HOL-λσ: An Intentional First-Order Expression of Higher-Order Logic

Gilles Dowek Thérèse Hardin 1 Claude Kirchner
1 SPI - Sémantiques, preuves et implantation
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : We propose a first-order presentation of higher-order logic based on explicit substitutions. It is intentionally equivalent to the usual presentation of higher-order logic based on λ-calculus, i.e. a proposition can be proved without the extensionality axioms in one theory if and only if it can in the other. The tiExtended Narrowing and Resolution first-order proof-search method can be applied to this theory. This allows to simulate higher-order resolution step by step and furthermore leaves room for further optimizations and extensions.
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Conference papers
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https://hal.archives-ouvertes.fr/hal-01574463
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Submitted on : Monday, August 14, 2017 - 4:00:18 PM
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Gilles Dowek, Thérèse Hardin, Claude Kirchner. HOL-λσ: An Intentional First-Order Expression of Higher-Order Logic. 10th International Conference, RTA'99, Jul 1999, Trento, Italy. pp.317-331, ⟨10.1007/3-540-48685-2_26⟩. ⟨hal-01574463⟩

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