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A Modal Herbrand Theorem


We state and prove a modal Herbrand theorem that is, we believe, a more natural analog of the classical version than has appeared before. The statement itself requires the enlargement of the usual machinery of first-order modal logic—we use the device of predicate abstraction, something that has been considered elsewhere as well. This expands the expressive power of modal logic in a natural way. Our proof of the modal version of Herbrand's theorem uses a tableau system that takes predicate abstraction into account. It is somewhat simpler than other systems for the same purpose that have previously appeared.