On the Equivalence between Assumption-Based Argumentation and Logic Programming

Abstract

Assumption-Based Argumentation (ABA) has been shown to subsume various other non-monotonic reasoning formalisms, among them normal logic programming (LP). We re-examine the relationship between ABA and LP and show that normal LP also subsumes (flat) ABA. More precisely, we specify a procedure that given a (flat) ABA framework yields an associated logic program with almost the same syntax whose semantics coincide with those of the ABA framework. That is, the 3-valued stable (respectively well-founded, regular, 2-valued stable, and ideal) models of the associated logic program coincide with the complete (respectively grounded, preferred, stable, and ideal) assumption labellings and extensions of the ABA framework. Moreover, we show how our results on the translation from ABA to LP can be reapplied for a reverse translation from LP to ABA, and observe that some of the existing results in the literature are in fact special cases of our work. Overall, we show that (flat) ABA frameworks can be seen as normal logic programs with a slightly different syntax. This implies that methods developed for one of these formalisms can be equivalently applied to the other by simply modifying the syntax.

Assumption‐Based Argumentation Equipped with Preferences and its Application to Decision Making, Practical Reasoning, and Epistemic Reasoning

“…2.3 For Sname D preferred (resp. grounded), it is proved in the same way as the proof shown in point 3 of (Caminada et al 2015, Theorem 6) based on the results obtained in the case Sname D complete.…”

“…Definition 4. (Dung 1995;Fan and Toni 2014;Caminada et al 2015) Let hL; R; A; Ci be an ABA framework and AR the associated set of arguments. Then Args  AR is admissible iff Args is conflict-free and defends all its elements.…”

“…Definition 5. (Fan and Toni 2014;Caminada et al 2015) -A set of assumptions Asms attacks an assumption˛iff Asms enables the construction of an argument for the claim 9c 2 C.˛/. -A set of assumptions Asms 1 attacks a set of assumptions Asms 2 iff Asms 1 attacks some assumption˛2 Asms 2 .…”

Labellings for assumption-based and abstract argumentation

“…For example, logic programs are special instances of flat ABA frameworks [4], so the results presented here for flat ABA frameworks also apply to the instance of ABA which corresponds to logic programs. Caminada and Schulz [29] show that, conversely, a specific fragment of (flat) ABA frameworks is as an instance of logic programs, where the models of the logic program and the assumption labellings of the ABA framework coincide. Furthermore, Dung [3] as well as Caminada et al [40] study logic programs as an instance of AA frameworks, proving that the models of the logic program and the argument labellings of the AA framework correspond.…”

Reasoning over Assumption-Based Argumentation Frameworks via Direct Answer Set Programming Encodings

“…While previous approaches are based on either specialized algorithms or translating ABA reasoning to reasoning over AFs, we propose a direct approach to ABA reasoning based on encoding ABA reasoning tasks in answer set programming (ASP) (Gelfond and Lifschitz 1988;Niemelä 1999). While related encodings have been considered previously focusing on representational aspects in the context of ABA (Egly and Woltran 2006;Caminada and Schulz 2017), motivated by the success of ASP encodings for AFs (Toni and Sergot 2011) we present novel types of ASP encodings for ABA, and for ABA + (Cyras and Toni 2016a;2016c;Bao, Cyras, and Toni 2017) that integrates preferences into ABA, and in particular provide a first empirical evaluation of this approach. Our approach significantly improves on the empirical performance of currently available ABA reasoning systems, in particular the dispute derivation approach (Gaertner and Toni 2007a;2007b;Dung, Mancarella, and Toni 2007;Craven et al 2012;Toni 2013;Craven, Toni, and Williams 2013) implemented in the abagraph system (Craven and Toni 2016) and the translation-based approach (Dung, Mancarella, and Toni 2007;Caminada et al 2013) implemented in the aba2af system (Lehtonen, Wallner, and Järvisalo 2017) for ABA, as well as the ABAplus system (Bao, Cyras, and Toni 2017) for ABA + to the extent applicable.…”