 2424 of Lecture Notes in Computer Science, pages 320-331. Springer-Verlag, 2002.
13. P. Besnard, T. Schaub, H. Tompits, and S. Woltran. Paraconsistent reasoning via quantified Boolean formulas, II: Circumscribing inconsistent theories. In Proceedings of the Seventh European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU '03), volume 2711 of Lecture Notes in Computer Science, pages 528-539. Springer-Verlag, 2003.
14. G. Brewka. Preferred subtheories: An extended logical framework for default reasoning. In N. S. Sridharan, editor, Proceedings of the Eleventh International Joint Conference on Artificial Intelligence (IJCAI '89), pages 1043-1048. Morgan Kaufmann Publishers, 1989.
15. R. E. Bryant. Graph-based algorithms for Boolean function manipulation. IEEE Transactions on Computers, C-35(8):677-691, 1986.
16. T. Bylander. The computational complexity of propositional STRIPS planning. Artificial Intelligence, 69(1-2):165-204, 1994.
17. 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), pages 262-267. AAAI Press/MIT Press, 1998.
18. M. Cadoli and M. Schaerf. On the complexity of entailment in propositional multivalued logics. Annals of Mathematics and Artificial Intelligence, 18:29-50, 1996.
19. C. Cayrol, M. Lagasquie-Schiex, and T. Schiex. Nonmonotonic reasoning: From complexity to algorithms. Annals of Mathematics and Artificial Intelligence, 22(34):207-236, 1998.
20. C. Cayrol and M.-C. Lagasquie-Schiex. Non-monotonic syntax-based entailment: A classification of consequence relations. In C. Froidevaux and J. Kohlas, editors, Proceedings of the Third European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU '95), volume 946 of Lecture Notes in Computer Science, pages 107-114. Springer-Verlag, 1995.
21. A. Church. Introduction to Mathematical Logic, Volume I. Princeton University Press, 1956.
22. S. Coste-Marquis and P. Marquis. Complexity results for paraconsistent inference relations. In D. Fensel, F. Giunchiglia, D. McGuiness, and M. Williams, editors, Proceedings of the Eighth International Conference on Principles of Knowledge Representation and Reasoning (KR '02), pages 61-72. Morgan Kaufmann Publishers, 2002.
23. M. Davis, G. Logemann, and D. Loveland. A machine program for theorem proving. Communications of the ACM, 5(7):394-397, 1962.
24. M. Davis and H. Putman. A computing procedure for quantification theory. Journal of the ACM, 7(3):201-215, 1960.
25. J. Delgrande, T. Schaub, H. Tompits, and S. Woltran. On computing solutions to belief change scenarios. In S. Benferhat and P. Besnard, editors, Proceedings of the Sixth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU '01), volume 2143 of Lecture Notes in Computer Science, pages 510-521. Springer-Verlag, 2001.
26. I. D'Ottaviano and N. da Costa. Sur un problème de Jaśkowski. In Comptes Rendus de l'Académic des Sciences de Paris, volume 270, pages 1349-1353, 1970.
27. 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), pages 417-422. AAAI Press/MIT Press, 2000.
28. U. Egly, R. Pichler, and S. Woltran. On deciding subsumption problems. In Proceedings of the Fifth International Symposium on the Theory and Applications of Satisfiability Testing (SAT 2002), pages 89-97, 2002.
29. U. Egly, H. Tompits, and S. Woltran. On quantifier shifting for quantified Boolean formulas. In Proceedings of the SAT 2002 Workshop on Theory and Applications of Quantified Boolean Formulas (QBF 2002), pages 48-61, 2002.
30. T. Eiter and G. Gottlob. On the computational cost of disjunctive logic programming: Propositional case. Annals of Mathematics and Artificial Intelligence, 15(3-4) :289-323, 1995.
