Thresholded semantic framework for a fully integrated fuzzy logic language

This work proposes a declarative semantics based on a fuzzy variant of the classical notion of least Herbrand model for the so-called FASILL programming language (acronym of “Fuzzy Aggregators and Similarity Into a Logic Language”) which has been recently designed and implemented for coping with implicit/explicit truth degree annotations, a great variety of connectives and unification by similarity. Also, we define an immediate consequence operator that allows us to give a fixpoint characterization of the least Herbrand model for a FASILL program. A remarkable aspect of our declarative and fixpoint semantics is the fact that both have been enriched with the use of thresholds thanks to the natural ability of the underlying fuzzy language for managing such constructs. Moreover, we have connected both semantics with an operational one, which also manages thresholds in an efficient way, by proving the correctness of the whole semantic framework.