Simple contrapositive assumption-based argumentation frameworks

Assumption-based argumentation is one of the most prominent formalisms for logical (or structured) argumentation, with tight links to different forms of defeasible reasoning. In this paper we study the Dung semantics for extended forms of assumption-based argumentation frameworks (ABFs), based on any contrapositive propositional logic, and whose defeasible assumptions are expressed by arbitrary formulas in that logic. We show that unless the falsity propositional constant is part of the defeasible assumptions, the grounded and the well-founded semantics for ABFs lack most of the desirable properties they have in abstract argumentation frameworks (AAFs), and that for simple definitions of the contrariness operator and the attacks relations, preferred and stable semantics are reduced to naive semantics. We also show the redundancy of the closure condition in the standard definition of Dung's semantics for ABFs, and investigate the use of disjunctive attacks in this setting. Finally, we show some close relations of reasoning with ABFs to reasoning with maximally consistent sets of premises, and consider some properties of the induced entailments, such as being cumulative, preferential, or rational relations that satisfy non-interference.