A Comparative Study of Some Central Notions of ASPIC+ and DeLP

TL;DR

This paper compares core concepts of ASPIC+ and DeLP argumentation frameworks, analyzing their properties, differences, and potential for unification under grounded semantics, with implications for rationality and warrant notions.

Contribution

It provides a formal comparison of ASPIC+ and DeLP, proposing a variant of DeLP with grounded semantics and establishing conditions for their notions of warrant and justification to align.

Findings

DeLP's definitions are intuitively appealing but may violate some rationality postulates.

A variant of DeLP with grounded semantics can address counterintuitive warrant issues.

Under certain assumptions, ASPIC+ and DeLP warrant notions can be made equivalent.

Abstract

This paper formally compares some central notions from two well-known formalisms for rule-based argumentation, DeLP and ASPIC+. The comparisons especially focus on intuitive adequacy and inter-translatability, consistency, and closure properties. As for differences in the definitions of arguments and attack, it turns out that DeLP's definitions are intuitively appealing but that they may not fully comply with Caminada and Amgoud's rationality postulates of strict closure and indirect consistency. For some special cases, the DeLP definitions are shown to fare better than ASPIC+. Next, it is argued that there are reasons to consider a variant of DeLP with grounded semantics, since in some examples its current notion of warrant arguably has counterintuitive consequences and may lead to sets of warranted arguments that are not admissible. Finally, under some minimality and consistency assumptions on ASPIC+ arguments, a one-to-many correspondence between ASPIC+ arguments and DeLP arguments is identified in such a way that if the DeLP warranting procedure is changed to grounded semantics, then DeLP notion of warrant and ASPIC+'s notion of justification are equivalent. This result is proven for three alternative definitions of attack.