Extensional Higher-Order Resolution

In this paper we present an extensional higher-order resolution calculus that is complete relative to Henkin model semantics. The treatment of the extensionality principles — necessary for the completeness result — by specialized (goal-directed) inference rules is of practical applicability, as an implentation of the calculus in the LEO-System shows. Furthermore, we prove the long-standing conjecture, that it is sufficient to restrict the order of primitive substitutions to the order of input formulae.

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