Abductive Logic Programming for Normative Reasoning and Ontologies

  • Marco Gavanelli
  • Evelina Lamma
  • Fabrizio Riguzzi
  • Elena Bellodi
  • Zese Riccardo
  • Giuseppe Cota
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10091)

Abstract

Abductive Logic Programming (ALP) has been exploited to formalize societies of agents, commitments and norms, taking advantage from ALP operational support as a (static or dynamic) verification tool. In [7], the most common deontic operators (obligation, prohibition, permission) are mapped into the abductive expectations of an ALP framework for agent societies. Building upon such correspondence, in [5], authors introduced \(Deon^{+}\), a language where obligation and prohibition deontic operators are enriched with quantification over time, by means of ALP and Constraint Logic Programming (CLP).

In recent work [30, 31], we have shown that the same ALP framework can be suitable to represent Datalog\(^\pm \) ontologies. Ontologies are a fundamental component of both the Semantic Web and knowledge-based systems, even in the legal setting, since they provide a formal and machine manipulable model of a domain.

In this work, we show that ALP is a suitable framework for representing both norms and ontologies. Normative reasoning and ontological query answering are obtained by applying the same abductive proof procedure, smoothly achieving their integration. In particular, we consider the ALP framework named \(\mathcal {S}\text {CIFF}\)  and derived from the IFF abductive framework, able to deal with existentially (and universally) quantified variables in rule heads and CLP constraints.

The main advantage is that this integration is achieved within a single language, grounded on abduction in computational logic.

