Modular Logic Programming and Generalized Quantifiers

The research on systems of logic programming with modules has followed two mainstreams, programming-in-the-large, where compo-sitional operators are provided for combining separate and independent modules, and programming-in-the-small, which aims at enhancing logic programming with new logical connectives. In this paper, we present a general model theoretic approach to modular logic programming which combines programming in-the-large and in-the-small in a satisfactory way. Rather than inventing completely new constructs, however, we resort to a well-known concept in formal logic: generalized quantiiers. We show how generalized quantiiers can be incorporated into logic programs, both for Horn logic programs as well as in the presence of negation. Our basic observation is then that a logic program can be seen as a generalized quantiier, and we obtain a semantics for modular logic programs this way. Generalized quantiiers in logic programs gives rise to interesting classes of logic programs. We present a taxonomy of natural such classes, and investigate their properties. In particular, their expressive power over nite structures is analyzed.