Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-05T21:40:39.994Z Has data issue: false hasContentIssue false
  • English
  • Français

Justifications for programs with disjunctive and causal-choice rules*

Published online by Cambridge University Press:  14 October 2016

PEDRO CABALAR  and
JORGE FANDINNO Open the ORCID record for JORGE FANDINNO [Opens in a new window]
PEDRO CABALAR
Affiliation:
Department of Computer Science, University of Corunna, Corunna, Spain (email: [email protected], [email protected])
JORGE FANDINNO
Affiliation:
Department of Computer Science, University of Corunna, Corunna, Spain (email: [email protected], [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we study an extension of the stable model semantics for disjunctive logic programs where each true atom in a model is associated with an algebraic expression (in terms of rule labels) that represents its justifications. As in our previous work for non-disjunctive programs, these justifications are obtained in a purely semantic way, by algebraic operations (product, addition and application) on a lattice of causal values. Our new definition extends the concept of causal stable model to disjunctive logic programs and satisfies that each (standard) stable model corresponds to a disjoint class of causal stable models sharing the same truth assignments, but possibly varying the obtained explanations. We provide a pair of illustrative examples showing the behaviour of the new semantics and discuss the need of introducing a new type of rule, which we call causal-choice. This type of rule intuitively captures the idea of “A may cause B” and, when causal information is disregarded, amounts to a usual choice rule under the standard stable model semantics.

Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 16 , Special Issue 5-6: 32nd International Conference on Logic Programming , September 2016 , pp. 587 - 603
Copyright
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

This research was partially supported by Spanish Project TIN2013-42149-P.

