Stratified and Three-valued Logic Programming Semantics.

Abstract

The familiar fixed point semantics for Horn clause programs gives both smallest and biggest fixed points fundamental roles. We show how to extend this idea to the family of stratified logic programs, producing a semantics we call weak stratified, that is compatible with but not the same as the conventional stratified semantics. And we show weak stratified semantics coincides with one based on three valued logic, a semantics that is generally applicable, and that does not require stratification assumptions. 1 Introduction A beautiful fixed point semantics for Horn clause logic programming has been developed, based on classical logic ([16], [2]). But it can not deal adequately with negations when they are allowed in clause bodies. Two kinds of generalizations have been proposed to deal with this problem. The best known is stratification [1], [17]. Here the kind of logic programs one is allowed to write is restricted; recursions through negations are forbidden. For such programs...