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Counterfactuals, Logic Programming and Agent Morality

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Applications of Formal Philosophy

Part of the book series: Logic, Argumentation & Reasoning ((LARI,volume 14))

Abstract

This paper supplies a computational model, via Logic Programming (LP), of counterfactual reasoning of autonomous agents with application to morality. Counterfactuals are conjectures about what would have happened had an alternative event occurred. The first contribution of the paper is showing how counterfactual reasoning is modeled using LP, benefiting from LP abduction and updating. The approach is inspired by Pearl’s structural causal model of counterfactuals, where causal direction and conditional reasoning are captured by inferential arrows of rules in LP. Herein, LP abduction hypothesizes background conditions from given evidence or observations, whereas LP updating frame these background conditions as a counterfactual’s context, and then imposes causal interventions on the program through defeasible LP rules. The second contribution it to apply counterfactuals to agent morality using this LP-based approach. We demonstrate its potential for specifying and querying moral issues, by examining viewpoints on moral permissibility via classic moral principles and examples taken from the literature. Application results were validated on a prototype implementing the approach on top of an integrated LP abduction and updating system supporting tabling.

Some main parts of this chapter are to be found adapted and integrated into a subsequently elaborated book by the same authors [47], comprising many materials from the authors’ previous works. This chapter defines and uses common notations and semantics as the book—which are standard. The chapter, however, is concentrated and self-contained; and especially geared to those concerned with just a logic formulation of counterfactuals in Logic Programming, and their use in computational morality, in a self-sufficient manner. The book is much more ample in scope, and combines a number of other computational logic aspects of morality, and of which counterfactual reasoning is just one, and where it is entwined with other facets present in the book. This chapter focusses only on the formulation, treatment and morality application of counterfactuals.

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Notes

  1. 1.

    In the sequel, unless otherwise specified, we generally write logic programs, or simply programs, to refer to normal logic programs.

  2. 2.

    In the sequel, we simply write interpretations and models to refer to Herbrand interpretations and Herbrand models, respectively.

  3. 3.

    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 [23].

  4. 4.

    This interpretation is in line with the corresponding English construct, cf. [27], commonly known as third conditionals.

  5. 5.

    This replacement of abducible \(A\not \in {E}\) with \({\mathsf {u}} \) in P and \(\mathcal {I} \) is an alternative but equivalent to adding \({A}\leftarrow {{\mathsf {u}}}\) into \(P\cup E\), as foreseen by Definition 12.

  6. 6.

    Both WFS and 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 \(a\leftarrow false\) enforces CWA in WCS. In this paper, positive loops are not needed and do not appear throughout examples we consider.

References

  1. Alferes, J. J., Brogi, A., Leite, J. A. & Pereira, L. M. (2002). Evolving logic programs. In Proceedings of European Conference on Artificial Intelligence (JELIA 2002)(Vol. 2424, pp. 50–61). LNCS, Springer.

    Google Scholar 

  2. Alferes, J. J., Leite, J. A., Pereira, L. M., Przymusinska, H., & Przymusinski, T. (2000). Dynamic updates of non-monotonic knowledge bases. Journal of Logic Programming, 45(1–3), 43–70.

    Article  Google Scholar 

  3. Alferes, J. J., & Pereira, L. M. (1996). Reasoning with logic programming (Vol. 1111). LNAI, Berlin: Springer.

    Google Scholar 

  4. Alferes, J. J., Pereira, L. M., & Swift, T. (2004). Abduction in well-founded semantics and generalized stable models via tabled dual programs. Theory and Practice of Logic Programming, 4(4), 383–428.

    Article  Google Scholar 

  5. Anderson, M. & Anderson, S. L. (2008). EthEl: Toward a principled ethical eldercare robot. In Proceedings AAAI 2008 Fall Symposium on AI in Eldercare.

    Google Scholar 

  6. Anderson, M., Anderson, S. L. & Armen, C. (2006). MedEthEx: a prototype medical ethics advisor. In Proceedings of 18th Innovative Applications of Artificial Intelligence Conference (IAAI 2006).

    Google Scholar 

  7. Aquinas, T. (1998). Summa Theologica II-II, Q.64, art. 7, Of Killing. In W. P. Baumgarth & R. J. Regan, Eds, On Law, Morality, and Politics. Hackett.

    Google Scholar 

  8. Baral, C. & Hunsaker, M. (2007). Using the probabilistic logic programming language P-log for causal and counterfactual reasoning and non-naive conditioning. In Proceedings of 20th International Joint Conference on Artificial Intelligence (IJCAI).

