Complexity of Credulous and Skeptical Acceptance in Epistemic Argumentation Framework

Abstract

Dung’s Argumentation Framework (AF) has been extended in several directions. Among the numerous proposed extensions, three of them seem to be of particular interest and have correlations between them. These extensions are: constrained AF (CAF), where AF is augmented with (strong) constraints; epistemic AF (EAF), where AF is augmented with epistemic constraints; and incomplete AF (iAF), where arguments and attacks can be uncertain. While the complexity and expressiveness of CAF and iAF have been studied, that of EAF has not been explored so far. In this paper we investigate the complexity and expressivity of EAF. To this end, we first introduce the Labeled CAF (LCAF), a variation of CAF where constraints are defined over the alphabet of labeled arguments. Then, we investigate the complexity of credulous and skeptical reasoning and show that: i) EAF is more expressive than iAF (under preferred semantics), ii) although LCAF is a restriction of EAF where modal operators are not allowed, these frameworks have the same complexity, iii) the results for LCAF close a gap in the characterization of the complexity of CAF. Interestingly, even though EAF has the same complexity as LCAF, it allows modeling domain knowledge in a more natural and easy-to-understand way.