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Holls: an Intentional First-Order Expression of Higher-Order Logic

Identifieur interne : 00BE07 ( Main/Merge ); précédent : 00BE06; suivant : 00BE08

Holls: an Intentional First-Order Expression of Higher-Order Logic

Auteurs : Gilles Dowek [France] ; Thérèse Hardin ; Claude Kirchner [France]

Source :

RBID : Hal:inria-00077202

English descriptors

mix :
- automated theorem proving, deduction modulo, higher-order logic, rewriting, skolemization.

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 $\lambda$-calculus, i.e. a proposition can be proved without the extensionality axioms in one theory if and only if it can in the other. We show that we can apply the \em Extended Narrowing and Resolution first-order proof-search method to this theory. We get this way 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 at least as efficient as a direct implementation. Furthermore, 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, are easier to handle.

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https://hal.inria.fr/inria-00077202

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Le document en format XML

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<front><div type="abstract" xml:lang="en">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 $\lambda$-calculus, i.e. a proposition can be proved without the extensionality axioms in one theory if and only if it can in the other. We show that we can apply the \em Extended Narrowing and Resolution first-order proof-search method to this theory. We get this way 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 at least as efficient as a direct implementation. Furthermore, 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, are easier to handle.</div>
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Holls: an Intentional First-Order Expression of Higher-Order Logic

Holls: an Intentional First-Order Expression of Higher-Order Logic

Source :

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri