Skip to main content Accessibility help
×
Home

Justifications for programs with disjunctive and causal-choice rules*

  • PEDRO CABALAR (a1) and JORGE FANDINNO (a1)

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.

Copyright

Footnotes

Hide All
*

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

Footnotes

References

Hide All
Baral, C. 2003. Knowledge representation, reasoning and declarative problem solving. Cambridge university press.
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.
Cabalar, P. and Fandinno, J. 2016b. Justifications for programs with disjunctive and causal-choice rules. CoRR abs/1608.00870.
Cabalar, P., Fandinno, J. and Fink, M. 2014a. Causal graph justifications of logic programs. Theory and Practice of Logic Programming (TPLP) 14, 4–5, 603618.
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, 297310.
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, 530542.
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, 250264.
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, 289323.
Fandinno, J. 2015a. A causal semantics for logic programming. Ph.D. thesis, University of Corunna.
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.
Fandinno, J. 2016. Deriving conclusions from non-monotonic cause-effect relations. Theory and Practice of Logic Programming (TPLP). (to appear).
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, 448453.
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, 10701080.
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 3–4, 365386.
Hall, N. 2004. Two concepts of causation. In Causation and counterfactuals, Collins, J., Hall, N., and Paul, L. A., Eds. Cambridge, MA: MIT Press, 225276.
Hitchcock, C. and Knobe, J. 2009. Cause and norm. Journal of Philosophy 11, 587612.
Lewis, D. K. 1973. Causation. The Journal of Philosophy 70, 17, 556567.
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.
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, 375398.
McCain, N. C. 1997. Causality in commonsense reasoning about actions. Ph.D. thesis, University of Texas at Austin.
McCarthy, J. 1987. Epistemological problems of artificial intelligence. Readings in artificial intelligence, 459.
Niemelä, I. 1999. Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25, 3–4, 241273.
Oetsch, J., Pührer, J. and Tompits, H. 2010. Catching the ouroboros: On debugging non-ground answer-set programs. CoRR abs/1007.4986.
Pearce, D. 2006. Equilibrium logic. Annals of Mathematics and Artificial Intelligence 47, 1–2, 341.
Pearl, J. 2000. Causality: models, reasoning, and inference. Cambridge University Press, New York, NY, USA.
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, 2438.
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, 156.
Schulz, C. and Toni, F. 2016. Justifying answer sets using argumentation. Theory and Practice of Logic Programming (TPLP) 16, 1, 59110.
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.
Thielscher, M. 1997. Ramification and causality. Artificial Intelligence 89, 1–2, 317364.
Vennekens, J. 2011. Actual causation in CP-logic. Theory and Practice of Logic Programming (TPLP) 11, 4–5, 647662.

Justifications for programs with disjunctive and causal-choice rules*

  • PEDRO CABALAR (a1) and JORGE FANDINNO (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed