Planning for an Efficient Implementation of Hypothetical Bousi~Prolog

This paper explores the integration of hypothetical reasoning into an efficient implementation of the fuzzy logic language Bousi~Prolog. To this end, we first analyse what would be expected from a logic inference system, equipped with what is called embedded implication, to model solving goals with respect to assumptions. We start with a propositional system and incrementally build more complex systems and implementations to satisfy the requirements imposed by a system like Bousi~Prolog. Finally, we propose an inference system, operational semantics, and the translation function to generate efficient Prolog programs from Bousi~Prolog programs.