31. T. Eiter, V. Klotz, H. Tompits, and S. Woltran. Modal nonmonotonic logics revisited: Efficient encodings for the basic reasoning tasks. In U. Egly and C. Fermüller, editors, Proceedings of the Eleventh International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2002), volume 2381 of Lecture Notes in Computer Science, pages 100-114. Springer-Verlag, 2002.
32. 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), pages 285-290. AAAI Press/MIT Press, 2000.
33. A. Frisch. Inference without chaining. In J. McDermott, editor, Proceedings of the Tenth International Joint Conference on Artificial Intelligence (IJCAI '87), pages 515-519. Morgan Kaufmann Publishers, 1987.
34. M. R. Garey and D. S. Johnson. Computers and Intractability. W. H. Freeman, 1979.
35. E. Giunchiglia, M. Narizzano, and A. Tacchella. QuBE: A system for deciding quantified Boolean formulas satisfiability. In R. Goré, A. Leitsch, and T. Nipkow, editors, Proceedings of the First International Joint Conference on Automated Reasoning (IJCAR 2001), volume 2083 of Lecture Notes in Computer Science, pages 364-369. Springer-Verlag, 2001.
36. G. Gottlob. Complexity results for nonmonotonic logics. Journal of Logic and Computation, 2(3):397-425, 1992.
37. H. Kautz, D. McAllester, and B. Selman. Encoding plans in propositional logic. In L. Aiello, J. Doyle, and S. Shapiro, editors, Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning (KR '96), pages 374-384. Morgan Kaufmann Publishers, 1996.
38. H. Kautz and B. Selman. Planning as satisfiability. In B. Neumann, editor, Proceedings of the Tenth European Conference on Artificial Intelligence (ECAI '92), pages 359-363. John Wiley & Sons, 1992.
39. H. Kleine Büning, M. Karpinski, and A. Flögel. Resolution for quantified Boolean formulas. Information and Computation, 117(1):12-18, 1995.
40. S. Konieczny and P. Marquis. Three-valued logics for inconsistency handling. In S. Flesca, S. Greco, N. Leone, and G.Ianni, editors, Proceedings of the Eighth European Conference on Logics in Artificial Intelligence (JELIA '02), volume 2424 of Lecture Notes in Computer Science, pages 332-344. Springer-Verlag, 2002.
41. R. E. Ladner. The computational complexity of provability in systems of modal propositional logic. SIAM Journal on Computing, 6(3):467-480, 1977.
42. S. Leśniewski. Grundzüge eines neuen System der Grundlagen der Mathematik. Fundamenta Mathematica, 14:1-81, 1929.
43. R. Letz. Lemma and model caching in decision procedures for quantified Boolean formulas. In U. Egly and C. Fermüller, editors, Proceedings of the Eleventh International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2002), volume 2381 of Lecture Notes in Computer Science, pages 160-175. Springer-Verlag, 2002.
44. H. Levesque. A knowledge-level account of abduction. In N. S. Sridharan, editor, Proceedings of the Eleventh International Joint Conference on Artificial Intelligence (IJCAI '89), pages 1061-1067. Morgan Kaufmann Publishers, 1989.
45. J. Lukasiewicz and A. Tarski. Untersuchungen über den Aussagenkalkül. Comptes Rendus Séances Société des Sciences et Lettres Varsovie, 23(Cl. III):30-50, 1930.
46. J. McCarthy. Circumscription - A form of nonmonotonic reasoning. Artificial Intelligence, 13:27-39, 1980.
47. A. R. Meyer and L. J. Stockmeyer. The equivalence problem for regular expressions with squaring requires exponential space. In 13th Annual Symposium on Switching and Automata Theory, pages 125-129, 1972.
48. A. R. Meyer and L. J. Stockmeyer. Word problems requiring exponential time. In ACM Symposium on Theory of Computing (STOC '73), pages 1-9. ACM Press, 1973.
