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We present HYPROLOG, a novel integration of Prolog with assumptions and abduction which is implemented in and partly borrows syntax from Constraint Handling Rules (CHR) for integrity constraints. Assumptions are a mechanism inspired by linear logic and taken over from Assumption Grammars. The language shows a novel flexibility in the interaction between the different paradigms, including all additional built-in predicates and constraints solvers that may be available. Assumptions and abduction are especially useful for language processing, and we can show how HYPROLOG works seamlessly together with the grammar notation provided by the underlying Prolog system. An operational semantics is given which complies with standard declarative semantics for the “pure” sublanguages, while for the full HYPROLOG language, it must be taken as definition. The implementation is straightforward and seems to provide for abduction, the most efficient of known implementations; the price, however, is a limited use of negations. The main difference wrt. previous implementations of abduction is that we avoid any level of metainterpretation by having Prolog execute the deductive steps directly and by treating abducibles (and assumptions as well) as CHR constraints.

HYPROLOG: A New Logic Programming Language with Assumptions and Abduction