    Google Scholar 

  9. Bidoit, N., & Froidevaux, C. (1991). General logic databases and programs: default logic semantics and stratification. Journal of Information and Computation, 91(1), 15–54.

    Article  Google Scholar 

  10. Bringsjord, S., Arkoudas, K., & Bello, P. (2006). Toward a general logicist methodology for engineering ethically correct robots. IEEE Intelligent Systems, 21(4), 38–44.

    Article  Google Scholar 

  11. Byrne, R. M. J. (2007). The rational imagination: How people create alternatives to reality. Cambridge, MA: MIT Press.

    Google Scholar 

  12. Chockler, H., & Halpern, J. Y. (2004). Responsibility and blame: A structural-model approach. Journal of Artificial Intelligence Research, 22, 93–115.

    Google Scholar 

  13. Collins, J., Hall, N., & Paul, L. A. (Eds.). (2004). Causation and counterfactuals. Cambridge, MA: MIT Press.

    Google Scholar 

  14. Dell’Acqua, P., & Pereira, L. M. (2007). Preferential theory revision. Journal of Applied Logic, 5(4), 586–601.

    Article  Google Scholar 

  15. Dietz, E.-A., Hölldobler, S. & Pereira, L. M. (2015). On indicative conditionals. In Procs. 1st International Workshop on Semantic Technologies (IWOST) (Vol. 1339), CEUR Workshop Proceedings.

    Google Scholar 

  16. Epstude, K., & Roese, N. J. (2008). The functional theory of counterfactual thinking. Personality and Social Psychology Review, 12(2), 168–192.

    Article  Google Scholar 

  17. Fitting, M. (1985). A Kripke-Kleene semantics for logic programs. Journal of Logic Programming, 2(4), 295–312.

    Article  Google Scholar 

  18. Foot, P. (1967). The problem of abortion and the doctrine of double effect. Oxford Review, 5, 5–15.

    Google Scholar 

  19. Ganascia, J.-G. (2007). Modelling ethical rules of lying with answer set programming. Ethics and Information Technology, 9(1), 39–47.

    Article  Google Scholar 

  20. Gelfond, M. (1987). On stratified autoepistemic theories. In Proceedings of 6th National Conference on Artificial Intelligence (AAAI).

    Google Scholar 

  21. Gelfond, M. & Lifschitz, V. (1988). The stable model semantics for logic programming. In Proceedings of 5th International Logic Programming Conference. MIT Press.

    Google Scholar 

  22. Ginsberg, M. L. (1986). Counterfactuals. Artificial Intelligence, 30(1), 35–79.

    Article  Google Scholar 

  23. Grice, Paul. (1991). Studies in the way of words. Cambridge, MA: Harvard University Press.

    Google Scholar 

  24. Halpern, J. Y., & Hitchcock, C. (2015). Graded causation and defaults. British Journal for the Philosophy of Science, 66, 413–457.

    Article  Google Scholar 

  25. Han, T. A., Saptawijaya, A. & Pereira, L. M. (2012). Moral reasoning under uncertainty. In Proceedings of 18th International Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR) (Vol. 7180, pp. 212–227). LNCS, Springer.

    Google Scholar 

  26. Hauser, M., Cushman, F., Young, L., Jin, R. K., & Mikhail, J. (2007). A dissociation between moral judgments and justifications. Mind and Language, 22(1), 1–21.

    Article  Google Scholar 

  27. Hewings, M. (2013). Advanced grammar in use with answers: A self-study reference and practice book for advanced learners of english. New York, NY: Cambridge University Press.

    Google Scholar 

  28. Hoerl, C., McCormack, T., & Beck, S. R. (Eds.). (2011). Understanding counterfactuals, understanding causation: Issues in philosophy and psychology. Oxford, UK: Oxford University Press.

    Google Scholar 

  29. Hölldobler, S. & Kencana Ramli, C. D. P. (2009). Logic programs under three-valued Łukasiewicz semantics. In Proceedings of 25th International Conference on Logic Programming (ICLP) (Vol. 5649, pp. 464–478). LNCS, Springer.

    Google Scholar 

  30. Kakas, A., Kowalski, R., & Toni, F. (1992). Abductive logic programming. Journal of Logic and Computation, 2(6), 719–770.

    Article  Google Scholar 

  31. Kamm, F. M. (2006). Intricate ethics: Rights, responsibilities, and permissible harm. Oxford, UK: Oxford University Press.

