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Argumentative Characterizations of (Extended) Disjunctive Logic Programs (2306.07126v1)

Published 12 Jun 2023 in cs.AI

Abstract: This paper continues an established line of research about the relations between argumentation theory, particularly assumption-based argumentation, and different kinds of logic programs. In particular, we extend known result of Caminada, Schultz and Toni by showing that assumption-based argumentation can represent not only normal logic programs, but also disjunctive logic programs and their extensions. For this, we consider some inference rules for disjunction that the core logic of the argumentation frameworks should respect, and show the correspondence to the handling of disjunctions in the heads of the logic programs' rules.

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References (44)
  1. Simple contrapositive assumption-based argumentation part II: Reasoning with preferences. Journal of Approximate Reasoning, 139:28–53, 2021.
  2. Simple contrapositive assumption-based argumentation with partially-ordered preferences. In Proc. KR’2023, 2023. Accepted.
  3. Abstract argumentation frameworks and their semantics. In P. Baroni, D. Gabbay, M. Giacomin, and L. van der Torre, editors, Handbook of Formal Argumentation, volume 1, pages 159–236. College Publications, 2018.
  4. Reasoning by cases in structured argumentation. In Proceedings of the 32nd ACM Symposium on Applied Computing (SAC’17), pages 989–994. ACM, 2017.
  5. A critical assessment of Pollock’s work on logic-based argumentation with suppositions. In Proceedings of NMR’18, pages 63–72, 2018.
  6. Alexander Bochman. Collective argumentation and disjunctive logic programming. Journal of logic and computation, 13(3):405–428, 2003.
  7. An abstract, argumentation-theoretic approach to default reasoning. Artificial Intelligence, 93(1):63–101, 1997.
  8. Characterizations of the disjunctive well-founded semantics: confluent calculi and iterated gcwa. Journal of automated reasoning, 20(1-2):143–165, 1998.
  9. On the equivalence between assumption-based argumentation and logic programming. Journal of Artificial Intelligence Research, 60:779–825, 2017.
  10. On the equivalence between assumption-based argumentation and logic programming (extended abstract). In Proc. IJCAI’2018, pages 5578–5582. ijcai.org, 2018.
  11. Keith L. Clark. Negation as failure. In M. L. Ginsberg, editor, Readings in Nonmonotonic Reasoning, pages 311–325. Morgan Kaufmann, 1978.
  12. Graph-based dispute derivations in assumption-based argumentation. In International Workshop on Theorie and Applications of Formal Argumentation, pages 46–62. Springer, 2013.
  13. Non-monotonic inference properties for assumption-based argumentation. In International Workshop on Theory and Applications of Formal Argumentation, pages 92–111. Springer, 2015.
  14. On the computational complexity of assumption-based argumentation for default reasoning. Artificial Intelligence, 141(1-2):57–78, 2002.
  15. Phan Minh Dung. On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence, 77:321–358, 1995.
  16. Dialectic proof procedures for assumption-based, admissible argumentation. Artificial Intelligence, 170(2):114–159, 2006.
  17. A dialectic procedure for sceptical, assumption-based argumentation. 144:145–156, 2006.
  18. Disjunctive datalog. ACM Transactions on Database Systems (TODS), 22(3):364–418, 1997.
  19. On the partial semantics for disjunctive deductive databases. Annals of Mathematics and Artificial Intelligence, 19(1-2):59–96, 1997.
  20. Michael Gelfond. Logic programming and reasoning with incomplete information. Annals of mathematics and artificial intelligence, 12(1-2):89–116, 1994.
  21. The stable model semantics for logic programming. In Prog. ICLP’88, pages 1070–1080. MIT Press, 1988.
  22. Classical negation in logic programs and disjunctive databases. New generation computing, 9(3-4):365–385, 1991.
  23. Parametrized logic programming. In European Workshop on Logics in Artificial Intelligence, pages 182–194. Springer, 2010.
  24. Georg Gottlob. Complexity and expressive power of disjunctive logic programming (research overview). In Proceedings of the 1994 International Symposium on Logic programming, pages 23–42. Mit Press, 1994.
  25. An argumentative characterization of disjunctive logic programming. In Paulo Moura Oliveira, Paulo Novais, and Luís Paulo Reis, editors, Proceedings of the 19th EPIA Conference on Artificial Intelligence, Part II, volume 11805 of Lecture Notes in Computer Science, pages 526–538. Springer, 2019.
  26. Simple contrapositive assumption-based argumentation frameworks. Journal of Approximate Reasoning, 121:103–124, 2020.
  27. S. C. Kleene. Introduction to Metamathematics. Van Nostrand, 1950.
  28. John W. Lloyd. Foundations of Logic Programming. Springer, 1987.
  29. Teodor Przymusinski. Stationary semantics for normal and disjunctive logic programs. In DOOD, volume 91. Citeseer, 1991.
  30. Teodor C. Przymusinski. The well-founded semantics coincides with the three-valued stable semantics. Fundam. Inform., 13(4):445–463, 1990.
  31. Raymond Reiter. On closed world data bases. In Hervé Gallaire and Jack Minker, editors, Logic and Data Bases, pages 119–140. 1978.
  32. Kenneth A Ross. A procedural semantics for well-founded negation in logic programs. The Journal of Logic Programming, 13(1):1–22, 1992.
  33. Chiaki Sakama. Possible model semantics for disjunctive databases. In Deductive and Object-Oriented Databases, pages 369–383. Elsevier, 1990.
  34. Claudia Schulz. Graphical representation of assumption-based argumentation. In Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015.
  35. Characterising and explaining inconsistency in logic programs. In International Conference on Logic Programming and Nonmonotonic Reasoning, pages 467–479. Springer, 2015.
  36. Justifying answer sets using argumentation. Theory and Practice of Logic Programming, 16(1):59–110, 2016.
  37. Complete assumption labellings, 2017.
  38. Labellings for assumption-based and abstract argumentation. J. Approximate Reasoning, 84:110–149, 2017.
  39. Ezgi Su. Extensions of equilibrium logic by modal concepts. PhD thesis, IRIT-Institut de recherche en informatique de Toulouse, 2015.
  40. Francesca Toni. A generalised framework for dispute derivations in assumption-based argumentation. Artificial Intelligence, 195:1–43, 2013.
  41. The well-founded semantics for general logic programs. Journal of the ACM, 38(3):619–649, 1991.
  42. Toshiko Wakaki. Consistency in assumption-based argumentation. In Henry Prakken, Stefano Bistarelli, Francesco Santini, and Carlo Taticchi, editors, Proceedings of the the 8th International Conference on Computational Models of Argument (COMMA’20), volume 326 of Frontiers in Artificial Intelligence and Applications, pages 371–382. IOS Press, 2020.
  43. Toshiko Wakaki. Assumption-based argumentation for extended disjunctive logic programming. In Ivan Varzinczak, editor, Proceedings of the 12th International Symposium on Foundations of Information and Knowledge Systems (FoIKS-2022), volume 13388 of Lecture Note in Computer Science, pages 35–54. Springer, 2022.
  44. Kewen Wang. Argumentation-based abduction in disjunctive logic programming. The Journal of Logic Programming, 45(1-3):105–141, 2000.

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