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- W2023145007 abstract "We give a first-order presentation of higher-order logic based on explicit substitutions. This presentation is intentionally equivalent to the usual presentation of higher-order logic based on λ-calculus, that is, a proposition can be proved without the extensionality axioms in one theory if and only if it can be in the other. We show that the Extended Narrowing and Resolution first-order proof-search method can be applied to this theory. In this way we get a step-by-step simulation of higher-order resolution. Hence, expressing higher-order logic as a first-order theory and applying a first-order proof search method is a relevant alternative to a direct implementation. In particular, the well-studied improvements of proof search for first-order logic could be reused at no cost for higher-order automated deduction. Moreover, as we stay in a first-order setting, extensions, such as equational higher-order resolution, may be easier to handle." @default.
- W2023145007 created "2016-06-24" @default.
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- W2023145007 date "2001-02-01" @default.
- W2023145007 modified "2023-09-25" @default.
- W2023145007 title "HOL-λσ: an intentional first-order expression of higher-order logic" @default.
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- W2023145007 doi "https://doi.org/10.1017/s0960129500003236" @default.
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