We present a mathematical approach to defeasible reasoning based on arguments. This approach integrates the notion of specificity introduced by Poole and the theory of warrant presented by Pollock. The main contribution of this paper is a precise, well-defined system which exhibits correct behavior when applied to the benchmark examples in the literature. It aims for usability rather than novelty. We prove that an order relation can be introduced among equivalence classes of arguments under the equi-specificity relation. We also prove (...) a theorem that ensures the termination of the process of finding the justified facts. Two more lemmas define a reduced search space for checking specificity. In order to implement the theoretical ideas, the language is restricted to Horn clauses for the evidential context. The language used to represent defeasible rules has been restricted in a similar way. The authors intend this work to unify the various existing approaches to argument-based defeasible reasoning. (shrink)

ABSTRACT Inspired by legal reasoning, this paper presents a semantics and proof theory of a system for defeasible argumentation. Arguments are expressed in a logic-programming language with both weak and strong negation, conflicts between arguments are decided with the help of priorities on the rules. An important feature of the system is that these priorities are not fixed, but are themselves defeasibly derived as conclusions within the system. Thus debates on the choice between conflicting arguments can also be modelled. The (...) semantics of the system is given with a fixpoint definition, while its proof theory is stated in dialectical style, where a proof takes the form of a dialogue between a proponent and an opponent of an argument: an argument is shown to be justified if the proponent can make the opponent run out of moves in whatever way the opponent attacks. (shrink)