On Dynamics in Structured Argumentation Formalisms

Abstract

In this paper we contribute to the investigation of dynamics in assumption-based argumentation (ABA) and 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. Interestingly, these problems are both tractable for abstract argumentation frameworks (AFs) which admit a close correspondence to ABA by constructing semantics-preserving 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 AF. 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 ABA also in dynamic scenarios. This yields the desired tractable ABA fragment. We furthermore discuss consequences for the corresponding problems for logic programs.