On the Declarative Semantics of Multi-Adjoint Logic Programs

Authors:
P. Julián;G. Moreno;J. Penabad
Affiliations:
Dep. Information Technologies and Systems, UCLM, Ciudad Real, Spain 13071;Dep. Computing Systems, UCLM, Albacete, Spain 02071;Dep. Mathematics, UCLM, Albacete, Spain 02071
Venue:
IWANN '09 Proceedings of the 10th International Work-Conference on Artificial Neural Networks: Part I: Bio-Inspired Systems: Computational and Ambient Intelligence
Year:
2009

Citing 7
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Abstract

The notion of least Herbrand model has been traditionally accepted as the declarative semantics for programs in the context of pure logic programming. Some adaptations of this concept, using model-theory, were made for a few number of fuzzy logic programming frameworks in the recent years. Unfortunately, this is not the case of multi-adjoint logic programming, one of the most expressive, powerful approaches for fuzzifying logic programming. To fulfill this gap, in this paper we propose a declarative semantics for such kind of fuzzy logic programs based on the so-called least fuzzy Herbrand model. We prove and important "minimality" property of our construction which can not trivially be inherited from pure logic programming. Moreover, apart from relating our notion with other existing procedural and fix-point semantics (what is also instrumental to prove its properties), we provide evident cases where our construction exists even when the rest of the aforementioned fuzzy semantics remain undefined.