  This paper explores goal-directed proof search in first-order multi-modal
logic. The key issue is to design a proof system that respects the modularity
and locality of assumptions of many modal logics. By forcing ambiguities to be
considered independently, modular disjunctions in particular can be used to
construct efficiently executable specifications in reasoning tasks involving
partial information that otherwise might require prohibitive search. To achieve
this behavior requires prior proof-theoretic justifications of logic
programming to be extended, strengthened, and combined with proof-theoretic
analyses of modal deduction in a novel way.
