A Note on Logic Programming Fixed-Point Semantics

$P$ , 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

${T}_P$ on the category of Herbrand interpretations for

$P$ such that category of algebras for

${T}_P$ 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

${T}_P$ and is the reflection of the empty Herbrand interpretation.

logic programming, semantics of logic programming

Sassone, V.

df7d3c83-2aa0-4571-be94-9473b07b03e7

1993

Sassone, V.

df7d3c83-2aa0-4571-be94-9473b07b03e7

Sassone, V. (1993) A Note on Logic Programming Fixed-Point Semantics. 8th Meeting on Logic Programming, GULP '93.

Record type: Conference or Workshop Item (Paper)

Abstract

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 ${T}_P$ on the category of Herbrand interpretations for $P$ such that category of algebras for ${T}_P$ 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 ${T}_P$ and is the reflection of the empty Herbrand interpretation.