Term-generic logic

Popescu, Andrei and Roşu, Grigore (2015) Term-generic logic. Theoretical Computer Science, 577 . pp. 1-24. ISSN 0304-3975 [Article] (doi:10.1016/j.tcs.2015.01.047)

Abstract

We introduce term-generic logic (TGL), a first-order logic parameterized with terms defined axiomatically (rather than constructively), by requiring terms to only provide free variable and substitution operators satisfying some reasonable axioms. TGL has a notion of model that generalizes both first-order models and Henkin models of the lambda-calculus. The abstract notions of term syntax and model are shown to be sufficient for obtaining the completeness theorem of a Gentzen system generalizing that of first-order logic. Various systems featuring bindings and contextual reasoning, ranging from pure type systems to the pi-calculus, are captured as theories inside TGL. For two particular, but rather typical instances—untyped lambda-calculus and System F—the general-purpose TGL models are shown to be equivalent with standard ad hoc models.

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