A Modal Herbrand Theorem

Authors:
Melvin Fitting
Affiliations:
Dept. Mathematics and Computer Science, Lehman College (CUNY), Bronx, NY 10468, Depts. Computer Science, Philosophy, Mathematics, Graduate Center (CUNY), 33 West 42nd Street, NYC, NY 10036. e-mail ...
Venue:
Fundamenta Informaticae
Year:
1996

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Abstract

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. (I want to thank a referee for pointing out a serious error in an earlier version of this paper and for being generally uncompromising.)