A Note on Logic Programming Fixed-Point Semantics

In this paper, we present an account of classical Logic Programming fixed-point semantics in terms of two standard categorical constructions in which the least Herbrand model is characterized by properties of universality. In particular, we show that, given a program P , the category of models of P is reflective in the category of interpretations for P . In addition, we show that the immediate consequence operator gives rise to an endofunctor TP on the category of Herbrand interpretations for P such that category of algebras for TP is the category of Herbrand models of P . As consequences, we have that the least Herbrand model of P is the least fixed-point of TP and is the reflection of the empty Herbrand interpretation.