Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-28T16:10:12.680Z Has data issue: false hasContentIssue false
  • English
  • Français

Deriving conclusions from non-monotonic cause-effect relations*

Published online by Cambridge University Press:  14 October 2016

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

Abstract

We present an extension of Logic Programming (under stable models semantics) that, not only allows concluding whether a true atom is a cause of another atom, but also deriving new conclusions from these causal-effect relations. This is expressive enough to capture informal rules like “if some agent's actions have been necessary to cause an event E then conclude atom caused(, E),” something that, to the best of our knowledge, had not been formalised in the literature. To this aim, we start from a first attempt that proposed extending the syntax of logic programs with so-called causal literals. These causal literals are expressions that can be used in rule bodies and allow inspecting the derivation of some atom A in the program with respect to some query function ψ. Depending on how these query functions are defined, we can model different types of causal relations such as sufficient, necessary or contributory causes, for instance. The initial approach was specifically focused on monotonic query functions. This was enough to cover sufficient cause-effect relations but, unfortunately, necessary and contributory are essentially non-monotonic. In this work, we define a semantics for non-monotonic causal literals showing that, not only extends the stable model semantics for normal logic programs, but also preserves many of its usual desirable properties for the extended syntax. Using this new semantics, we provide precise definitions of necessary and contributory causal relations and briefly explain their behaviour on a pair of typical examples from the Knowledge Representation literature.

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. 670 - 687
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

Bochman, A. and Lifschitz, V. 2015. Pearl's causality in a logical setting. In Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, January 25-30, 2015, Austin, Texas, USA., Bonet, B. and Koenig, S., Eds. AAAI Press, 1446–1452.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. Theory and Practice of Logic Programming (TPLP). (to appear).CrossRefGoogle 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. Proceedings, 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 International Conference, LPNMR 2013, Corunna, Spain, September 15-19, 2013. Proceedings, 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 International Conference, LPNMR 2015, Lexington, KY, USA, September 27-30, 2015. Proceedings, Calimeri, F., Ianni, G., and Truszczynski, M., Eds. Lecture Notes in Computer Science, vol. 9345. Springer, 250–264.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 International Workshop on Answer Set Programming and Other Computing Paradigms, ASPOCP 2015, Cork, Ireland, August 31, 2015. Extended version under revison for publication in Fundamenta Informaticae.Google Scholar
Fandinno, J. 2016. Deriving conclusions from non-monotonic cause-effect relations. CoRR abs/1608.00867.Google Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Logic Programming, Proceedings of the Fifth International Conference and Symposium, Seattle, Washington, August 15-19, Kowalski, R. A. and Bowen, K. A., Eds. MIT Press, 1070–1080.Google Scholar
Giunchiglia, E., Lee, J., Lifschitz, V., McCain, N. and Turner, H. 2004. Nonmonotonic causal theories. Artificial Intelligence 153, 1–2, 49–104.Google Scholar
Hall, N. 2007. Structural equations and causation. Philosophical Studies 132, 1, 109–136.Google Scholar
Halpern, J. Y. 2008. Defaults and normality in causal structures. In Principles of Knowledge Representation and Reasoning: Proceedings of the Eleventh International Conference, KR 2008, Sydney, Australia, September 16-19, 2008, Brewka, G. and Lang, J., Eds. AAAI Press, 198–208.Google Scholar
Halpern, J. Y. 2015. A modification of the halpern-pearl definition of causality. In Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, July 25-31, 2015, Yang, Q. and Wooldridge, M., Eds. AAAI Press, 3022–3033.Google Scholar
Halpern, J. Y. and Pearl, J. 2005. Causes and explanations: A structural-model approach. part I: Causes. British Journal for Philosophy of Science 56, 4, 843–887.Google Scholar
Hitchcock, C. and Knobe, J. 2009. Cause and norm. Journal of Philosophy 11, 587–612.Google Scholar
Hopkins, M. and Pearl, J. 2003. Clarifying the usage of structural models for commonsense causal reasoning. In Proceedings of the AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning. 83–89.Google Scholar
Lewis, D. K. 1973. Causation. The journal of philosophy 70, 17, 556–567.Google Scholar
Lifschitz, V. and Turner, H. 1994. Splitting a logic program. In Logic Programming, Proceedings of the Eleventh International Conference on Logic Programming, Santa Marherita Ligure, Italy, June 13-18, 1994, Hentenryck, P. V., Ed. MIT Press, 23–37.Google Scholar
Maudlin, T. 2004. Causation, counterfactuals, and the third factor. In Causation and Counterfactuals, Collins, J., Hall, E. J., and Paul, L. A., Eds. MIT Press.Google Scholar
McCarthy, J. 1987. Epistemological problems of artificial intelligence. Readings in artificial intelligence, 459.Google Scholar
McCarthy, J. 1998. Elaboration tolerance. In Proceedings of the Fourth Symposium on Logical Formalizations of Commonsense Reasoning, Common Sense. London, UK, 198–217.Google Scholar
McCarthy, J. and Hayes, P. 1969. Some philosophical problems from the standpoint of artificial intelligence. Machine Intelligence Journal 4, 463–512.Google 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, Seventh International Symposium, FLOPS 2004, Nara, Japan, April 7-9, 2004, Proceedings, 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.Google 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 Proceedings of the Fifth Workshop on Logic Programming Environments (LPE 1993), October 29-30, 1993, In conjunction with ILPS 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
van Emden, M. H. and Kowalski, R. A. 1976. The semantics of predicate logic as a programming language. Journal of the ACM (JACM) 23, 4, 733–742.Google Scholar
Vennekens, J. 2011. Actual causation in CP-logic. Theory and Practice of Logic Programming (TPLP) 11, 4–5, 647–662.Google Scholar