Decomposition of linear recursive logic programs

Abstract

In practise, most recursive logic queries to a deductive database are expressed by linear recursive datalog programs with exactly one linear recursive rule, so-called linear datalog sirups. The notion of k-sided linear datalog sirups has been introduced by Naughton, who characterized one-sided linear datalog sirups based on a graph model. We use another graph representation of linear datalog sirups for extending this characterization to arbitrary sidedness k. It is shown that 0 ≤ k ≤ n′, where n′ is the dimension of the sirup, i.e. the arity of its recursive predicate symbol. An efficient (quadratic time) algorithm for the determination of the sidedness k is presented. We will define the canonicalk-sided normal form (CKNF) for linear datalog sirups. Every k-sided linear datalog sirup can be normalized to an equivalent k-sided CKNF sirup. Every k-sided CKNF sirup can be decomposed by counting techniques into k lower-dimensional linear sirups in a very simple normal form for non-datalog sirups, the generalized form for transitive closure, which allows for the usage of very efficient query evaluation algorithms.