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

摘要

This paper formally compares some central notions from two well-known formalisms for rulebasedargumentation, DeLP and ASPIC~+. The comparisons especially focus on intuitive adequacyand inter-translatability, consistency, and closure properties. As for differences in thedefinitions of arguments and attack, it turns out that DeLP’s definitions are intuitively appealingbut that they may not fully comply with Caminada and Amgoud’s rationality postulates ofstrict closure and indirect consistency. For some special cases, the DeLP definitions are shownto fare better than ASPIC~+. Next, it is argued that there are reasons to consider a variant ofDeLP with grounded semantics, since in some examples its current notion of warrant arguablyhas counterintuitive consequences and may lead to sets of warranted arguments that are notadmissible. Finally, under some minimality and consistency assumptions on ASPIC+ arguments,a one-to-many correspondence between ASPIC~+ arguments and DeLP arguments is identifiedin such a way that if the DeLP warranting procedure is changed to grounded semantics, thenDeLP’s notion of warrant and ASPIC~+’s notion of justification are equivalent. This result isproven for three alternative definitions of attack.