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On Complexity and Generality of Contrary Prioritized Defeasible Theory

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New Frontiers in Artificial Intelligence (JSAI-isAI 2022)

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Abstract

This paper studies defeasible logic for representing legal theories. In defeasible logic, a literal can be ambiguous since a theory can support both the literal and its contrary. There have been several policies in handling ambiguities but choosing a policy is under judges’ discretion, which is unpredictable and possibly contradicts the legislators’ intentions. To prevent such a problem, this paper studies contrary prioritization, which restricts a defeasible theory to prioritize all pairs of rules in which heads are contrary to each other. This paper analyzes the complexity of contrary prioritization and the generality of contrary prioritized defeasible theories in the translations between such defeasible theories and stratified logic programs. This paper presents that contrary prioritization requires an effort of finding a correct assignment of the priorities between contrary pairs, and the effort makes the problem of contrary prioritization NP-complete. Furthermore, every contrary prioritized defeasible theory can be translated to a stratified logic program and vice versa. Hence, a contrary prioritized defeasible theory is as general as a stratified logic program.

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Notes

  1. 1.

    Generally, > in defeasible logic is not required to be transitive. However, in this paper, we assume the transitivity to ensure that a closure of the priority is acyclic.

  2. 2.

    This is a simplified representation for ease of exposition. A proper representation requires considering deontic modalities and strengths of permission cf. [13].

References

  1. Antoniou, G.: Relating defeasible logic to extended logic programs. In: Vlahavas, I.P., Spyropoulos, C.D. (eds.) SETN 2002. LNCS (LNAI), vol. 2308, pp. 54–64. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46014-4_6

    Chapter  Google Scholar 

  2. Antoniou, G., Billington, D., Governatori, G., Maher, M.J.: Embedding defeasible logic into logic programming. Theory Pract. Logic Program. 6(6), 703–735 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Antoniou, G., Maher, M.J., Billington, D.: Defeasible logic versus logic programming without negation as failure. J. Log. Program. 42(1), 47–57 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. Apt, K.R., Blair, H.A., Walker, A.: Towards a theory of declarative knowledge. In: Foundations of Deductive Databases and Logic Programming, pp. 89–148. Morgan Kaufmann, Burlington (1988)

    Google Scholar 

  5. Araszkiewicz, M., Płeszka, K.: The concept of normative consequence and legislative discourse. In: Araszkiewicz, M., Płeszka, K. (eds.) Logic in the Theory and Practice of Lawmaking. Legisprudence Library, pp. 253–297. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19575-9_10

    Chapter  Google Scholar 

  6. Billington, D., Antoniou, G., Governatori, G., Maher, M.: An inclusion theorem for defeasible logics. ACM Trans. Comput. Log. (TOCL) 12(1), 1–27 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Brewka, G.: On the relationship between defeasible logic and well-founded semantics. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 121–132. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45402-0_9

    Chapter  MATH  Google Scholar 

  8. Fungwacharakorn, W., Tsushima, K., Satoh, K.: On semantics-based minimal revision for legal reasoning. In: Proceedings of the 18th International Conference on Artificial Intelligence and Law - ICAIL 2021. ACM, New York (2021)

    Google Scholar 

  9. Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R., Bowen, Kenneth (eds.) Proceedings of International Logic Programming Conference and Symposium, vol. 88, pp. 1070–1080. MIT Press, Cambridge (1988)

    Google Scholar 

  10. Governatori, G., Maher, M.J.: Annotated defeasible logic. Theory Pract. Logic Program. 17(5–6), 819–836 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  11. Governatori, G., Maher, M.J., Antoniou, G., Billington, D.: Argumentation semantics for defeasible logic. J. Log. Comput. 14(5), 675–702 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Governatori, G., Olivieri, F., Cristani, M., Scannapieco, S.: Revision of defeasible preferences. Int. J. Approximate Reasoning 104, 205–230 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  13. Governatori, G., Olivieri, F., Rotolo, A., Scannapieco, S.: Computing strong and weak permissions in defeasible logic. J. Philos. Log. 42(6), 799–829 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  14. Governatori, G., Olivieri, F., Scannapieco, S., Cristani, M.: Superiority based revision of defeasible theories. In: Dean, M., Hall, J., Rotolo, A., Tabet, S. (eds.) RuleML 2010. LNCS, vol. 6403, pp. 104–118. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16289-3_10

    Chapter  Google Scholar 

  15. Governatori, G., Olivieri, F., Scannapieco, S., Cristani, M.: The hardness of revising defeasible preferences. In: Bikakis, A., Fodor, P., Roman, D. (eds.) RuleML 2014. LNCS, vol. 8620, pp. 168–177. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09870-8_12

    Chapter  Google Scholar 

  16. Governatori, G., Sartor, G.: Burdens of proof in monological argumentation. In: Legal Knowledge and Information Systems, pp. 57–66. IOS Press (2010)

    Google Scholar 

  17. Ito, S.: Basis of Ultimate Facts. Yuhikaku (2001)

    Google Scholar 

  18. Kunen, K.: Signed data dependencies in logic programs. Technical report, University of Wisconsin-Madison Department of Computer Sciences (1987)

    Google Scholar 

  19. Maher, M.J.: Propositional defeasible logic has linear complexity. Theory Pract. Logic Program. 1(6), 691–711 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  20. Maranhão, J.S.A.: Conservative coherentist closure of legal systems. In: Araszkiewicz, M., Płeszka, K. (eds.) Logic in the Theory and Practice of Lawmaking. LL, vol. 2, pp. 115–136. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19575-9_4

    Chapter  Google Scholar 

  21. McCarty, L.T.: Some arguments about legal arguments. In: Proceedings of the 6th International Conference on Artificial Intelligence and Law, pp. 215–224 (1997)

    Google Scholar 

  22. Merigoux, D., Chataing, N., Protzenko, J.: Catala: a programming language for the law. In: International Conference on Functional Programming. Proceedings of the ACM on Programming Languages, pp. 1–29. ACM, Virtual, South Korea (2021)

    Google Scholar 

  23. Nute, D.: Defeasible logic. In: Bartenstein, O., Geske, U., Hannebauer, M., Yoshie, O. (eds.) INAP 2001. LNCS (LNAI), vol. 2543, pp. 151–169. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36524-9_13

    Chapter  Google Scholar 

  24. Prakken, H.: Logical Tools for Modelling Legal Argument: A Study of Defeasible Reasoning in Law. Kluwer Academic Publishers (1997)

    Google Scholar 

  25. Prakken, H., Sartor, G.: Formalising arguments about the burden of persuasion. In: Proceedings of the 11th International Conference on Artificial Intelligence and Law, pp. 97–106 (2007)

    Google Scholar 

  26. Prakken, H., Wyner, A., Bench-Capon, T., Atkinson, K.: A formalization of argumentation schemes for legal case-based reasoning in ASPIC+. J. Log. Comput. 25(5), 1141–1166 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  27. Przymusinska, H., Przymusinski, T.: Semantic issues in deductive databases and logic programs. In: Formal Techniques in Artificial Intelligence. Citeseer (1990)

    Google Scholar 

  28. Rotolo, A., Roversi, C.: Constitutive rules and coherence in legal argumentation: the case of extensive and restrictive interpretation. In: Dahlman, C., Feteris, E. (eds.) Legal Argumentation Theory: Cross-Disciplinary Perspectives. Law and Philosophy Library, vol. 102, pp. 163–188. Springer, Dordrecht (2013). https://doi.org/10.1007/978-94-007-4670-1_11

    Chapter  Google Scholar 

  29. Satoh, K., et al.: PROLEG: an implementation of the presupposed ultimate fact theory of Japanese civil code by PROLOG technology. In: Onada, T., Bekki, D., McCready, E. (eds.) JSAI-isAI 2010. LNCS (LNAI), vol. 6797, pp. 153–164. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25655-4_14

    Chapter  Google Scholar 

  30. Satoh, K., Kogawa, T., Okada, N., Omori, K., Omura, S., Tsuchiya, K.: On generality of PROLEG knowledge representation. In: Proceedings of the 6th International Workshop on Juris-Informatics (JURISIN 2012), Miyazaki, Japan, pp. 115–128 (2012)

    Google Scholar 

  31. Satoh, K., Kubota, M., Nishigai, Y., Takano, C.: Translating the Japanese presupposed ultimate fact theory into logic programming. In: Proceedings of the 2009 Conference on Legal Knowledge and Information Systems: JURIX 2009: The Twenty-Second Annual Conference, pp. 162–171. IOS Press, Amsterdam (2009)

    Google Scholar 

  32. Satoh, K., Tojo, S., Suzuki, Y.: Formalizing a switch of burden of proof by logic programming. In: Proceedings of the First International Workshop on Juris-Informatics (JURISIN 2007), pp. 76–85 (2007)

    Google Scholar 

  33. Sergot, M.J., Sadri, F., Kowalski, R.A., Kriwaczek, F., Hammond, P., Cory, H.T.: The British nationality act as a logic program. Commun. ACM 29(5), 370–386 (1986)

    Article  Google Scholar 

  34. Sherman, D.M.: A prolog model of the income tax act of Canada. In: Proceedings of the 1st International Conference on Artificial Intelligence and Law, pp. 127–136. Association for Computing Machinery, New York (1987)

    Google Scholar 

  35. Stein, L.A.: Resolving ambiguity in nonmonotonic inheritance hierarchies. Artif. Intell. 55(2–3), 259–310 (1992)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors would like to thank all anonymous reviewers for insightful suggestions and comments. This work was supported by JSPS KAKENHI Grant Numbers, JP17H06103 and JP19H05470 and JST, AIP Trilateral AI Research, Grant Number JPMJCR20G4.

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Authors and Affiliations

  1. National Institute of Informatics, Sokendai University, Tokyo, Japan

    Wachara Fungwacharakorn, Kanae Tsushima & Ken Satoh

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  1. Wachara Fungwacharakorn
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  2. Kanae Tsushima
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  3. Ken Satoh
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Correspondence to Wachara Fungwacharakorn .

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Editors and Affiliations

  1. Tokyo Metropolitan University, Tokyo, Japan

    Yasufumi Takama

  2. Kansai University, Osaka, Japan

    Katsutoshi Yada

  3. National Institute of Informatics, Tokyo, Japan

    Ken Satoh

  4. Chiba University, Chiba, Japan

    Sachiyo Arai

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Fungwacharakorn, W., Tsushima, K., Satoh, K. (2023). On Complexity and Generality of Contrary Prioritized Defeasible Theory. In: Takama, Y., Yada, K., Satoh, K., Arai, S. (eds) New Frontiers in Artificial Intelligence. JSAI-isAI 2022. Lecture Notes in Computer Science(), vol 13859. Springer, Cham. https://doi.org/10.1007/978-3-031-29168-5_2

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  • DOI: https://doi.org/10.1007/978-3-031-29168-5_2

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