Abstract
A well-studied trait of human reasoning and decision-making is the ability to not only make decisions in the presence of contradictions, but also to explain why a decision was made, in particular if a decision deviates from what is expected by an inquirer who requests the explanation. In this paper, we examine this phenomenon, which has been extensively explored by behavioral economics research, from the perspective of symbolic artificial intelligence. In particular, we introduce four levels of intelligent reasoning in face of contradictions, which we motivate from a microeconomics and behavioral economics perspective. We relate these principles to symbolic reasoning approaches, using abstract argumentation as an exemplary method. This allows us to ground the four levels in a body of related previous and ongoing research, which we use as a point of departure for outlining future research directions.
Keywords
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- 1.
Let us highlight that we do not introduce the so-called AGM postulates [2] here, because the success postulate stipulates (colloquially speaking) that “new” logical formulas are always added to the belief base and never rejected; however, we assume that, intuitively, an intelligent agent should be able to reject new beliefs under some circumstances.
- 2.
Less formal models of human decision-making and reasoning have been, of course, subject of in-depth study for much longer. Indeed, the management of contradictions that is at the center of this paper is also the subject of the Shev Shema’tata, a book on the treatment of doubt in Rabbinic law, written at the turn from the 18th to the 19th century [18].
- 3.
Indeed, empirical studies (conducted decades after the publication of Simon’s paper) show that humans sometimes do exactly this [6].
- 4.
Note that this statement precedes a defense of the approach it describes.
- 5.
- 6.
More semantics exist, some of which address well-known issues with the semantics whose definitions we provide in this paper. However, we consider an in-depth overview of argumentation semantics out-of-scope.
- 7.
Note that this would be a violation of the language independence principle.
- 8.
In these works, we name the principle weak reference independence.
- 9.
Let us note that stage semantics does not generally establish consistent preferences, given any argumentation framework and any of its normal expansions, see [22].
- 10.
Given an argumentation framework and a semantics’ extension of this framework, the undecided arguments are all arguments that are neither in the extension, nor attacked by any of the arguments in the extension.
- 11.
This is a constructed example that does not fully reflect real-world legal reasoning.
- 12.
This notion is reflected by loop-busting approaches that have been proposed in the context of formal argumentation and that are based on Talmudic logic [1].
- 13.
For the sake of conciseness we do not introduce CF2 semantics in this paper; the semantics is introduced by Baroni et al. in [5].
References
Abraham, M., Gabbay, D.M., Schild, U.J.: The handling of loops in talmudic logic, with application to odd and even loops in argumentation. HOWARD-60: a Festschrift on the Occasion of Howard Barringer’s 60th Birthday (2014)
Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change: partial meet contraction and revision functions. J. Symbolic Logic 50(2), 510–530 (1985)
Anjomshoae, S., Najjar, A., Calvaresi, D., Främling, K.: Explainable agents and robots: results from a systematic literature review. In: Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems. AAMAS 2019, pp. 1078–1088. International Foundation for Autonomous Agents and Multiagent Systems, Richland, SC (2019)
Baroni, P., Giacomin, M.: On principle-based evaluation of extension-based argumentation semantics. Artif. Intell. 171(10), 675–700 (2007). Argumentation in Artificial Intelligence. https://doi.org/10.1016/j.artint.2007.04.004, http://www.sciencedirect.com/science/article/pii/S0004370207000744
Baroni, P., Giacomin, M., Guida, G.: SCC-recursiveness: a general schema for argumentation semantics. Artif. Intell. 168(1), 162–210 (2005). https://doi.org/10.1016/j.artint.2005.05.006
Bateman, I., Munro, A., Rhodes, B., Starmer, C., Sugden, R.: A test of the theory of reference-dependent preferences. Q. J. Econ. 112(2), 479–505 (1997)
Baumann, R., Brewka, G.: Expanding argumentation frameworks: enforcing and monotonicity results. COMMA 10, 75–86 (2010)
Cabrio, E., Villata, S.: Five years of argument mining: a data-driven analysis. In: Proceedings of the 27th International Joint Conference on Artificial Intelligence. IJCAI 2018, pp. 5427–5433. AAAI Press (2018)
Calegari, R., Riveret, R., Sartor, G.: The burden of persuasion in structured argumentation. In: Proceedings of the Nineteenth International Conference on Artificial Intelligence and Law. ICAIL 2021, Association for Computing Machinery, New York, NY, USA (2021)
