Term-generic logic

Article

Popescu, A. and Roşu, G. 2015. