Abstract
In this work, we revisit a recently proposed multi-valued semantics for logic programs where each true atom in a stable model is associated with a set of expressions (or causal justifications) involving rule labels. For positive programs, these causal justifications correspond to the possible alternative proofs of the atom that further satisfy some kind of minimality or lack of redundancy. This information can be queried for different purposes such as debugging, program design, diagnosis or causal explanation. Unfortunately, in the worst case, the number of causal justifications for an atom can be exponential with respect to the program size, so that computing the complete causal model may become intractable in the general case. However, we may instead just be interested in querying whether some particular set of rules are involved in the atom derivation, either as a sufficient cause (they provide one of the alternative proofs) or as a necessary cause (they are mandatorily used in all proofs). In this paper, we formally define sufficient and necessary causation for this setting and provide precise complexity characterizations of the associated decision problems, showing that they remain within the first two levels of the polynomial hierarchy.
This research was partially supported by Spanish MEC project TIN2009-14562-C05-04, by Xunta de Galicia, Spain, grant GPC2014/070 and program INCITE 2011, Inditex-University of Corunna 2013 grants, as well as by the Austrian Science Fund (FWF) project P24090.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cabalar, P., Fandinno, J., Fink, M.: Causal graph justifications of logic programs. In: Proc. of the 30th Intl. Conf. on Logic Programming (ICLP 2014) (to appear, 2014)
Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R.A., Bowen, K.A. (eds.) Logic Programming: Proc. of the Fifth International Conference and Symposium, vol.Ā 2, pp. 1070ā1080. MIT Press, Cambridge (1988)
Cabalar, P., Fandinno, J.: An algebra of causal chains. In: Proc. of the 6th Workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP 2013) (2013)
Hall, N.: Two concepts of causality, pp. 181ā276 (2004)
Gebser, M., PĆ¼hrer, J., Schaub, T., Tompits, H.: Meta-programming technique for debugging answer-set programs. In: Proc. of the 23rd Conf. on Artificial Inteligence (AAAI 2008), 448ā453 (2008)
Pontelli, E., Son, T.C., El-Khatib, O.: Justifications for logic programs under answer set semantics. Theory and Practice of Logic ProgrammingĀ 9(1), 1ā56 (2009)
Schulz, C., Sergot, M., Toni, F.: Argumentation-based answer set justification. In: Proc. of the 11th Intl. Symposium on Logical Formalizations of Commonsense Reasoning (Commonsense 2013) (2013)
Viegas DamĆ”sio, C., Analyti, A., Antoniou, G.: Justifications for logic programming. In: Cabalar, P., Son, T.C. (eds.) LPNMR 2013. LNCS, vol.Ā 8148, pp. 530ā542. Springer, Heidelberg (2013)
Pereira, L.M., AparĆcio, J.N., Alferes, J.J.: Derivation procedures for extended stable models. In: Mylopoulos, J., Reiter, R. (eds.) Proceedings of the 12th International Joint Conference on Artificial Intelligence, pp. 863ā869. Morgan Kaufmann (1991)
Denecker, M., De Schreye, D.: Justification semantics: A unifiying framework for the semantics of logic programs. In: Proc. of the Logic Programming and Nonmonotonic Reasoning Workshop, pp. 365ā379 (1993)
Vennekens, J.: Actual causation in cp-logic. TPLPĀ 11(4-5), 647ā662 (2011)
Green, T.J., Karvounarakis, G., Tannen, V.: Provenance semirings. In: Proceedings of the Twenty-sixth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, pp. 31ā40. ACM (2007)
Green, T.J.: Containment of conjunctive queries on annotated relations. Theory of Computing SystemsĀ 49(2), 429ā459 (2011)
Meliou, A., Gatterbauer, W., Halpern, J.Y., Koch, C., Moore, K.F., Suciu, D.: Causality in databases. IEEE Data Eng. Bull. 33(EPFL-ARTICLE-165841), 59ā67 (2010)
Mackie, J.L.: Causes and Conditions, vol.Ā 2 (1965)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
Ā© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Cabalar, P., FandiƱo, J., Fink, M. (2014). A Complexity Assessment for Queries Involving Sufficient and Necessary Causes. In: FermƩ, E., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2014. Lecture Notes in Computer Science(), vol 8761. Springer, Cham. https://doi.org/10.1007/978-3-319-11558-0_21
Download citation
DOI: https://doi.org/10.1007/978-3-319-11558-0_21
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11557-3
Online ISBN: 978-3-319-11558-0
eBook Packages: Computer ScienceComputer Science (R0)