49. S. Minato. Binary Decision Diagrams and Applications for VLSI CAD. Kluwer, 1996.
50. D. Mundici. Satisfiability in many-valued sentential logic is NP-complete. Theoretical Computer Science, 52(1-2):145-153, 1987.
51. B. Nebel. Belief revision and default reasoning: Syntax-based approaches. In J. Allen, R. Fikes, and E. Sandewall, editors, Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning (KR '91), pages 417-428. Morgan Kaufmann Publishers, 1991.
52. C. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.
53. D. Pearce, H. Tompits, and S. Woltran. Encodings for equilibrium logic and logic programs with nested expressions. In P. Brazdil and A. Jorge, editors, Proceedings of the Tenth Portuguese Conference on Artificial Intelligence (EPIA '01), volume 2258 of Lecture Notes in Computer Science, pages 306-320. Springer-Verlag, 2001.
54. D. Plaisted, A. Biere, and Y. Zhu. A satisfiability procedure for quantified Boolean formulae. Discrete Applied Mathematics, 130:291-328, 2003.
55. G. Priest. Logic of paradox. Journal of Philosophical Logic, 8:219-241, 1979.
56. G. Priest. Reasoning about truth. Artificial Intelligence, 39:231-244, 1989.
57. R. Reiter. A logic for default reasoning. Artificial Intelligence, 13(1-2):81-132, 1980.
58. N. Rescher. Plausible Reasoning. Van Gorcum, Amsterdam, 1976.
59. N. Rescher and R. Manor. On inference from inconsistent premises. Theory and Decision, 1:179-219, 1970.
60. J. Rintanen. Constructing conditional plans by a theorem prover. Journal of Artificial Intelligence Research, 10:323-352, 1999.
61. J. Rintanen. Improvements to the evaluation of quantified Boolean formulae. In T. Dean, editor, Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI '99), pages 1192-1197. Morgan Kaufmann Publishers, 1999.
62. J. A. Robinson. A machine-oriented logic based on the resolution principle. Journal of the ACM, 12(1):23-41, 1965.
63. B. Russell. The theory of implication. American Journal of Mathematics, 28(2):159-202, 1906.
64. S. Schamberger. Ein paralleler Algorithmus zum Lösen von Quantifizierten Boole'schen Formeln. Master's thesis, Universität Gesamthochschule Paderborn, 2000.
65. J. Srzednicki and Z. Stachniak, editors. Lesniewski's Systems Protothetic. Dordrecht, 1998.
66. R. Statman. Intuitionistic propositional logic is polynomial-space complete. Theoretical Computer Science, 9:67-72, 1979.
67. L. J. Stockmeyer. The polynomial-time hierarchy. Theoretical Computer Science, 3(1):1-22, 1976.
68. H. Tompits. Expressing default abduction problems as quantified Boolean formulas. AI Communications, 16:89-105, 2003.
69. H. Turner. Polynomial-length planning spans the polynomial hierarchy. In S. Flesca, S. Greco, N. Leone, and G. Ianni, editors, Proceedings of the Eighth European Conference on Logics in Artificial Intelligence (JELIA '02), volume 2424 of Lecture Notes in Computer Science, pages 111-124. Springer-Verlag, 2002.
70. A. N. Whitehead and B. Russell. Principia Mathematica, volume 1-3. Cambridge University Press, 1910-13.
71. S. Woltran. Quantified Boolean Formulas - From Theory to Practice. PhD thesis, Technische Universität Wien, Institut für Informationssysteme, 2003.
72. C. Wrathall. Complete sets and the polynomial-time hierarchy. Theoretical Computer Science, 3(1):23-33, 1976.
73. L. Zhang and S. Malik. Towards a symmetric treatment of satisfaction and conflicts in quantified Boolean formula evaluation. In P. V. Hentenryck, editor, Proceedings of the Eighth International Conference on Principles and Practice of Constraint Programming (CP 2002), volume 2470 of Lecture Notes in Computer Science, pages 200-215. Springer-Verlag, 2002.