Abstract
AbstractThis 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 ’s DeLP notion of warrant and ASPIC+ ’s notion of justification are equivalent. This result is proven for three alternative definitions of attack.
Highlights
ASPIC + (Prakken 2010) and defeasible logic programming, or DeLP for short (Garcıa and Simari 2004), are two well-known rule-based formalisms for argumentation
After observing that the motivation behind DeLP ’s semantics is similar to the intuitions underlying (Dung’s 1995) grounded semantics, we propose a version of DeLP with grounded semantics, arguing that all the examples given by Garcıa and Simari (2004) as reasons for their special semantics are treated as they want by grounded semantics
Prakken (2016) agrees with the second position that strict closure should only hold in general for sets of arguments that are not attackable. He argues that whether strict closure and indirect consistency should hold for other cases depends on whether it makes sense to require that the argument ordering is “reasonable,” and, so he argues, this depends on the nature of the knowledge and inference rules
Summary
ASPIC + (Prakken 2010) and defeasible logic programming, or DeLP for short (Garcıa and Simari 2004), are two well-known rule-based formalisms for argumentation. A comparative study of ASPIC + and DeLP based approach, arguments are formed by chaining applications of inference rules into inference trees or graphs This approach can be contrasted with approaches defined in terms of logical consequence notions, in which arguments are premises–conclusion pairs where the premises are consistent and imply the conclusion according to the consequence notion of some adopted “base logic.”. Under some minimality and consistency assumptions on ASPIC + arguments, a one-to-many correspondence between ASPIC +arguments and DeLP arguments will be identified in such a way that if the DeLP warranting procedure is changed to grounded semantics, DeLP ’s notion of warrant and ASPIC +’s notion of justification are equivalent This result will be proven for three alternative definitions of attack.
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