    Google Scholar 

  32. Kleiman-Weiner, M., Gerstenberg, T., Levine, S. & Tenenbaum, J. B. (2015). Inference of intention and permissibility in moral decision making. In Proceedings of 37th Annual Conference of the Cognitive Science Society.

    Google Scholar 

  33. Kowalski, R. (2011). Computational logic and human thinking: How to be artificially intelligent. New York, NY: Cambridge University Press.

    Book  Google Scholar 

  34. Lewis, D. (1973). Counterfactuals. Cambridge, MA: Harvard University Press.

    Google Scholar 

  35. Markman, K. D., Gavanski, I., Sherman, S. J., & McMullen, M. N. (1993). The mental simulation of better and worse possible worlds. Journal of Experimental Social Psychology, 29, 87–109.

    Article  Google Scholar 

  36. McCloy, R., & Byrne, R. M. J. (2000). Counterfactual thinking about controllable events. Memory and Cognition, 28, 1071–1078.

    Article  Google Scholar 

  37. McCormack, T., Frosch, C., & Burns, P. (2011). The relationship between children’s causal and counterfactual judgements. In C. Hoerl, T. McCormack, & S. R. Beck (Eds.), Understanding Counterfactuals., Understanding causation Oxford, UK: Oxford University Press.

    Google Scholar 

  38. McIntyre, A. (2004). Doctrine of double effect. In E. N. Zalta (Eds.), The Stanford Encyclopedia of Philosophy. Center for the Study of Language and Information, Stanford University (Fall 2011 edition) http://plato.stanford.edu/archives/fall2011/entries/double-effect/.

  39. Migliore, S., Curcio, G., Mancini, F., & Cappa, S. F. (2014). Counterfactual thinking in moral judgment: an experimental study. Frontiers in Psychology, 5, 451.

    Article  Google Scholar 

  40. Otsuka, M. (2008). Double effect, triple effect and the trolley problem: Squaring the circle in looping cases. Utilitas, 20(1), 92–110.

    Article  Google Scholar 

  41. Pearl, J. (2009). Causality: Models reasoning and inference. Cambridge, MA: Cambridge University Press.

    Book  Google Scholar 

  42. Pereira, L. M., Aparício, J. N. & Alferes, J. J. (1991). Counterfactual reasoning based on revising assumptions. In Proceedings of International Symposium on Logic Programming (ILPS 1991) (pp. 566–577). MIT Press.

    Google Scholar 

  43. Pereira, L. M., Aparício, J. N. & Alferes, J. J.(1991). Hypothetical reasoning with well founded semantics. In Proceedings of 3rd Scandinavian Conference on Artificial Intelligence. IOS Press.

    Google Scholar 

  44. Pereira, L. M., Dell’Acqua, P., Pinto, A. M. & Lopes, G. (2013). Inspecting and preferring abductive models. In K. Nakamatsu & L. C. Jain (Eds.), The Handbook on Reasoning-Based Intelligent Systems (pp. 243–274). World Scientific Publishers.

    Google Scholar 

  45. Pereira, L. M., Dietz, E.-A. & Hölldobler, S. (2016). Abductive framework for counterfactual reasoning in logic programming. Available from http://userweb.fct.unl.pt/~lmp/publications/online-papers/counterfactuals.pdf.

  46. Pereira, L. M. & Saptawijaya, A. (2011). Modelling morality with prospective logic. In M. Anderson & S. L. Anderson (Eds.), Machine Ethics (pp. 398–421) Cambridge, U. K.

    Google Scholar 

  47. Pereira, L. M. & Saptawijaya, A. (2011). Programming Machine Ethics, volume 26 of Studies in Applied Philosophy, Epistemology and Rational Ethics. Springer, Switzerland, 2016.

    Google Scholar 

  48. Powers, T. M. (2006). Prospects for a Kantian machine. IEEE Intelligent Systems, 21(4), 46–51.

    Article  Google Scholar 

  49. Przymusinska, H. & Przymusinski, T. C. (1990). Semantic issues in deductive databases and logic programs. In Formal Techniques in Artificial Intelligence: A Sourcebook (pp 321–367). North-Holand.

    Google Scholar 

  50. Przymusinski, T. C. (1989a). Every logic program has a natural stratification and an iterated least fixed point model. In Proceedings of 8th ACM Symposium on Principles Of Database Systems (PODS) (pp. 11–21).

