Abstract
Possibilistic answer set programming (PASP) unites answer set programming (ASP) and possibilistic logic (PL) by associating certainty values with rules. The resulting framework allows to combine both non-monotonic reasoning and reasoning under uncertainty in a single framework. While PASP has been well-studied for possibilistic definite and possibilistic normal programs, we argue that the current semantics of possibilistic disjunctive programs are not entirely satisfactory. The problem is twofold. First, the treatment of negation-as-failure in existing approaches follows an all-or-nothing scheme that is hard to match with the graded notion of proof underlying PASP. Second, we advocate that the notion of disjunction can be interpreted in several ways. In particular, in addition to the view of ordinary ASP where disjunctions are used to induce a non-deterministic choice, the possibilistic setting naturally leads to a more epistemic view of disjunction. In this paper, we propose a semantics for possibilistic disjunctive programs, discussing both views on disjunction. Extending our earlier work, we interpret such programs as sets of constraints on possibility distributions, whose least specific solutions correspond to answer sets.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Baral, C.: Knowledge, Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge (2003)
Baral, C., Gelfond, M., Rushton, N.: Probabilistic reasoning with answer sets. Theory and Practice of Logic Programming 9(1), 57–144 (2009)
Bauters, K., Schockaert, S., De Cock, M., Vermeir, D.: Possibilistic answer set programming revisited. In: Proc. of UAI 2010 (2010)
Confalonieri, R., Nieves, J.C., Vázquez-Salceda, J.: Pstable semantics for logic programs with possibilistic ordered disjunction. In: Proc. of AI*IA 2009, pp. 52–61 (2009)
Damásio, C.V., Pereira, L.M.: Monotonic and residuated logic programs. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, pp. 748–759. Springer, Heidelberg (2001)
Dubois, D., Lang, J., Prade, H.: Towards possibilistic logic programming. In: Proc. of ICLP 1991, pp. 581–595 (1991)
Dubois, D., Lang, J., Prade, H.: Possibilistic logic. Handbook of Logic for Artificial Intelligence and Logic Programming 3(1), 439–513 (1994)
Dubois, D., Prade, H.: Can we enforce full compositionality in uncertainty calculi? In: Proc. of AAAI 1994, pp. 149–154 (1994)
Dubois, D., Prade, H., Schockaert, S.: Rules and meta-rules in the framework of possibility theory and possibilistic logic. Scientia Iranica (to appear, 2011)
Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385 (1991)
Gelfond, M., Lifzchitz, V.: The stable model semantics for logic programming. In: Proc. of ICLP 1988, pp. 1081–1086 (1988)
Lifschitz, V., Schwarz, G.: Extended logic programs as autoepistemic theories. In: Proc. of LPNMR 1993, pp. 101–114 (1993)
Nicolas, P., Garcia, L., Stéphan, I., Lefèvre, C.: Possibilistic uncertainty handling for answer set programming. Annals of Mathematics and Artificial Intelligence 47(1–2), 139–181 (2006)
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)
Osorio, M., Pérez, J.A.N., Ramírez, J.R.A., Macías, V.B.: Logics with common weak completions. Journal of Logic and Computation 16(6), 867–890 (2006)
Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics 5(2), 285–309 (1955)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 3–28 (1978)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bauters, K., Schockaert, S., De Cock, M., Vermeir, D. (2011). Weak and Strong Disjunction in Possibilistic ASP. In: Benferhat, S., Grant, J. (eds) Scalable Uncertainty Management. SUM 2011. Lecture Notes in Computer Science(), vol 6929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23963-2_37
Download citation
DOI: https://doi.org/10.1007/978-3-642-23963-2_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23962-5
Online ISBN: 978-3-642-23963-2
eBook Packages: Computer ScienceComputer Science (R0)