References

Baral, C. 2003. Knowledge representation, reasoning and declarative problem solving. Cambridge university press.Google Scholar
Cabalar, P. and Fandinno, J. 2016a. Enablers and inhibitors in causal justifications of logic programs. Theory and Practice of Logic Programming (TPLP), (First View), 1–26.Google Scholar
Cabalar, P. and Fandinno, J. 2016b. Justifications for programs with disjunctive and causal-choice rules. CoRR abs/1608.00870.Google Scholar
Cabalar, P., Fandinno, J. and Fink, M. 2014a. Causal graph justifications of logic programs. Theory and Practice of Logic Programming (TPLP) 14, 4–5, 603–618.Google Scholar
Cabalar, P., Fandinno, J. and Fink, M. 2014b. A complexity assessment for queries involving sufficient and necessary causes. In Logics in Artificial Intelligence - 14th European Conference, JELIA 2014, Funchal, Madeira, Portugal, September 24-26, 2014. Proc., Fermé, E. and Leite, J., Eds. Lecture Notes in Computer Science, vol. 8761. Springer, 297–310.Google Scholar
Damásio, C. V., Analyti, A. and Antoniou, G. 2013. Justifications for logic programming. In Logic Programming and Nonmonotonic Reasoning, Twelfth Intl. Conference, LPNMR 2013, Corunna, Spain, September 15-19, 2013. Proc., Cabalar, P. and Son, T. C., Eds. Lecture Notes in Computer Science, vol. 8148. Springer, 530–542.Google Scholar
Denecker, M., Brewka, G. and Strass, H. 2015. A formal theory of justifications. In Logic Programming and Nonmonotonic Reasoning - 13th Intl. Conference, LPNMR 2015, Lexington, KY, USA, September 27-30, 2015. Proc., Calimeri, F., Ianni, G., and Truszczynski, M., Eds. Lecture Notes in Computer Science, vol. 9345. Springer, 250–264.Google Scholar
Eiter, T. and Gottlob, G. 1995. On the computational cost of disjunctive logic programming: Propositional case. Annals of Mathematics and Artificial Intelligence 15, 3–4, 289–323.Google Scholar
Fandinno, J. 2015a. A causal semantics for logic programming. Ph.D. thesis, University of Corunna.Google Scholar
Fandinno, J. 2015b. Towards deriving conclusions from cause-effect relations. In in Proc. of the 8th Intl. Workshop on Answer Set Programming and Other Computing Paradigms, ASPOCP 2015, Cork, Ireland, August 31, 2015. Google Scholar
Fandinno, J. 2016. Deriving conclusions from non-monotonic cause-effect relations. Theory and Practice of Logic Programming (TPLP). (to appear).Google Scholar
Gebser, M., Pührer, J., Schaub, T. and Tompits, H. 2008. A meta-programming technique for debugging answer-set programs. In Proc. of the 23rd AAAI Conf. on Artificial Intelligence, Chicago, USA, July 13-17, 2008, Fox, D. and Gomes, C. P., Eds. AAAI Press, 448–453.Google Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Logic Programming, Proc. of the Fifth Intl. Conference and Symposium, Seattle, Washington, August 15-19, Kowalski, R. A. and Bowen, K. A., Eds. MIT Press, 1070–1080.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 3–4, 365–386.Google Scholar
Hall, N. 2004. Two concepts of causation. In Causation and counterfactuals, Collins, J., Hall, N., and Paul, L. A., Eds. Cambridge, MA: MIT Press, 225–276.Google Scholar
Hitchcock, C. and Knobe, J. 2009. Cause and norm. Journal of Philosophy 11, 587–612.Google Scholar
Lewis, D. K. 1973. Causation. The Journal of Philosophy 70, 17, 556–567.Google Scholar
Lin, F. 1995. Embracing causality in specifying the indirect effects of actions. In Proc. of the Fourteenth Intl. Joint Conference on Artificial Intelligence, IJCAI 95, Montréal Québec, Canada, August 20-25 1995, 2 Volumes. Morgan Kaufmann, 1985–1993.Google Scholar
Marek, V. W. and Truszczyński, M. 1999. Stable models and an alternative logic programming paradigm. In The Logic Programming Paradigm, Apt, K. R., Marek, V. W., Truszczyński, M., and Warren, D., Eds. Artificial Intelligence. Springer, 375–398.Google Scholar
McCain, N. C. 1997. Causality in commonsense reasoning about actions. Ph.D. thesis, University of Texas at Austin.Google Scholar
McCarthy, J. 1987. Epistemological problems of artificial intelligence. Readings in artificial intelligence, 459.Google Scholar
Niemelä, I. 1999. Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25, 3–4, 241–273.Google Scholar
Oetsch, J., Pührer, J. and Tompits, H. 2010. Catching the ouroboros: On debugging non-ground answer-set programs. CoRR abs/1007.4986.CrossRefGoogle Scholar
Pearce, D. 2006. Equilibrium logic. Annals of Mathematics and Artificial Intelligence 47, 1–2, 3–41.Google Scholar
Pearl, J. 2000. Causality: models, reasoning, and inference. Cambridge University Press, New York, NY, USA.Google Scholar
Pemmasani, G., Guo, H., Dong, Y., Ramakrishnan, C. R. and Ramakrishnan, I. V. 2004. Online justification for tabled logic programs. In Functional and Logic Programming, 7th Intl. Symposium, FLOPS 2004, Nara, Japan, April 7-9, 2004, Proc., Kameyama, Y. and Stuckey, P. J., Eds. Lecture Notes in Computer Science, vol. 2998. Springer, 24–38.Google Scholar
Pontelli, E., Son, T. C. and El-Khatib, O. 2009. Justifications for logic programs under answer set semantics. Theory and Practice of Logic Programming (TPLP) 9, 1, 1–56.CrossRefGoogle Scholar
Schulz, C. and Toni, F. 2016. Justifying answer sets using argumentation. Theory and Practice of Logic Programming (TPLP) 16, 1, 59–110.Google Scholar
Specht, G. 1993. Generating explanation trees even for negations in deductive database systems. In Proc. of the 5th Workshop on Logic Programming Environments (LPE 1993), October 29-30, 1993, Vancouver, British Columbia, Canada, Ducassé, M., Charlier, B. L., Lin, Y., and Yalçinalp, L. Ü., Eds. IRISA, Campus de Beaulieu, France, 8–13.Google Scholar
Thielscher, M. 1997. Ramification and causality. Artificial Intelligence 89, 1–2, 317–364.Google Scholar
Vennekens, J. 2011. Actual causation in CP-logic. Theory and Practice of Logic Programming (TPLP) 11, 4–5, 647–662.Google Scholar