Abstract

In this report we introduce a new proof-theoretic approach to the semantics of Constraint Logic Programming, based on an intuitionistic first-order modal logic, called QLL. The distinguishing feature of this new approach is that the logic calculus of QLL is used not only to capture the usual extensional aspects of Logic Programming, i.e. "which queries are successful, " but also some of the intensional aspects, i.e. "what is the answer constraint and how is it constructed." It provides for a direct link between the model-theoretic and the operational semantics following a formulas-as-programs and proofs-as-constraints principle. This approach makes use of logic in a different way than other approaches based on logic calculi. On the one side it is to be distinguished from the well-known provability semantics which is concerned merely with what is derivable as opposed to how it is derivable, paying attention to the fact that it is the how that determines the answer constraint. ...

Citations