A Note on Logic Programming Fixed-Point Semantics

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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.
Vladimiro Sassone
Added 08 Aug 2010
Updated 08 Aug 2010
Type Conference
Year 1993
Where AGP
Authors Vladimiro Sassone
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