On Dynamics in Structured Argumentation Formalisms

Abstract

This paper is a contribution to the research on dynamics in assumption-based argumentation (ABA). We investigate situations where a given knowledge base undergoes certain changes. We show that two frequently investigated problems, namely enforcement of a given target atom and deciding strong equivalence of two given ABA frameworks, are intractable in general. Notably, these problems are both tractable for abstract argumentation frameworks (AFs) which admit a close correspondence to ABA by constructing semanticspreserving instances. Inspired by this observation, we search for tractable fragments for ABA frameworks by means of the instantiated AFs. We argue that the usual instantiation procedure is not suitable for the investigation of dynamic scenarios since too much information is lost when constructing the abstract framework. We thus consider an extension of AFs, called cvAFs, equipping arguments with conclusions and vulnerabilities in order to better anticipate their role after the underlying knowledge base is extended. We investigate enforcement and strong equivalence for cvAFs and present syntactic conditions to decide them. We show that the correspondence between cvAFs and ABA frameworks is close enough to capture dynamics in ABA. This yields the desired tractable fragment. We furthermore discuss consequences for the corresponding problems for logic programs.

Attack semantics and collective attacks revisited

“…Finally, we want to point out that a model that is similar to our inside-out AF has been studied in the context of dynamics in argumentation. For any given SETAF, the resulting inside-out AF resembles a cvAF [46] -an argumentation framework with explicit claims (conclusions) and vulnerabilities. For an arrow (M, A) of the original SETAF SF (i.e., a node of the associated inside-out argumentation framework AF SF ) the claim is A and the vulnerabilities are the elements of M.…”