We study the semantics of dialectical proof procedures. As dialectical proof procedures are in general sound but not complete wrt admissibility semantics, a natural question here is whether we could give a more precise semantical characterization of what they compute. Based on a new notion of infinite arguments representing loops, we introduce a stricter notion of admissibility, referred to as strict admissibility, and show that dialectical proof procedures are in general sound and complete wrt strict admissibility.

Dung’s argumentation frameworks are formalisms widely used to model interaction among arguments. Although their study has been profusely developed in the field of Artificial Intelligence, it is not common to see its treatment among those less connected to computer science within the logical-philosophical community. In this paper we propose to bring to that audience a proof-theory for argument justification based on tableaux, very similar to those the Logic students are familiar with. The tableaux enable to calculate whether an argument or (...) subset of arguments are accepted or rejected in accordance to Dung’s preferred and grounded extension-based semantics. Soundness and completeness results regarding those semantics are provided. (shrink)

Dialectical proof procedures in assumption-based argumentation are in general sound but not complete with respect to both the credulous and skeptical semantics (due to non-terminating loops). This raises the question of whether we could describe exactly what such procedures compute. In a previous paper, we introduce infinite arguments to represent possibly non-terminating computations and present dialectical proof procedures that are both sound and complete with respect to the credulous semantics of assumption-based argumentation with infinite arguments. In this paper, we study (...) whether and under what conditions dialectical proof procedures are both sound and complete with respect to the grounded semantics of assumption-based argumentation with infinite arguments. We introduce the class of ω-grounded and finitary-defensible argumentation frameworks and show that finitary assumption-based argumentation is ω-grounded and finitary-defensible. We then present dialectical procedures that are sound and complete wrt finitary assumption-based argumentation. (shrink)

1. The benefits resulting from a combination of quantitative (e.g. probabilistic) and qualitative (e.g. logic-based) reasoning are widely acknowledged (e.g. see Domingos et al., 2006; Poole, 2011)....