Argumentation Frameworks Induced by Assumption-Based Argumentation: Relating Size and Complexity

Abstract

A key ingredient of computational argumentation in AI is the generation of arguments in favor or against claims under scrutiny. In this paper we look at the complexity of the argument generation procedure in the prominent structured formalism of assumption-based argumentation (ABA). We show several results connecting expressivity of ABA fragments and number of constructed arguments. First, for several NP-hard fragments of ABA, the number of generated arguments is not bounded polynomially. Even under equivalent rewritings of the given ABA framework there are situations where one cannot avoid an exponential blow-up. We establish a weaker notion of equivalence under which this blow-up can be avoided. As a general tool for analyzing ABA frameworks and resulting arguments and their conflicts, we extend results regarding dependency graphs of ABA frameworks, from which one can infer structural properties on the induced attacks among arguments.