Computing argumentation in logic programming

Abstract

In recent years, argumentation has been shown to be an appropriate framework in which logic programming with negation as failure as well as other logics for non-monotonic reasoning can be encompassed. Many of the existing semantics for negation as failure in logic programming can be understood in a uniform way using argumentation. Moreover, other logics for non-monotonic reasoning that can also be formulated via argumentation can be given new semantics, by a direct extension of the logic programming semantics. In this paper we develop an abstract computational framework where various argumentation semantics can be computed via different parametric variations of a simple basic proof theory. This proof theory is given in terms of derivations of trees where each node in a tree contains an argument (or attack) against its corresponding parent node. The proposed proof theory, defined here for the case of logic programming, generalizes directly to other logics for non-monotonic reasoning that can also be formalized via argumentation. The abstract proof theory forms the basis for developing concrete top-down proof procedures for query evaluation. These proof procedures are obtained by adopting specific search strategies and ways of computing attacks in the particular argumentation framework. For logic programming these procedures can be seen as a generalization of the Eshghi-Kowalski abductive proof procedure that in turn generalizes SLDNF.