How to use modalities and sorts in Prolog

Abstract

Standard logic programming languages like Prolog lack the possibility of dealing with modalities and/or sorts. A first idea how to overcome this problem (and that without changing anything on Prolog itself) would be to apply the well-known relational translation approaches from modal and sorted logic into first-order predicate logic and to feed this translation result into Prolog. This, however, leads into other problems: firstly, the transformed problem is usually of much bigger size (number of clauses) than the original one and, secondly, very often it is not even in Horn form anymore.

In this paper a translation approach is proposed which avoids both of these problems, i.e. the number of clauses after translation is exactly as big as it would have been if we simply ignored the modal operators and sort restrictions and, also, the result is in Horn form provided it was already before (modulo modal operators and sorts).