On the Semantics of Abstract Argumentation Frameworks: A Logic Programming Approach

Abstract

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 Δ can be translated into a logic program PΔ so that the extensions prescribed by different semantics of Δ coincide with subsets of the PSMs of PΔ. 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.

Argumentation frameworks with necessities and their relationship with logic programs

“…Various other semantics are defined on the basis of P-stable semantics. 3 Definition 2.7 (Different kinds of models). Let be an LP and I = T , F be a 3-valued interpretation of .…”

“…2 I is a fixed-point of iff (I ) = I . 3 Except for P-stable semantics which defines a P-stable model as a 3-valued interpretation I , in the original definitions of the other semantics, the corresponding models are defined as the set T of true atoms of a particular P-stable model I = T , F . For the sake of homogeneity we define in this paper all kinds of models as 3-valued interpretations.…”

“…In the same spirit, the work by Alfano et al [2,3] presents how to translate different kinds of extensions of dung AFs (called AF-based frameworks) into logic programs and shows how the acceptability semantics of such AF-based frameworks are related to particular cases of partial stable models of the corresponding LPs. The considered AF-based frameworks include: Original Dung AFs [53]; bipolar AFs (BAF), namely AFs with necessity support (AFN) [71] and AFs with deductive support (AFD) [19,91]; recursive AFs (Rec-AF) namely, AFs with recursive attack (AFRA) [14] and recursive AFs (RAF) [37] and recursive bipolar AFs (Rec-BAF) namely, attack-support AFs (ASAF) [62], recursive AFs with necessities (RAFN) [35], AFs with recursive attack and deductive support (AFRAD) [3] and recursive AFs with deductive support (RAFD) [3]. Our work differs from that by Alfano et al [2,3] in two main respects: First, the work in [2,3] considers only the restricted version of AFNs where the necessary support relation is binary and acyclic while our proposal considers a more general framework where the support relation may relate a set of arguments to a single one and no restriction is made about its cyclicality.…”

“…The considered AF-based frameworks include: Original Dung AFs [53]; bipolar AFs (BAF), namely AFs with necessity support (AFN) [71] and AFs with deductive support (AFD) [19,91]; recursive AFs (Rec-AF) namely, AFs with recursive attack (AFRA) [14] and recursive AFs (RAF) [37] and recursive bipolar AFs (Rec-BAF) namely, attack-support AFs (ASAF) [62], recursive AFs with necessities (RAFN) [35], AFs with recursive attack and deductive support (AFRAD) [3] and recursive AFs with deductive support (RAFD) [3]. Our work differs from that by Alfano et al [2,3] in two main respects: First, the work in [2,3] considers only the restricted version of AFNs where the necessary support relation is binary and acyclic while our proposal considers a more general framework where the support relation may relate a set of arguments to a single one and no restriction is made about its cyclicality. The second issue is that the work in [2,3] considers only the representation of AF-based frameworks as LPs and does not study the opposite direction (representing an LP as an AF-based framework).…”

From Weighted Conditionals of Multilayer Perceptrons to Gradual Argumentation and Back

“…Argumentation is a reasoning approach which, in its different formulations and semantics, has been used in different contexts in the multi-agent setting, from social networks [52] to classification [5], and it is very relevant for decision making and for explanation [59]. The argumentation semantics are strongly related to other non-monotonic reasoning formalisms and semantics [26,1].…”