On the semantics of abstract argumentation frameworks: a logic programming approach. (English) Zbl 1468.68211

Summary: Recently there has been an increasing interest in frameworks extending Dung’s abstract Argumentation Framework (AF). Popular extensions include bipolar AFs and AFs with recursive attacks and necessary supports. Although the relationships between AF semantics and Partial Stable Models (PSMs) of logic programs has been deeply investigated, this is not the case for more general frameworks extending AF.
In this paper we explore the relationships between AF-based frameworks and PSMs. We show that every AF-based framework \(\Delta\) can be translated into a logic program \(P_\Delta\) so that the extensions prescribed by different semantics of \(\Delta\) coincide with subsets of the PSMs of \(P_\Delta \). We provide a logic programming approach that characterizes, in an elegant and uniform way, the semantics of several AF-based frameworks. This result allows also to define the semantics for new AF-based frameworks, such as AFs with recursive attacks and recursive deductive supports.


68T27 Logic in artificial intelligence
68N17 Logic programming
68T30 Knowledge representation


Full Text: DOI arXiv


[1] Alcântara, J. F. L., Sá, S., and Guadarrama, J. C. A.2019. On the equivalence between abstract dialectical frameworks and logic programs. TPLP 19, 5-6, 941-956. · Zbl 1434.68553
[2] Alfano, G., Cohen, A., Gottifredi, S., Greco, S., Parisi, F., and Simari, G. R.2020. Dynamics in abstract argumentation frameworks with recursive attack and support relations. In ECAI (To appear).
[3] Alfano, G., Greco, S., and Parisi, F.2017. Efficient computation of extensions for dynamic abstract argumentation frameworks: An incremental approach. In IJCAI.49-55.
[4] Alfano, G., Greco, S., and Parisi, F.2018. A meta-argumentation approach for the efficient computation of stable and preferred extensions in dynamic bipolar argumentation frameworks. Intelligenza Artificiale 12, 2, 193-211.
[5] Amgoud, L. and Vesic, S.2011. A new approach for preference-based argumentation frameworks. Ann. Math. Artif. Intell. 63,2, 149-183. · Zbl 1234.68371
[6] Baroni, P., Cerutti, F., Giacomin, M., and Guida, G.2011. AFRA: Argumentation Framework with Recursive Attacks. IJAR 52, 1, 19-37. · Zbl 1211.68433
[7] Bench-Capon, T. and Dunne, P. E.2007. Argumentation in artificial intelligence. AI 171, 619-641. · Zbl 1168.68560
[8] Bistarelli, S., Rossi, F., and Santini, F.2018. A novel weighted defence and its relaxation in abstract argumentation. IJAR 92, 66-86. · Zbl 1423.68479
[9] Bondarenko, A., Dung, P. M., Kowalski, R. A., and Toni, F.1997. An abstract, argumentation-theoretic approach to default reasoning. AI 93, 63-101. · Zbl 1017.03511
[10] Caminada, M., Sá, S., Alcântara, J. F. L., and Dvorák, W.2015. On the equivalence between logic programming semantics and argumentation semantics. IJAR 58, 87-111. · Zbl 1328.68211
[11] Caminada, M. and Schulz, C.2017. On the equivalence between assumption-based argumentation and logic programming. JAIR 60, 779-825. · Zbl 1423.68480
[12] Cayrol, C., Fandinno, J., Del Cerro, L. F., and Lagasquie-Schiex, M.2017. Valid attacks in argumentation frameworks with recursive attacks. In Proc. of COMMONSENSE. · Zbl 06894598
[13] Cayrol, C., Fandinno, J., Del Cerro, L. F., and Lagasquie-Schiex, M.2018. Structure-based semantics of argumentation frameworks with higher-order attacks and supports. In COMMA.29-36. · Zbl 1430.68301
