Extended Abduction in Assumption-Based Argumentation

Abstract

Assumptions are needed to perform non-monotonic reasoning in assumption-based argumentation (ABA), while hypotheses are used to perform abductive or hypothetical reasoning. However not only were hypotheses sometimes confused with assumptions when representing them in ABA frameworks but no work has been done to perform extended abduction in ABA frameworks whose languages contain explicit negation \(\lnot \). Hence first we define consistency of ABA frameworks w.r.t. \(\lnot \). Second based on it, we present the framework to perform extended abduction in ABA while treating hypotheses along with assumptions in the framework. Theoretically it is shown that Sakama and Inoue’s extended abduction w.r.t. an abductive logic program (ALP) containing classical negation can be captured by our extended abduction in ABA instantiated with the ALP. Finally we provide the method to compute extended abduction in ABA based on answer set programming.