New Completeness Results For Lazy Conditional Narrowing

In this paper we consider the lazy conditional narrowing calculus LCNC of [4]. LCNC is the extension of lnc to conditional term rewrite systems (CTRSs for short). The extension is motivated by the observation that CTRSs are much more expressive than unconditional TRSs for describing interesting problems in natural and concise way. However, the additional expressive power raises two problems: (1) confluence is insufficient to guarantee the completeness with respect to normalized solutions, and (2) the search space increases dramatically because the conditions of the applied rewrite rule are added to the current goal. In [4] several completeness results for lcnc are presented. The only result which does not assume some kind of termination assumption does not permit extra variables in the conditions and right-hand sides of the rewrite rules. In this paper we show the completeness of LCNC with leftmost selection for the class of (confluent) deterministic oriented CTRSs. Determinism was introduced by Ganzinger [1] and has proved to be very useful for the study of the (unique) termination behavior of well-moded Horn clause programs (cf. [5])

New Completeness Results for Lazy Conditional Narrowing

We show the completeness of the lazy conditional narrowing calculus (LCNC) with leftmost selection for the class of deterministic conditional rewrite systems (CTRSs). Deterministic CTRSs permit extra variables in the right-hand sides and conditions of their rewrite rules. From the completeness proof we obtain several insights to make the calculus more deterministic. Furthermore, and similar to the refinements developed for the unconditional case, we succeeded in removing all nondeterminism due to the choice of the inference rule of LCNC by imposing further syntactic conditions on the participating CTRSs and restricting the set of solutions for which completeness needs to be established. Categories and Subject Descriptor