We propose afirst-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 Extended Narrowing and Resolutionfirstorder 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.
CITATION STYLE
Dowek, G., Hardin, T., & Kirchner, C. (1999). HOL-λσ: An intentional first-order expression of higher-order logic. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1631, pp. 317–331). Springer Verlag. https://doi.org/10.1007/3-540-48685-2_26
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