Entailment and inference in fuzzy logic using fuzzy preorders

Within the framework of fuzzy logic, the notion of semantic entailment and its relationship with inference is analysed. In particular, the case of conditional statements modeled through fuzzy preorders is considered. The main results exhibit a strong relationship between the notions of entailment and implication, driven by the pointwise order of the unit interval In the case of R-implications, and by suitable modifications of this order, in the case of general fuzzy preorders