A Dynamic Logic-Based Modal Prolog

The field of modal logic programming has been developed to extend the expressiveness of logic programming. By introducing the modal operators of necessity and possibility within the language of Horn clauses, modal logic programming languages retain its declarative nature without resorting to non-logical features. DL Prolog is a modal logic programming language extending pure Prolog with dynamic logic modalities able to embed efficient imperative programs, while retaining a declarative reading. Furthermore it provides the means to isolate non-logical features of metapredicates (like cut and is) into semantically equivalent dynamic logic modalities. The contributions of this paper are twofold: firstly, the application of the dynamic logic-based modal Prolog to embed efficient programs for numeric computation, and secondly, the soundness proof of this modal Prolog through a logical system with inference rules written in the Gentzen sequent style.