References

  1. 1.
    Alberti, M., Chesani, F., Gavanelli, M., Lamma, E., Mello, P., Montali, M.: An abductive framework for a-priori verification of web services. In: Maher, M. (ed.) Proceedings of the Eighth Symposium on Principles and Practice of Declarative Programming, pp. 39–50. ACM Press, New York (2006)Google Scholar
  2. 2.
    Alberti, M., Chesani, F., Gavanelli, M., Lamma, E., Mello, P., Torroni, P.: Compliance verification of agent interaction: a logic-based software tool. Appl. Artif. Intell. 20(2–4), 133–157 (2006)CrossRefMATHGoogle Scholar
  3. 3.
    Alberti, M., Chesani, F., Gavanelli, M., Lamma, E., Mello, P., Torroni, P.: Security protocols verification in abductive logic programming: a case study. In: Dikenelli, O., Gleizes, M.-P., Ricci, A. (eds.) ESAW 2005. LNCS (LNAI), vol. 3963, pp. 106–124. Springer, Heidelberg (2006). doi:10.1007/11759683_7 CrossRefGoogle Scholar
  4. 4.
    Alberti, M., Chesani, F., Gavanelli, M., Lamma, E., Mello, P., Torroni, P.: Verifiable agent interaction in abductive logic programming: the SCIFF framework. ACM Trans. Comput. Logic 9(4), 29:1–29:43 (2008)CrossRefGoogle Scholar
  5. 5.
    Alberti, M., Gavanelli, M., Lamma, E.: \({\mathit{Deon}^{+}}\): abduction and constraints for normative reasoning. In: Artikis, A., Craven, R., Kesim Çiçekli, N., Sadighi, B., Stathis, K. (eds.) Logic Programs, Norms and Action. LNCS (LNAI), vol. 7360, pp. 308–328. Springer, Heidelberg (2012). doi:10.1007/978-3-642-29414-3_17 CrossRefGoogle Scholar
  6. 6.
    Alberti, M., Gavanelli, M., Lamma, E.: The CHR-based implementation of the SCIFF abductive system. Fundamenta Informaticae 124(4), 365–381 (2013)MathSciNetGoogle Scholar
  7. 7.
    Alberti, M., Gavanelli, M., Lamma, E., Mello, P., Sartor, G., Torroni, P.: Mapping deontic operators to abductive expectations. Comput. Math. Organ. Theory 12(2–3), 205–225 (2006)CrossRefMATHGoogle Scholar
  8. 8.
    Alberti, M., Gavanelli, M., Lamma, E., Mello, P., Torroni, P.: Specification and verification of agent interactions using social integrity constraints. Electr. Notes Theor. Comput. Sci. 85(2), 94–116 (2003)CrossRefMATHGoogle Scholar
  9. 9.
    Alberti, M., Gomes, A.S., Gonçalves, R., Leite, J., Slota, M.: Normative systems represented as hybrid knowledge bases. In: Leite, J., Torroni, P., Ågotnes, T., Boella, G., Torre, L. (eds.) CLIMA 2011. LNCS (LNAI), vol. 6814, pp. 330–346. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22359-4_23 CrossRefGoogle Scholar
  10. 10.
    ALFEBIITE: a logical framework for ethical behaviour between infohabitants in the information trading economy of the universal information ecosystem. IST-1999-10298 (1999)Google Scholar
  11. 11.
    Arisha, K.A., Ozcan, F., Ross, R., Subrahmanian, V.S., Eiter, T., Kraus, S.: IMPACT: a platform for collaborating agents. IEEE Intell. Syst. 14(2), 64–72 (1999)CrossRefGoogle Scholar
  12. 12.
    Boella, G., van der Torre, L., Verhagen, H.: Introduction to normative multiagent systems. Comput. Math. Organ. Theory 12, 71–79 (2006)CrossRefGoogle Scholar
  13. 13.
    Boella, G., van der Torre, L.: Attributing mental attitudes to normative systems. In: Rosenschein, J.S., Sandholm, T., Wooldridge, M., Yokoo, M. (eds.) Proceedings of AAMAS-2003, 14–18 July 2003, pp. 942–943. ACM Press (2003)Google Scholar
  14. 14.
    Bracciali, A., Demetriou, N., Endriss, U., Kakas, A., Lu, W., Mancarella, P., Sadri, F., Stathis, K., Terreni, G., Toni, F.: The KGP model of agency for global computing: computational model and prototype implementation. In: Priami, C., Quaglia, P. (eds.) GC 2004. LNCS, vol. 3267, pp. 340–367. Springer, Heidelberg (2005). doi:10.1007/978-3-540-31794-4_18 CrossRefGoogle Scholar
  15. 15.
    Broersen, J., Dignum, F., Dignum, V., Meyer, J.-J.C.: Designing a deontic logic of deadlines. In: Lomuscio, A., Nute, D. (eds.) DEON 2004. LNCS (LNAI), vol. 3065, pp. 43–56. Springer, Heidelberg (2004). doi:10.1007/978-3-540-25927-5_5 CrossRefGoogle Scholar
  16. 16.
    Bürckert, H.: A resolution principle for constrained logics. Artif. Intell. 66, 235–271 (1994)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Calì, A., Gottlob, G., Kifer, M.: Taming the infinite chase: query answering under expressive relational constraints. In: International Conference on Principles of Knowledge Representation and Reasoning, pp. 70–80. AAAI Press (2008)Google Scholar
  18. 18.
    Calì, A., Gottlob, G., Lukasiewicz, T.: A general datalog-based framework for tractable query answering over ontologies. In: Symposium on Principles of Database Systems, pp. 77–86. ACM (2009)Google Scholar
  19. 19.
    Calì, A., Gottlob, G., Lukasiewicz, T.: Tractable query answering over ontologies with Datalog\(^\pm \). In: International Workshop on Description Logics, CEUR Workshop Proceedings, vol. 477. CEUR-WS.org (2009)Google Scholar
  20. 20.
    Clark, K.L.: Negation as failure. In: Gallaire, H., Minker, J. (eds.) Logic and Data Bases, pp. 293–322. Plenum Press, New York (1978)CrossRefGoogle Scholar
  21. 21.
    Console, L., Theseider Dupré, D., Torasso, P.: On the relationship between abduction and deduction. J. Logic Comput. 1(5), 661–690 (1991)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    De Vos, M., Padget, J., Satoh, K.: Legal modelling and reasoning using institutions. In: Onada et al. [42], pp. 129–140 (2010)Google Scholar
  23. 23.
    Denecker, M., De Schreye, D.: SLDNFA: an abductive procedure for abductive logic programs. J. Logic Program. 34(2), 111–167 (1998)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Dignum, V., Meyer, J.J., Weigand, H.: Towards an organizational model for agent societies using contracts. In: Castelfranchi, C., Lewis Johnson, W. (eds.) AAMAS-2002, 15–19 July 2002, pp. 694–695. ACM Press, Bologna, Italy (2002)Google Scholar
