Every Formula-Based Logic Program Has a Least Infinite-Valued Model

Details Every Formula-Based Logic Program Has a Least Infinite-Valued Model Every Formula-Based Logic Program Has a Least Infinite-Valued Model

2011-08-31

arxiv.org/abs/1108.6274v1

Computer Science

Logic in Computer Science

This paper appears in the Proceedings of the 19th International Conference on Applications of Declarative Programming and Know

Scientific paper

Every definite logic program has as its meaning a least Herbrand model with respect to the program-independent ordering "set-inclusion". In the case of normal logic programs there do not exist least models in general. However, according to a recent approach by Rondogiannis and Wadge, who consider infinite-valued models, every normal logic program does have a least model with respect to a program-independent ordering. We show that this approach can be extended to formula-based logic programs (i.e., finite sets of rules of the form A\leftarrowF where A is an atom and F an arbitrary first-order formula). We construct for a given program P an interpretation M_P and show that it is the least of all models of P. Keywords: Logic programming, semantics of programs, negation-as-failure, infinite-valued logics, set theory

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