Abstract Argumentation with Qualitative Uncertainty: An Analysis in Dynamic Logic

Abstract

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Qualitative uncertainty and dynamics of argumentation through dynamic logic

“…This approach was pushed further in [35,37,36,48], where it was proposed to go beyond the characterisation of extensions and exploit DL-PA programs to describe the computation of extensions. The most basic way to do so is a 'generate and test' approach: the generic program…”

“…This can be done in a compact way by means of the extensionbuilding programs makeExt σ : 1 lists all the encodings. That of stable and complete semantics slightly simplifies that of [37,48]. Our encoding of grounded, complete, and preferred semantics straightforwardly adapts those of [36] for computing minimality and maximality criteria.…”

“…In particular, we cover: incomplete argumentation frameworks [13], their enriched version [53], constrained incomplete argumentation frameworks [48,54], and incomplete argumentation frameworks with dependencies [41,42]. The main motivation for the study of these formalisms is that there are several sources of uncertainty in real-life argumentation.…”

“…However, the kind of situations that we can model with them is rather limited (as we will discuss in detail later on). This is the main motivation for the development of more expressive formalisms, and it actually led to concurrent proposals during the last year, either under the name of constrained incomplete argumentation frameworks [48,54] or incomplete argumentation frameworks with dependencies [41,42]. We start by presenting our version of constrained incomplete AFs (the one introduced in [48]), and then move to alternative approaches.…”

“…Concurrently, a considerable amount of work in formal argumentation has focused on building a suitable logical theory for reasoning about argumentation formalisms, with a special focus on AFs and their dynamics; see [18] for a recent survey. The dynamic logic of propositional assignments (DL-PA) [6] has been shown to be a useful tool for this enterprise [35,37,36,48]. DL-PA is a well-behaved variant of propositional dynamic logic (PDL) [46], where atomic programs are restricted to assignments of propositional variables to either Truth or Falsity.…”