Abstract
Every definite logic program has as its meaning a least Herbrand model with respect to the program-independent ordering \(\subseteq \). 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 \(A\leftarrow \phi \) where \(A\) is an atom and \(\phi \) 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 \(P\).
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Acknowledgements.
This work has been financed through a grant made available by the Carl Zeiss Foundation. The author is grateful to Prof. Dr. Peter Schroeder-Heister, Hans-Joerg Ant, M. Comp. Sc., and three anonymous reviewers for helpful comments and suggestions.
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Lüdecke, R. (2013). Every Formula-Based Logic Program Has a Least Infinite-Valued Model. In: Tompits, H., et al. Applications of Declarative Programming and Knowledge Management. INAP WLP 2011 2011. Lecture Notes in Computer Science(), vol 7773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41524-1_9
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DOI: https://doi.org/10.1007/978-3-642-41524-1_9
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