Theory of Semi-Instantiation in Abstract Argumentation

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. 1 Motivation and Orientation This paper studies semi-instantiated argumentation network of the form (S ,R, I), where (S ,R), R ⊆ S×S is an abstract argumentation network and I is an instantiation function, giving for each x ∈ S a formula I(x) of some logic L. The attack relation R is not instantiated and remains abstract. We are not told, in terms of the logic L, why there is an attack. There are several possibilities for such a system to arise. Option 1. We can view such a system as semi-ASPIC like instantiation. The APPIC approach (see [32]) will start with a theory ∆ in a logic, L define the notion of L-proofs for ∆ and will elt S be the set of all possible such proofs and will further define the attack relation R ⊆ S × S in terms of relationships among these proofs. In our case we just take ∆ as the arguments (no proof theory avaiable) and simply tell you abstractly what is supposed to attack what. Research supported by the Israel Science Foundation Project 1321/10: Integrating Logic and Networks.