A foundational characterization of Hoare Logic

Daniel Leivant

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arXiv · 2605.13944

A foundational characterization of Hoare Logic

Daniel Leivant

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Abstract

We show that a partial-correctness assertion about an iterative program is provable in Hoare Logic iffit is provable in standard second-order logic with comprehension restricted to first-order predicates. This equivalence was claimed twice in the past, both with faulty proofs, and seems to be the first foundational characterization of Hoare Logic.

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Daniel Leivant. 2026-05-13. A foundational characterization of Hoare Logic. https://arxiv.org/abs/2605.13944

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