Theory of Semi-Instantiation in Abstract Argumentation

TL;DR

This paper develops a theoretical framework for semi-instantiated abstract argumentation, integrating logical formulas into argumentation frameworks and proposing methods to identify complete extensions.

Contribution

It introduces a novel approach to instantiate abstract argumentation with various logics and develops algorithms for computing complete extensions within this framework.

Findings

Defined properties of semi-instantiated argumentation systems

Developed algorithms for finding complete extensions

Compared new framework with existing literature

Abstract

We study instantiated abstract argumentation frames of the form $(S,R,I)$, where $(S,R)$ is an abstract argumentation frame and where the arguments $x$ of $S$ are instantiated by $I(x)$ as well formed formulas of a well known logic, for example as Boolean formulas or as predicate logic formulas or as modal logic formulas. We use the method of conceptual analysis to derive the properties of our proposed system. We seek to define the notion of complete extensions for such systems and provide algorithms for finding such extensions. We further develop a theory of instantiation in the abstract, using the framework of Boolean attack formations and of conjunctive and disjunctive attacks. We discuss applications and compare critically with the existing related literature.