Interpretations and models for assumption-based argumentation

Abstract

This work investigates an alternative characterization of semantics for Assumption-Based Argumentation (ABA) frameworks. The semantics of ABA frameworks are traditionally retrieved by the corresponding concepts of assumption extensions and assumption labellings, which only evaluate a subset of literals in the framework's language which are called assumptions. We argue about the interplay of non-assumptions in ABA frameworks and take inspiration from similarities between ABA and Logic Programming (LP) to propose new operations and semantic computation concerning ABA frameworks. To do so, we followed Przymusinski's work on Three-Valued Stable Models for LP to define interpretations and models for ABA frameworks (which also evaluate non-assumptions) and investigate whether this approach provides different results from the original. Amongst other results, we show that our complete model semantics is equivalent to the complete assumption labelling semantics for flat ABA frameworks, but the semi-stable model semantics is not equivalent to the semi-stable assumption labelling semantics.