Abstract Argumentation in Dynamic Logic: Representation, Reasoning and Change

Abstract

We provide a logical analysis of Dung’s abstract argumentation frameworks and their dynamics. We express attack relation and argument status by means of propositional variables and define acceptability criteria by formulas of propositional logic, which enables us to formulate the standard reasoning problems in logic. While the approaches in the literature express these problems as Boolean or quantified Boolean formulas, we here take advantage of a variant of Propositional Dynamic Logic \(\mathsf {PDL}\): Dynamic Logic of Propositional Assignments \(\mathsf {DL\text {-}PA} \), whose atomic programs are assignments of propositional variables to truth values. One of the benefits is that algorithms computing extensions of argumentation frameworks can be viewed as particular \(\mathsf {DL\text {-}PA} \) programs. This allows us to formally prove the correctness of these algorithms. Another benefit is that in the same logic, we can also design and study programs which modify argumentation frameworks. Indeed, the basic operations on these propositional variables, viz. change of the truth values of the attack variables and the argument status variables, are nothing but atomic programs of \(\mathsf {DL\text {-}PA} \). We mainly focus on how the acceptance of one or more arguments can be enforced and show how this can be achieved by changing the truth values of the propositional variables describing the attack relation in a minimal way.