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Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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Bousi~Prolog is a fuzzy logic programming language with an operational semantics which is an adaptation of the SLD resolution principle, where classical unification has been replaced by a fuzzy unification algorithm based on proximity relations. Hence, it is a programming language well suited for dealing with uncertainty and approximate reasoning. There are several practical applications where Bousi~Prolog can be useful: flexible query answering; advanced pattern matching; information retrieval where textual information is selected or analyzed using an ontology; text cataloging and analysis; etc. In this paper we give a model-theoretic semantics for a pure subset of this language: we formalize the notion of least fuzzy Herbrand model as the declarative semantics for definite programs. We prove various important properties of these models. Finally we define an immediate consequences operator, which is proved monotonous and continuous, obtaining a fixpoint characterization of the least fuzzy Herbrand model.