9 accepted papers
We present two new algorithms for the problem of lexicographic inference from conditional knowledge bases. These algorithms are based on SAT and MaxSAT encodings of the underlying problem of lexicographic comparisons of classical interpretations and require only a polynomial number of SAT solver cal
We introduce initial models for abstract dialectical frameworks (ADFs) as a notion of minimal justifiable valuations and based on that, generalise the concept of serialisability of argumentation semantics to ADFs. In particular, we show that the characteristic operator-based semantics for ADFs can b
We introduce a notion of conditional independence in (flat) assumption-based argumentation (ABA), where independence between (sets of) assumptions amounts to the presence of information about one set of assumptions not impacting the acceptability of another. We study general properties, computationa
We analyse two soft notions of stable extensions in abstract argumentation, one that weakens the requirement of having full range and one that weakens the requirement of conflict-freeness. We then consider optimisation problems over these two notions that represent optimisation variants of the credu…
We introduce the notion of an undisputed set for abstract argumentation frameworks, which is a conflict-free set of arguments, such that its reduct contains no non-empty admissible set. We show that undisputed sets, and the stronger notion of strongly undisputed sets, provide a meaningful approach t…
Abstract dialectical frameworks (in short, ADFs) are a unifying model of formal argumentation, where argumentative relations between arguments are represented by assigning acceptance conditions to atomic arguments. This idea is generalized by letting acceptance conditions being assigned to complex f…
Abstract dialectical frameworks (in short, ADFs) are one of the most general and unifying approaches to formal argumentation. As the semantics of ADFs are based on three-valued interpretations, we ask which monotonic three-valued logic allows to capture the main semantic concepts underlying ADFs. We…
Extension-based semantics in abstract argumentation provide a criterion to determine whether a set of arguments is acceptable or not. In this paper, we present the notion of extension-ranking semantics, which determines a preordering over sets of arguments, where one set is deemed more plausible tha…
We address the problem of deciding skeptical acceptance wrt. preferred semantics of an argument in abstract argumentation frameworks, i.e., the problem of deciding whether an argument is contained in all maximally admissible sets, a.k.a. preferred extensions. State-of-the-art algorithms solve this p…