Diana Grooters and Henry Prakken (2016) Two Aspects of Relevance in Structured Argumentation: Minimality and Paraconsistency

This paper studies two issues concerning relevance in structured argumentation in the context of the ASPIC framework, arising from the combined use of strict and defeasible inference rules. One issue arises if the strict inference rules correspond to classical logic. A longstanding problem is how the trivialising effect of the classical Ex Falso principle can be avoided while satisfying consistency and closure postulates. In this paper, this problem is solved by disallowing chaining of strict rules, resulting in a variant of the ASPIC framework called ASPIC*, and then disallowing the application of strict rules to inconsistent sets of formulas. Another issue is minimality of arguments.