[14] Cayrol, C. and Lagasquie-Schiex, M.2013. Bipolarity in argumentation graphs: Towards a better understanding. IJAR 54, 7, 876-899. · Zbl 1316.68152
[15] Cohen, A., Gottifredi, S., Garcia, A. J., and Simari, G. R.2014. A survey of different approaches to support in argumentation systems. The Know. Eng. Rev. 29,5, 513-550.
[16] Cohen, A., Gottifredi, S., Garcia, A. J., and Simari, G. R.2015. An approach to abstract argumentation with recursive attack and support. J. Appl. Log. 13, 4, 509-533. · Zbl 1386.68156
[17] Craven, R. and Toni, F.2016. Argument graphs and assumption-based argumentation. AI 233, 1-59. · Zbl 1351.68264
[18] Dung, P. M.1991. Negations as hypotheses: An abductive foundation for logic programming. In ICLP. 3-17.
[19] Dung, P. M.1995. On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. AI 77, 321-358. · Zbl 1013.68556
[20] Fazzinga, B., Flesca, S., and Parisi, F.2015. On the complexity of probabilistic abstract argumentation frameworks. TOCL 16, 3, 22:1-22:39. · Zbl 1354.68253
[21] Gaggl, S. A., Manthey, N., Ronca, A., Wallner, J. P., and Woltran, S.2015. Improved answer-set programming encodings for abstract argumentation. TPLP 15, 4-5, 434-448. · Zbl 1379.68292
[22] Gebser, M., Leone, N., Maratea, M., Perri, S., Ricca, F., and Schaub, T.2018. Evaluation techniques and systems for answer set programming: a survey. In IJCAI.5450-5456.
[23] Gelfond, M. and Lifschitz, V.1988. The stable model semantics for logic programming. In ICSLP. 1070-1080.
[24] Gottifredi, S., Cohen, A., Garcia, A. J., and Simari, G. R.2018. Characterizing acceptability semantics of argumentation frameworks with recursive attack and support relations. AI 262, 336-368. · Zbl 1451.68262
[25] Greco, S. and Parisi, F.2016. Incremental computation of deterministic extensions for dynamic argumentation frameworks. In JELIA. 288-304. · Zbl 1483.68379
[26] Greco, S. and Saccà, D.1999. Complexity and expressive power of deterministic semantics for datalog_-. Inf. Comput. 153, 1, 81-98. · Zbl 1045.68514
[27] Janhunen, T., Niemelä, I., Seipel, D., Simons, P., and You, J.-H.2006. Unfolding partiality and disjunctions in stable model semantics. ACM Trans. Comput. Logic 7, 1. · Zbl 1367.68035
[28] Modgil, S.2009. Reasoning about preferences in argumentation frameworks. AI 173, 9-10, 901-934. · Zbl 1192.68663
[29] Nouioua, F. and Risch, V.2011. Argumentation frameworks with necessities. In SUM. 163-176.
[30] Saccà, D.1997. The expressive powers of stable models for bound and unbound DATALOG queries. J. Comput. Syst. Sci. 54,3, 441-464. · Zbl 0882.68088
[31] Saccà, D. and Zaniolo, C.1990. Stable models and non-determinism in logic programs with negation. In PODS. 205-217.
[32] Sakama, C. and Rienstra, T.2017. Representing argumentation frameworks in answer set programming. Fundam. Inform. 155, 3, 261-292. · Zbl 1377.68227
[33] Simari, G. R. and Rahwan, I., Eds. 2009. Argumentation in Artificial Intelligence.
[34] Villata, S., Boella, G., Gabbay, D. M., and Van Der Torre, L. W. N.2012. Modelling defeasible and prioritized support in bipolar argumentation. AMAI 66, 1-4, 163-197. · Zbl 1280.68255
[35] Wu, Y., Caminada, M., and Gabbay, D. M.2009. Complete extensions in argumentation coincide with 3-valued stable models in logic programming. Studia Logica 93, 2-3, 383-403. · Zbl 1189.68127
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.