A Note on Logic Programming Fixed-Point Semantics

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


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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.

Item Type: Conference or Workshop Item (Paper)
Keywords: logic programming, semantics of logic programming
Divisions : Faculty of Physical Sciences and Engineering > Electronics and Computer Science > Web & Internet Science
ePrint ID: 261945
Accepted Date and Publication Date:
Date Deposited: 12 Feb 2006
Last Modified: 31 Mar 2016 14:04
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/261945

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