A General Theory of Confluent rewriting Systems for Logic Programming and its Applications

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Recently, Brass and Dix showed (\emph{Journal of Automated Reasoning} \textbf{20(1)}, 1998) that the wellfounded semantics WFS can be defined as a confluent calculus of transformation rules. This lead not only to a simple extension to disjunctive programs (\emph{Journal of Logic Programming} \textbf{38(3)}, 1999), but also to a new computation of the wellfounded semantics which is \emph{linear} for a broad class of programs. We take this approach as a starting point and generalize it considerably by developing a general theory of \emph{Confluent LP-Systems} $\cfs$. Such a system $\cfs$ is a rewriting system on the set of all logic programs over a fixed signature $\Lang$ and it induces in a natural way a canonical semantics. Moreover, we show four important applications of this theory: \emph{(1) most of the well-known semantics are induced by
confluent LP-systems}, \emph{(2) there are many more transformation rules that lead to confluent LP-systems}, \emph{(3) semantics induced by such systems can be used to model aggregation}, \emph{(4) the new systems can be used to construct interesting counterexamples to some conjectures about the space of well-behaved semantics}. Also cross-referenced as UMIACS-TR-99-46