Abstract
Answer set programming (ASP) has been extended to possibilistic ASP (PASP), in which the notion of possibilistic stable models is defined for possibilistic logic programs. However, possibilistic inferences that correspond to the three inferences in ordinary possibilistic logic have not been explored in PASP yet. In this paper, based on the skeptical reasoning determined by possibilistic stable models, we define three inference relations for PASP, provide their equivalent characterisations in terms of possibility distribution, and develop algorithms for these possibilistic inferences. Our algorithms are achieved by generalising some important concepts (Clarke’s completion, loop formulas, and guarded resolution) and properties in ASP to PASP. Besides their theoretical importance, these results can be used to develop efficient implementations for possibilistic reasoning in ASP.
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References
Alsinet, T., Chesñevar, C.I., Godo, L., Simari, G.R.: A logic programming framework for possibilistic argumentation: Formalization and logical properties. Fuzzy Sets Syst. 159(10), 1208–1228 (2008)
Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge (2003)
Bauters, K., Schockaert, S., Cock, M.D., Vermeir, D.: Possibilistic answer set programming revisited. In: Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence (UAI 2010), pp. 48–55 (2010)
Bauters, K., Schockaert, S., Cock, M.D., Vermeir, D.: Possible and necessary answer sets of possibilistic answer set programs. In: Proceedings of the 24th International Conference on Tools with Artificial Intelligence (ICTAI 2012), pp. 836–843 (2012)
Bauters, K., Schockaert, S., Cock, M.D., Vermeir, D.: Semantics for possibilistic answer set programs: uncertain rules versus rules with uncertain conclusions. Int. J. Approximate Reasoning 55(2), 739–761 (2014)
Bauters, K., Schockaert, S., Cock, M.D., Vermeir, D.: Characterizing and extending answer set semantics using possibility theory. Theory Pract. Logic Program. 15(1), 79–116 (2015)
Benferhat, S., Bouraoui, Z.: Possibilistic DL-lite. In: Liu, W., Subrahmanian, V.S., Wijsen, J. (eds.) SUM 2013. LNCS, vol. 8078, pp. 346–359. Springer, Heidelberg (2013)
Clark, K.: Negation as failure. In: Ginsberg, M. (ed.) Readings in Nonmonotonic Reasoning, pp. 311–325. Morgan Kaufmann, San Francisco (1987)
Dubois, D., Berre, D.L., Prade, H., Sabbadin, R.: Using possibilistic logic for modeling qualitative decision: ATMS-based algorithms. Fundamenta of Informatica 37(1–2), 1–30 (1999)
Dubois, D., Lang, J., Prade, H.: Possibilistic logic. In: Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 439–513. Oxford University Press, New York (1994)
Dubois, D., Prade, H.: Possibility theory, probability theory and multiple-valued logics: a clarification. Ann. Math. Artif. Intell. 32(1–4), 35–66 (2001)
Dubois, D., Prade, H.: Possibilistic logic: a retrospective and prospective view. Fuzzy Sets Syst. 144(1), 3–23 (2004)
Gebser, M., Kaufmann, B., Schaub, T.: The conflict-driven answer set solver clasp: Progress report. In: Erdem, E., Lin, F., Schaub, T. (eds.) LPNMR 2009. LNCS, vol. 5753, pp. 509–514. Springer, Heidelberg (2009)
Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: ICLP/SLP 1988, pp. 1070–1080 (1988)
Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., Scarcello, F.: The DLV system for knowledge representation and reasoning. ACM Trans. Comput. Logic 7(3), 499–562 (2006)
Lin, F., Zhao, Y.: ASSAT: Computing answer sets of a logic program by SAT solvers. J. Artif. Intell. 157(1), 115–137 (2004)
Marek, V.W., Remmel, J.B.: Guarded resolution for answer set programming. Theory Pract. Logic Program. 11(1), 111–123 (2011)
Nicolas, P., Garcia, L., Stéphan, I., Lefèvre, C.: Possibilistic uncertainty handling for answer set programming. Ann. Math. Artif. Intell. 47(1–2), 139–181 (2006)
Nicolas, P., Garcia, L., Stéphan, I.: A possibilistic inconsistency handling in answer set programming. In: Godo, L. (ed.) ECSQARU 2005. LNCS (LNAI), vol. 3571, pp. 402–414. Springer, Heidelberg (2005)
Nieves, J.C., Osorio, M., Cortés, U.: Semantics for possibilistic disjunctive programs. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS (LNAI), vol. 4483, pp. 315–320. Springer, Heidelberg (2007)
Syrjänen, T., Niemelä, I.: The smodels system. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 434–438. Springer, Heidelberg (2001)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 100, 9–34 (1999)
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Jin, Y., Wang, K., Wang, Z. (2015). Possibilistic Inferences in Answer Set Programming. In: Pfahringer, B., Renz, J. (eds) AI 2015: Advances in Artificial Intelligence. AI 2015. Lecture Notes in Computer Science(), vol 9457. Springer, Cham. https://doi.org/10.1007/978-3-319-26350-2_23
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