Relating defeasible and normal logic programming through transformation properties

Abstract

This paper relates the Defeasible Logic Programming ( DeLP) framework and its semantics SEM DeLP to classical logic programming frameworks. In DeLP, we distinguish between two different sorts of rules: strict and defeasible rules. Negative literals ( ∼A) in these rules are considered to represent classical negation. In contrast to this, in normal logic programming ( NLP), there is only one kind of rules, but the meaning of negative literals ( not A) is different: they represent a kind of negation as failure, and thereby introduce defeasibility. Various semantics have been defined for NLP, notably the well-founded semantics (WFS) (van Gelder et al., Proceedings of the Seventh Symposium on Principles of Database Systems, 1988, pp. 221–230; J. ACM 38 (3) (1991) 620) and the stable semantics Stable (Gelfond and Lifschitz, Fifth Conference on Logic Programming, MIT Press, Cambridge, MA, 1988, pp. 1070–1080; Proceedings of the Seventh International Conference on Logical Programming, Jerusalem, MIT Press, Cambridge, MA, 1991, pp. 579–597). In this paper we consider the transformation properties for NLP introduced by Brass and Dix (J. Logic Programming 38(3) (1999) 167) and suitably adjusted for the DeLP framework. We show which transformation properties are satisfied, thereby identifying aspects in which NLP and DeLP differ. We contend that the transformation rules presented in this paper can help to gain a better understanding of the relationship of DeLP semantics with respect to more traditional logic programming approaches. As a byproduct, we obtain the result that DeLP is a proper extension of NLP.