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Journal Articles Journal of Automated Reasoning Year : 2023

Superposition for Higher-Order Logic

Abstract

We recently designed two calculi as stepping stones towards superposition for full higher-order logic: Boolean-free λ-superposition and superposition for first-order logic with interpreted Booleans. Stepping on these stones, we finally reach a sound and refutationally complete calculus for higher-order logic with polymorphism, extensionality, Hilbert choice, and Henkin semantics. In addition to the complexity of combining the calculus's two predecessors, new challenges arise from the interplay between λ-terms and Booleans. Our implementation in Zipperposition outperforms all other higher-order theorem provers and is on a par with an earlier, pragmatic prototype of Booleans in Zipperposition.
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hal-04298616 , version 1 (21-11-2023)

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Alexander Bentkamp, Jasmin Blanchette, Sophie Tourret, Petar Vukmirović. Superposition for Higher-Order Logic. Journal of Automated Reasoning, 2023, 67 (1), pp.10. ⟨10.1007/s10817-022-09649-9⟩. ⟨hal-04298616⟩
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