A Note on Logic Programming Fixed-Point Semantics

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 ${T}_P$ 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
At * 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.

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## More information

Published date: 1993

Venue - Dates:
8th Meeting on Logic Programming, GULP '93., 1993-01-01

Keywords:
logic programming, semantics of logic programming

Organisations:
Web & Internet Science

## Identifiers

Local EPrints ID: 261945

URI: http://eprints.soton.ac.uk/id/eprint/261945

PURE UUID: 5d33a74c-23f9-448d-a166-02e6f490d809

## Catalogue record

Date deposited: 12 Feb 2006

Last modified: 18 Jul 2017 08:56

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## Contributors

Author:
V. Sassone

## University divisions

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