Abstract
Counterfactuals capture the process of reasoning about a past event that did not occur, namely what would have happened had this event occurred; or, vice-versa, to reason about an event that did occur but what if it had not. In this chapter, we innovatively make use of LP abduction and updating in an implemented procedure for evaluating counterfactuals, taking the established structural approach of Pearl as reference. Our approach concentrates on pure non-probabilistic counterfactual reasoning in LP, resorting to abduction and updating, in order to determine the logical validity of counterfactuals under the Well-Founded Semantics. Nevertheless, the approach is adaptable to other semantics, too. Even though the LP technique introduced in this chapter is relevant for modeling counterfactual moral reasoning, its use is general, not specific to morality.
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Notes
- 1.
Both the Well-Founded Semantics (WFS) and the Weak Completion Semantics (WCS) are 3-valued semantics that differ in dealing with close world assumption (CWA) and rules with positive loops (e.g., \(p\leftarrow p\)). WFS enforces CWA, i.e., atom a that has no rule is interpreted as false, whereas in WCS undefined. Nevertheless, they can be transformed one to another: adding rules \(a\leftarrow u\) and \(u\leftarrow not\ u\) for a reserved atom u renders a unknown in WFS; alternatively, adding \(a\leftarrow \bot \), where \(\bot \) is false, enforces CWA in WCS. In this book, positive loops are not needed and do not appear throughout examples we consider.
- 2.
We assume that people are using counterfactuals to convey truly relevant information rather than to fabricate arbitrary subjunctive conditionals (e.g., “If I had been watching, then I would have seen the cheese on the moon melt during the eclipse”). Otherwise, implicit observations must simply be made explicit observations, to avoid natural language conundrums or ambiguities [10].
- 3.
This interpretation is in line with the corresponding English construct, cf. [12], commonly known as third conditionals.
- 4.
This replacement of abducible \(A\not \in {E}\) with \({\mathbf {\mathsf{{u}}}} \) in P and \(\mathcal {IC} \) is an alternative but equivalent to adding \({A}\leftarrow {{\mathbf {\mathsf{{u}}}}}\) into \(P\cup E\), as foreseen by Definition 4.15.
References
Anderson, A.R., Belnap, N.: Entailment: The Logic of Relevance and Necessity, vol. I. Princeton University Press, New Jersey (1975)
Anderson, A., Belnap, N., Dunn, J.: Entailment: The Logic of Relevance and Necessity, vol. II. Princeton University Press, New Jersey (1992)
Baral, C., Hunsaker, M.: Using the probabilistic logic programming language P-log for causal and counterfactual reasoning and non-naive conditioning. In: Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI) (2007)
Byrne, R.M.J.: The Rational Imagination: How People Create Alternatives to Reality. MIT Press, Cambridge (2007)
Collins, J., Hall, N., Paul, L.A. (eds.): Causation and Counterfactuals. MIT Press, Cambridge (2004)
Dietz, E.A., Hölldobler, S., Pereira, L.M.: On conditionals. In: Proceedings of Global Conference on Artificial Intelligence (GCAI 2015) (2015)
Dietz, E.A., Hölldobler, S., Pereira, L.M.: On indicative conditionals. In: Proceedings of the 1st International Workshop on Semantic Technologies (IWOST), CEUR Workshop Proceedings, vol. 1339 (2015)
Epstude, K., Roese, N.J.: The functional theory of counterfactual thinking. Pers. Soc. Psychol. Rev. 12(2), 168–192 (2008)
Ginsberg, M.L.: Counterfactuals. Artif. Intell. 30(1), 35–79 (1986)
Grice, P.: Studies in the Way of Words. Harvard University Press, Cambridge (1991)
Halpern, J.Y., Hitchcock, C.: Graded causation and defaults. B. J. Philos. Sci. 66, 413–457 (2015)
Hewings, M.: Advanced Grammar in Use with Answers: A Self-Study Reference and Practice Book for Advanced Learners of English. Cambridge University Press, New York (2013)
Hölldobler, S., Ramli, C.D.P.K.: Logic programs under three-valued Łukasiewicz semantics. In: Proceedings of the 25th International Conference on Logic Programming (ICLP), LNCS, vol. 5649, pp. 464–478. Springer, Berlin (2009)
Kleiman-Weiner, M., Gerstenberg, T., Levine, S., Tenenbaum, J.B.: Inference of intention and permissibility in moral decision making. In: Proceedings 37th Annual Conference of the Cognitive Science Society (2015)
Lewis, D.: Counterfactuals. Harvard University Press, Cambridge (1973)
Markman, K.D., Gavanski, I., Sherman, S.J., McMullen, M.N.: The mental simulation of better and worse possible worlds. J. Exp. Soc. Psychol. 29, 87–109 (1993)
McCloy, R., Byrne, R.M.J.: Counterfactual thinking about controllable events. Mem. Cognit. 28, 1071–1078 (2000)
Migliore, S., Curcio, G., Mancini, F., Cappa, S.F.: Counterfactual thinking in moral judgment: an experimental study. Front. Psychol. 5, 451 (2014)
Pearl, J.: Causality: Models. Reasoning and Inference. Cambridge University Press, Cambridge (2009)
Pereira, L.M., Aparício, J.N., Alferes, J.J.: Counterfactual reasoning based on revising assumptions. In: Proceedings of the International Symposium on Logic Programming (ILPS 1991), pp. 566–577. MIT Press (1991)
Pereira, L.M., Aparício, J.N., Alferes, J.J.: Hypothetical reasoning with well founded semantics. In: Proceedings of the 3rd Scandinavian Conference on Artificial Intelligence. IOS Press (1991)
Pereira, L.M., Dietz, E.A., Hölldobler, S.: An abductive counterfactual reasoning approach in logic programming (2015). Available from http://goo.gl/bx0mIZ
Roese, N.J.: Counterfactual thinking. Psychol. Bull. 121(1), 133–148 (1997)
Vennekens, J., Bruynooghe, M., Denecker, M.: Embracing events in causal modeling: Interventions and counterfactuals in CP-logic. In: JELIA 2010, LNCS, vol. 6341, pp. 313–325. Springer (2010)
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Pereira, L.M., Saptawijaya, A. (2016). Counterfactuals in Logic Programming. In: Programming Machine Ethics. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-29354-7_6
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