A fixpoint semantics for stratified databases

Abstract

Przymusinski extended the notion of stratified logic programs, developed by Apt, Blair and Walker, and by van Gelder, to stratified databases that allow both negative premises and disjunctive consequents. However, he did not provide a fixpoint theory for such class of databases. On the other hand, although a fixpoint semantics has been developed by Minker and Rajasekar for non-Horn logic programs, it is tantamount to traditional minimal model semantics which is not sufficient to capture the intended meaning of negation in the premises of clauses in stratified databases. In this paper, a fixpoint approach to stratified databases is developed, which corresponds with the perfect model semantics. Moreover, algorithms are proposed for computing the set of perfect models of a stratified database.