Theory of Semi-Instantiation in Abstract Argumentation
This work addresses foundational issues in argumentation theory for AI and logic communities, but it appears incremental as it builds on existing abstract argumentation frameworks.
The paper tackles the problem of defining complete extensions for instantiated abstract argumentation frames, where arguments are instantiated as logical formulas, and provides algorithms for finding these extensions. It develops a theory using Boolean attack formations and conjunctive/disjunctive attacks, with applications and critical comparisons to existing literature.
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.