Skip to main content
SpringerLink
Log in

t-DeLP: an argumentation-based Temporal Defeasible Logic Programming framework

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

The aim of this paper is to propose an argumentation-based defeasible logic, called t-DeLP, that focuses on forward temporal reasoning for causal inference. We extend the language of the DeLP logical framework by associating temporal parameters to literals. A temporal logic program is a set of basic temporal facts and (strict or defeasible) durative rules. Facts and rules combine into durative arguments representing temporal processes. As usual, a dialectical procedure determines which arguments are undefeated, and hence which literals are warranted, or defeasibly follow from the program. t-DeLP, though, slightly differs from DeLP in order to accommodate temporal aspects, like the persistence of facts. The output of a t-DeLP program is a set of warranted literals, which is first shown to be non-contradictory and be closed under sub-arguments. This basic framework is then modified to deal with programs whose strict rules encode mutex constraints. The resulting framework is shown to satisfy stronger logical properties like indirect consistency and closure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abadi, M., Manna, Z.: Temporal logic programming. In: Proc. of International Symposium on Logic Programming, pp. 4–16. San Francisco, USA (1987)

  2. Amgoud, L., Cayrol, C.: A reasoning model based on the production of acceptable arguments. Ann. Math. Artif. Intell. 34, 197–215 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Amgoud, L., Cayrol, C.: Inferring from inconsistency in preference-based argumentation frameworks. Int. J. Autom. Reason. 29(2), 125–169 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. Augusto, J., Simari, G.: Temporal defeasible reasoning. Knowl. Inf. Syst. 3, 287–318 (2001)

    Article  MATH  Google Scholar 

  6. Besnard, P., Hunter, A.: Argumentation based on classical logic. In: Rahwan, I., Simari, G. (eds.) Argumentation in Artificial Intelligence, ch. 7. Springer (2011)

  7. Billington, D.: Defeasible logic is stable. J. Log. Comput. 3, 379–400 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  8. Blackburn, P., van Benthem, J., Wolter, F. (eds.): Handbook of Modal Logic, vol. 3. Elsevier, New York (2006)

    Google Scholar 

  9. Brewka, G.: Adding priorities and specificity to default logic. In: Proc. of the 4th European Workshop on Logic in Artificial Intelligence JELIA’94, LNAI 838, pp. 247–260. Springer, York (1994)

    Chapter  Google Scholar 

  10. Brewka, G., Niemelä, I., Truszczyński, M.: Nonmonotonic reasoning. In: van Harmelen, F., Lifschitz, V., Porter, B. (eds.) Handbook of Knowledge Representation, ch. 6. Elsevier, Oxford (2007)

    Google Scholar 

  11. Broersen, J., Wieringa, R., Meyer, J.-J.: A semantics for persistency in propositional dynamic logic. In: Lloyd, J., et al. (eds.) Proceedings of 1st Conf. on Computation Logic (CL 2000), pp. 912–925 (2000)

  12. Caminada, M., Amgoud, L.: On the evaluation of argumentation formalisms. Artif. Intell. 171, 286–310 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  13. Capobianco, M., Chesñevar, C., Simari, G.: Argumentation and the dynamics of warranted beliefs in changing environments. J. Auton. Agents Multi-Agent Syst. 11, 127–151 (2005)

    Article  Google Scholar 

  14. Castilho, M., Gasquet, O., Herzig, A.: formalizing action and change in modal logic I: the frame problem. J. Log. Comput. 9(5), 701–735 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  15. Chellas, B.: Modal Logic, An Introduction. Cambridge Univ. Press, Cambridge (1980)

    Book  MATH  Google Scholar 

  16. Chesñevar, C., Dix, J., Stolzenburg, F., Simari, G.: Relating defeasible and normal logic programming through transformation properties. Theor. Comp. Sci. 290, 499–529 (2003)

    Article  MATH  Google Scholar 

  17. Cobo, L., Martínez, D., Simari, G.: Stable extensions in timed argumentation frameworks. In: Theories and Applications of Formal Argumentation TAFA 2011, pp. 181–196, Barcelona (2011)

  18. Cobo, L., Martínez, D., Simari, G.: Acceptability in timed frameworks with intermittent arguments. In: Artificial Intelligence Applications and Innovations, AIAI 2011 Part II, pp. 202–211 (2011)

  19. Craven, R., Sergot, M.: Distant causation in \(\mathcal{C}+\). Stud. Log. 79, 73–96 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  20. De Giacomo, G., Lenzerini, M.: PDL-based framework for reasoning about actions. In: Proceedings of the 4th Congress of the Italian Association for Artificial Intelligence IA*AI’95, LNAI 992, pp. 103–114 (1995)

  21. Delladio, T., Simari, G.: Relating DeLP and default logic. Intel. Artif. 35, 101–109 (2007)

    Google Scholar 

  22. Dung, P.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games* 1. Artif. Intell. 77(2), 321–357 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  23. Emerson, E.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, pp. 996–1072. Elsevier, New York (1990)

    Google Scholar 

  24. García, A., Simari, G.: Defeasible logic programming: An argumentative approach. Theory Pract. Log. Program. 4(1+2), 95–138 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  25. Gelfond, M., Lifschitz, V.: Representing action and change by logic programs. J. Log. Program. 17(2,3&4), 301–321 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  26. Ghallab, M., Nau, D., Traverso, P.: Automated Planning: Theory and Practice. Morgan Kaufmann, San Francisco (2004)