  25. 25.
    Dignum, V., Meyer, J.J., Weigand, H., Dignum, F.: An organizational-oriented model for agent societies. In: Proceedings of International Workshop on Regulated Agent-Based Social Systems: Theories and Applications, AAMAS 2002, Bologna (2002)Google Scholar
  26. 26.
    Du, J., Wang, K., Shen, Y.D.: A tractable approach to ABox abduction over description logic ontologies. In: Brodley, C., Stone, P. (eds.) Proceedings of AAAI 2014 (2014)Google Scholar
  27. 27.
    Eiter, T., Subrahmanian, V., Pick, G.: Heterogeneous active agents, I: semantics. Artif. Intell. 108(1–2), 179–255 (1999)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    ESTRELLA: European project for standardized transparent representations in order to extend legal accessibility. IST-2004-027655 (2004). http://www.estrellaproject.org
  29. 29.
    Fung, T.H., Kowalski, R.A.: The IFF proof procedure for abductive logic programming. J. Logic Program. 33(2), 151–165 (1997)MathSciNetCrossRefMATHGoogle Scholar
  30. 30.
    Gavanelli, M., Lamma, E., Riguzzi, F., Bellodi, E., Zese, R., Cota, G.: An abductive framework for Datalog\(^\pm \) ontologies. In: Eiter, T., Toni, F. (eds.) Technical Communications of the 31st International Conference on Logic Programming (ICLP 2015). CEUR Workshop Proceedings, Sun SITE Central Europe, Aachen, Germany (2015)Google Scholar
  31. 31.
    Gavanelli, M., Lamma, E., Riguzzi, F., Bellodi, E., Zese, R., Cota, G.: Abductive logic programming for Datalog\(^\pm \) ontologies. In: Ancona, D., Maratea, M., Mascardi, V. (eds.) Proceedings of the 30th Italian Conference on Computational Logic (CILC2015), Genova, Italy, 1–3 July 2015. CEUR Workshop Proceedings, vol. 1459, pp. 128–143. Sun SITE Central Europe, Aachen (2015)Google Scholar
  32. 32.
    Gottlob, G., Lukasiewicz, T., Simari, G.I.: Conjunctive query answering in probabilistic datalog+/– ontologies. In: Rudolph, S., Gutierrez, C. (eds.) RR 2011. LNCS, vol. 6902, pp. 77–92. Springer, Heidelberg (2011). doi:10.1007/978-3-642-23580-1_7 CrossRefGoogle Scholar
  33. 33.
    Governatori, G., Rotolo, A.: BIO logical agents: norms, beliefs, intentions in defeasible logic. Auton. Agents Multi-agent Syst. 17(1), 36–69 (2008)CrossRefGoogle Scholar
  34. 34.
    Jaffar, J., Maher, M.: Constraint logic programming: a survey. J. Logic Program. 19–20, 503–582 (1994)MathSciNetCrossRefMATHGoogle Scholar
  35. 35.
    Kakas, A.C., Kowalski, R.A., Toni, F.: Abductive logic programming. J. Logic Comput. 2(6), 719–770 (1993)MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    Kakas, A.C., Mancarella, P.: On the relation between truth maintenance and abduction. In: Fukumura, T. (ed.) Proceedings of PRICAI-90. Ohmsha Ltd. (1990)Google Scholar
  37. 37.
    Kakas, A.C., van Nuffelen, B., Denecker, M.: \({\cal{A}}\)-System: problem solving through abduction. In: Nebel, B. (ed.) Proceedings of IJCAI-01 (2001)Google Scholar
  38. 38.
    Klarman, S., Endriss, U., Schlobach, S.: ABox abduction in the description logic \(\cal{ALC}\). J. Autom. Reason. 46(1), 43–80 (2011)MathSciNetCrossRefMATHGoogle Scholar
  39. 39.
    Lloyd, J., Topor, R.: Making prolog more expressive. J. Logic Program. 1(3), 225–240 (1984)MathSciNetCrossRefMATHGoogle Scholar
  40. 40.
    Lloyd, J.W.: Foundations of Logic Programming. Springer, Heidelberg (1987)CrossRefMATHGoogle Scholar
  41. 41.
    Montali, M., Torroni, P., Alberti, M., Chesani, F., Gavanelli, M., Lamma, E., Mello, P.: Verification from declarative specifications using logic programming. In: Garcia de la Banda, M., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 440–454. Springer, Heidelberg (2008). doi:10.1007/978-3-540-89982-2_39 CrossRefGoogle Scholar
  42. 42.
    Onada, T., Bekki, D., McCready, E. (eds.): JSAI-isAI 2010. LNCS (LNAI), vol. 6797. Springer, Heidelberg (2011)MATHGoogle Scholar
  43. 43.
    Prakken, H., Sartor, G.: Argument-based extended logic programming with defeasible priorities. J. Appl. Non-classical Logics 7(1), 25–75 (1997)MathSciNetCrossRefMATHGoogle Scholar
  44. 44.
    Sadri, F., Stathis, K., Toni, F.: Normative KGP agents. Comput. Math. Organ. Theory 12(2–3), 101–126 (2006)CrossRefMATHGoogle Scholar
  45. 45.
    Sartor, G., Casanovas, P., Biasiotti, M.A., Fernández-Barrera, M. (eds.): Approaches to Legal Ontologies. Law, Governance and Technology, Springer, Netherlands (2011)Google Scholar
  46. 46.
    Satoh, K., Asai, K., Kogawa, T., Kubota, M., Nakamura, M., Nishigai, Y., Shirakawa, K., Takano, C.: PROLEG: an implementation of the presupposed ultimate fact theory of Japanese civil code by PROLOG technology. In: Onada et al. [42], pp. 153–164 (2010)Google Scholar
  47. 47.
    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, 370–386 (1986)CrossRefGoogle Scholar
  48. 48.
    Van Belleghem, K., Denecker, M., De Schreye, D.: A strong correspondence between description logics and open logic programming. In: Naish, L. (ed.) Proceedings of Fourteenth International Conference on Logic Programming. MIT Press, Cambridge (1997)Google Scholar
  49. 49.
    Wright, G.: Deontic logic. Mind 60, 1–15 (1951)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Marco Gavanelli
    • 1
  • Evelina Lamma
    • 1
  • Fabrizio Riguzzi
    • 2
  • Elena Bellodi
    • 1
  • Zese Riccardo
    • 1
  • Giuseppe Cota
    • 1
  1. 1.Dipartimento di IngegneriaUniversity of FerraraFerraraItaly
  2. 2.Dipartimento di Matematica e InformaticaUniversity of FerraraFerraraItaly

Personalised recommendations