    Google Scholar 

  51. Przymusinski, T. C. (1989b). Three-valued non-monotonics formalisms and logic programming. In Proceedings of 1st International Conference on Principles of Knowledge Representation and Reasoning (KR).

    Google Scholar 

  52. Roese, N. J. (1997). Counterfactual thinking. Psychological Bulletin, 121(1), 133–148.

    Article  Google Scholar 

  53. Saptawijaya, A. & Pereira, L. M. (2013). Incremental tabling for query-driven propagation of logic program updates. In Proceedings of 19th International Conference on Logic Programming, Artificial Intelligence and Reasoning (LPAR) (Vol. 8312, pp. 694–709). LNCS, Springer.

    Google Scholar 

  54. Saptawijaya, A. & Pereira, L. M. (2014a). Joint tabling of logic program abductions and updates (Technical Communication of ICLP 2014). Theory and Practice of Logic Programming, 14(4–5). Online Supplement. Available from http://arxiv.org/abs/1405.2058.

  55. Saptawijaya, A. & Pereira, L. M. (2014b). Towards modeling morality computationally with logic programming. In PADL 2014 (Vol. 8324, pp. 104–119). Springer.

    Google Scholar 

  56. Scanlon, T. M. (1998). What we owe to each other. Cambridge, MA: Harvard University Press.

    Google Scholar 

  57. Scanlon, T. M. (2008). Moral dimensions: Permissibility, meaning blame. Cambridge, MA: Harvard University Press.

    Book  Google Scholar 

  58. Swift, T., & Warren, D. S. (2012). XSB: Extending Prolog with tabled logic programming. Theory and Practice of Logic Programming, 12(1–2), 157–187.

    Google Scholar 

  59. Tetlock, P. E., Visser, P. S., Singh, R., Polifroni, M., Scott, A., Elson, S. B., et al. (2007). People as intuitive prosecutors: The impact of social-control goals on attributions of responsibility. Journal of Experimental Social Psychology, 43, 195–209.

    Article  Google Scholar 

  60. Thomson, J. J. (1985). The trolley problem. The Yale Law Journal, 279, 1395–1415.

    Article  Google Scholar 

  61. van Emden, M. H., & Kowalski, R. (1976). The semantics of predicate logic as a programming language. Journal of the ACM, 4(23), 733–742.

    Article  Google Scholar 

  62. van Gelder, A., Ross, K. A., & Schlipf, J. S. (1991). The well-founded semantics for general logic programs. Journal of the ACM, 38(3), 620–650.

    Google Scholar 

  63. Vennekens, J., Bruynooghe, M. & Denecker, M. (2010). Embracing events in causal modeling: Interventions and counterfactuals in CP-logic. In JELIA 2010 (Vol. 6341, pp. 313–325). LNCS. Springer.

    Google Scholar 

  64. Weiner, B. (1995). Judgments of responsibility: A foundation for a theory of social conduct. New York, NY: The Guilford Press.

    Google Scholar 

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Acknowledgements

We thank the anonymous reviewers for their constructive comments and suggestions. Both authors acknowledge the support from Fundação para a Ciência e a Tecnologia (FCT/MEC) NOVA LINCS PEst UID/CEC/04516/2013. Ari Saptawijaya acknowledges the support from FCT/MEC with the doctoral grant SFRH/BD/72795/2010. We thank Emmanuelle-Anna Dietz for the fruitful discussions.

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Authors and Affiliations

  1. NOVA Laboratory for Computer Science and Informatics (NOVA LINCS), Universidade Nova de Lisboa, Lisbon, Portugal

    Luís Moniz Pereira

  2. Faculty of Computer Science, Universitas Indonesia, Depok, Jawa Barat, Indonesia

    Ari Saptawijaya

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  1. Luís Moniz Pereira
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  2. Ari Saptawijaya
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Correspondence to Ari Saptawijaya .

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  1. Institute of Philosophy, Sociology and Journalism, University of Gdansk, Poland and , Centre for Logic and Philosophy of Science, Ghent University,, Ghent, Belgium

    Rafał Urbaniak

  2. Dalhousie University , Halifax, Nova Scotia, Canada

    Gillman Payette

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Pereira, L.M., Saptawijaya, A. (2017). Counterfactuals, Logic Programming and Agent Morality. In: Urbaniak, R., Payette, G. (eds) Applications of Formal Philosophy. Logic, Argumentation & Reasoning, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-58507-9_3

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