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A Resolution Calculus for Second-order Logic with Eager Unification
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The efficiency of the first-order resolution calculus is impaired when lifting it to higher-order logic. The main reason for that is the semi-decidability and infinitary natureof higher-order unification algorithms, which requires the integration of unification within the calculus and results in a non-efficient search for refutations.We present a modification of the constrained resolution calculus (Huet'72) which uses an eager unification algorithm while retaining completeness. Thealgorithm is complete with regard to bounded unification only, which for many cases, does not pose a problem in practice.
Title: A Resolution Calculus for Second-order Logic with Eager Unification
Description:
The efficiency of the first-order resolution calculus is impaired when lifting it to higher-order logic.
The main reason for that is the semi-decidability and infinitary natureof higher-order unification algorithms, which requires the integration of unification within the calculus and results in a non-efficient search for refutations.
We present a modification of the constrained resolution calculus (Huet'72) which uses an eager unification algorithm while retaining completeness.
Thealgorithm is complete with regard to bounded unification only, which for many cases, does not pose a problem in practice.
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