Type Correct programs A semantic approach

“Logic programming does not take types into account” is a general reproach. Naish presents in [15] an approach of types which is very general and well adapted to logic programming, in connection with the notion of specification. He gives a definition of "type correct program" Unfortunately, the semantics of the completion of the program and SLDNF-Resolution do not allow to generalize the results for definite programs to programs with negation and Naish raises the question of the choice of another semantics

We continue Naish study, and we consider explicitly Herbrand interpretations in a three-valued logic. We consider two semantics well-founded semantics and Fitting semantics. We give in our new framework necessary and sufficient conditions insuring that a program is type correct. Naish conditions are special case of ours. In this paper, we only consider well-founded semantics, but we obtain the same results for Fitting semantics

This work is also an application of methods of [7, 8, 13]