Assumption-Based Reasoning with Finite Set Constraints
In this paper we present an extension of the traditional approach to assumption-based reasoning. Instead of propositional logic we use the framework of finite set constraints. The idea is that a proposition x can also be considered as Boolean variable x ∈ {0, 1}. The literals x and ∼x are then represented by Boolean set constraints x ∈ {1} and x ∈ {0} respectively. More generally, arbitrary finite variables x with values in Θx and finite set constraints x ∈ X , X ⊆ Θx, can be considered. This improves the expressiveness of assumption-based systems significantly. This paper shows how assumption-based systems can be extended to finite set constraints and it describes a method to determine arguments for hypotheses in this more general situation.