Abstract

Even though higher-order calculi for automated theorem proving are rather old, tableau calculi have not been investigated yet. This paper presents two free variable tableau calculi for higher-order logic that use higher-order unification as the key inference procedure. These calculi differ in the treatment of the substitutional properties of equivalences. The first calculus is equivalent in deductive power to the machineoriented higher-order refutation calculi known from the literature, whereas the second is complete with respect to Henkin's general models.

Citations