  27. Giordano, L., Martelli, A., Schwind, C.: Ramification and causality in a modal action logic. J. Log. Comput. 10(5), 625–662 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  28. Giunchiglia, E., Lee, J., Lifschitz, V., McCain, N., Turner, H.: Non-monotonic causal theories. Artif. Intell. 153, 49–104 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  29. Goldblatt, R.: Logics of Time and Computation. CSLI, Stanford (1992)

  30. Governatori, G., Terenziani, P.: Temporal extensions to defeasible logic. In: Orgun, M., Thornton, J. (eds.) Proc. of 20th Australian Joint Conference on Artificial Intelligence, AI 2007, pp. 1–10. Springer (2007)

  31. Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)

    MATH  Google Scholar 

  32. Hunter, A.: Execution of defeasible temporal clauses for building preferred models. In: Proc. of Fundamentals of Artificial Intelligence Research, FAIR ’91, pp. 84–98 (1991)

  33. Hunter, A.: Merging structured text using temporal knowledge. Data Knowl. Eng. 41(1), 29–66 (2002)

    Article  MATH  Google Scholar 

  34. Konolige, K.: On the relation between default and autoepistemic logic. Artif. Intell. 35, 342–382 (1988)

    MathSciNet  Google Scholar 

  35. Kowalski, R., Sergot, M.: A logic-based calculus of events. New Gener. Comput. 4, 67–95 (1986)

    Article  Google Scholar 

  36. Lewis, D.: Counterfactuals. Basil Blackwell, Oxford (1973)

    Google Scholar 

  37. Mann, N., Hunter, A.: Argumentation using temporal knowledge. In: Proc. of Computer Models of Argumentation (COMMA’08), pp. 204–215. IOS Press (2008)

  38. McCarthy, J., Hayes, P.: Some philosophical problems from the standpoint of artificial intelligence. Mach. Intell. 4, 463–502 (1969)

    MATH  Google Scholar 

  39. Modgil, S.: Reasoning about preferences in argumentation frameworks. Artif. Intell. 173, 901–934 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  40. Nute, D.: Defeasible logic. In: Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 353–395. Oxford Univ. Press, Oxford (1994)

    Google Scholar 

  41. Pardo, P., Godo, L.: t-DeLP: a temporal extension of the defeasible logic programming argumentative framework. In: Proceedings of SUM 2011, LNAI, vol. 6929, pp. 489-503. Springer, Dayton (2011)

    Google Scholar 

  42. Poole, D.: On the comparison of theories: preferring the most specific explanation. In: Proceedings of 9th International Joint Conference in Artificial Intelligence IJCAI, pp. 144–147. Los Angeles, USA (1985)

  43. Prakken, H.: An abstract framework for argumentation with structured arguments. Argument & Computation 1(2), 93–124 (2010)

    Article  Google Scholar 

  44. Prakken, H., Sartor, G.: Argument-based extended logic programming with defeasible priorities. J. Appl. Non-Class. Log. 7, 25–75 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  45. Prendinger, H., Schurz, G.: Reasoning about action and change: a dynamic logic approach. J. Log. Lang. Inf. 5, 209–245 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  46. Rahwan, I., Simari, G. (eds.): Argumentation in Artificial Intelligence. Springer (2011)

  47. Reiter, R.: A logic for default reasoning. Artif. Intell. 13, 81–132 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  48. Rintanen, J.: On specificity in default logic. In: Proceedings of the 14th International Joint Conference on Artificial Intelligence IJCAI, pp. 1474–1479. Montreal, Canada (1995)

  49. Stolzenburg, F., García, A., Chesñevar, C., Simari, G.: Computing generalized specificity. J. Appl. Non-Class. Log. 12(1), 1–27 (2002)

    Google Scholar 

  50. Thimm, M., Kern-Isberner, G.: On the relationship of defeasible argumentation and answer set programming. In: Besnard, P., Doutre, S., Hunter, A. (eds.) Proc. of Computer Models of Argumentation (COMMA’08), pp. 393–404. IOS Press (2008)

  51. Zhang, D., Foo, N.: Frame problem in dynamic logic. J. Appl. Non-Class. Log. 15(2), 215–239 (2005)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut d’Investigació en Intel·ligència Artificial (IIIA), Spanish National Research Council (CSIC), 08193, Bellaterra, Spain

    Pere Pardo & Lluís Godo

  2. Dept. de Lògica, Hist. i Filo. Ciència, Universitat de Barcelona, 08001, Barcelona, Spain

    Pere Pardo

Authors
  1. Pere Pardo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lluís Godo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pere Pardo.

Additional information

This paper is a revised and extended version of the conference paper [41] which was presented at the 5th International Conference on Scalable Uncertainty Management (SUM 2011).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pardo, P., Godo, L. t-DeLP: an argumentation-based Temporal Defeasible Logic Programming framework . Ann Math Artif Intell 69, 3–35 (2013). https://doi.org/10.1007/s10472-013-9334-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-013-9334-1

Keywords

Mathematics Subject Classifications (2010)

Search

Navigation