Cramer, M., Guillaume, M.: Empirical cognitive study on abstract argumentation semantics. Front. Artif. Intell. Appl. 305, 413–424 (2018). https://ebooks.iospress.nl/volume/computational-models-of-argument-proceedings-of-comma-2018
Cramer, M., Guillaume, M.: Empirical study on human evaluation of complex argumentation frameworks. In: Calimeri, F., Leone, N., Manna, M. (eds.) JELIA 2019. LNCS (LNAI), vol. 11468, pp. 102–115. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-19570-0_7
Cramer, M., van der Torre, L.: SCF2-an argumentation semantics for rational human judgments on argument acceptability. In: Proceedings of the 8th Workshop on Dynamics of Knowledge and Belief (DKB-2019) and the 7th Workshop KI\(\backslash \) & Kognition (KIK-2019) co-located with 44nd German Conference on Artificial Intelligence (KI 2019), Kassel, Germany, pp. 24–35 (2019)
Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell. 77(2), 321–357 (1995)
Gabbay, D.M.: Theoretical Foundations for Non-Monotonic Reasoning in Expert Systems. In: Apt, K.R. (ed.) Logics and Models of Concurrent Systems. NATO ASI Series (Series F: Computer and Systems Sciences), vol. 13, pp. 439–457. Springer, Heidelberg (1985). https://doi.org/10.1007/978-3-642-82453-1_15
Garcez, A.S.D., Lamb, L.C., Gabbay, D.M.: Neural-symbolic learning systems. In: Lamb, L.C. (ed.) Neural-Symbolic Cognitive Reasoning. COGTECH, Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-540-73246-4_4
Geffner, H.: Model-free, model-based, and general intelligence. In: Proceedings of the 27th International Joint Conference on Artificial Intelligence. IJCAI 2018, pp. 10–17. AAAI Press (2018)
Haidt, J.: The emotional dog and its rational tail: a social intuitionist approach to moral judgment. Psychol. Rev. 108(4), 814 (2001)
Jacobs, L.: Rabbi aryeh laib heller’s theological introduction to his “shev shema’tata”. Modern Judaism 1(2), 184–216 (1981). http://www.jstor.org/stable/1396060
Kahneman, D.: Maps of bounded rationality: psychology for behavioral economics. Am. Econ. Rev. 93(5), 1449–1475 (2003)
Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47(2), 263–291 (1979)
Kampik, T., Gabbay, D.: Towards DIARG: an argumentation-based dialogue reasoning engine. In: SAFA@ COMMA, pp. 14–21 (2020)
Kampik, T., Nieves, J.C.: Abstract argumentation and the rational man. J. Logic Comput. 31(2), 654–699 (2021). https://doi.org/10.1093/logcom/exab003
Landsburg, S.: The Armchair Economist (revised and updated May 2012): Economics and Everyday Life. Free Press (2007)
Lehmann, D., Magidor, M.: What does a conditional knowledge base entail? Artif. Intell. 55(1), 1–60 (1992). http://www.sciencedirect.com/science/article/pii/000437029290041U
Osborne, M.J., Rubinstein, A.: Models in Microeconomic Theory. Open Book Publishers, Cambridge (2020). https://doi.org/10.11647/OBP.0204
Prakken, H., Sartor, G.: A logical analysis of burdens of proof. In: Legal Evidence and Proof: Statistics, Stories, Logic, pp. 223–253 (2009)
Rubinstein, A.: Modeling Bounded Rationality. MIT Press, Cambridge (1998)
Shao, C., Ciampaglia, G.L., Varol, O., Yang, K.C., Flammini, A., Menczer, F.: The spread of low-credibility content by social bots. Nat. Commun. 9(1), 1–9 (2018)
Simon, H.A.: A behavioral model of rational choice. Q. J. Econ. 69(1), 99–118 (1955). https://doi.org/10.2307/1884852
van der Torre, L., Vesic, S.: The principle-based approach to abstract argumentation semantics. IfCoLog J. Logics Appl. 4(8), 34 (2017)
Turing, A.M.: Computing machinery and intelligence. In: Epstein, R., Roberts, G., Beber, G. (eds.) Parsing the Turing Test, pp. 23–65. Springer, Dordrecht (2009). https://doi.org/10.1007/978-1-4020-6710-5_3
Verheij, B.: Two approaches to dialectical argumentation: admissible sets and argumentation stages. Proc. NAIC 96, 357–368 (1996)
Zhong, Q., Fan, X., Luo, X., Toni, F.: An explainable multi-attribute decision model based on argumentation. Expert Syst. Appl. 117, 42–61 (2019). https://doi.org/10.1016/j.eswa.2018.09.038, http://www.sciencedirect.com/science/article/pii/S0957417418306158
Acknowledgments
The authors thank Amro Najjar, Michele Persiani, and the anonymous reviewers for their useful feedback. This work was partially supported by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation.
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Kampik, T., Gabbay, D. (2021). Explainable Reasoning in Face of Contradictions: From Humans to Machines. In: Calvaresi, D., Najjar, A., Winikoff, M., Främling, K. (eds) Explainable and Transparent AI and Multi-Agent Systems. EXTRAAMAS 2021. Lecture Notes in Computer Science(), vol 12688. Springer, Cham. https://doi.org/10.1007/978-3-030-82017-6_17
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