First-order modal logics, as traditionally formulated, are not expressive enough. It is this that is behind the diﬃculties in formulating a good analog of Herbrand’s Theorem, as well as the well-known problems with equality, non-rigid designators, deﬁnite descriptions, and nondesignating terms. We show how all these problems disappear when modal language is made more expressive in a simple, natural way. We present a semantic tableaux system for the enhanced logic, and (very) brieﬂy discuss implementation issues.
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