A Theoretical Basis for Intensional Logic Programming∗

Intensional Logic Programming (ILP) is a new form of logic programming based on intensional logic. The denotations of formulas of an intensional first-order language are given according to intensional interpretations and to a set of possible worlds. ILP provides users with several intensional operators which are used to express relationships between different worlds. After introducing the formal syntax and semantics of the underlying intensional logic, we investigate the generate properties of intensional operators which will be used to impose certain constraints on intensional logic programming systems. Then the model-theoretic semantics of ILP are developed in conjunction with the notions of intensional Herbrand interpretations and minimum models of intensional logic programs. We will show that in particular our results apply to a temporal logic programming language called Chronolog in which the set of possible worlds is the collection of moments in time.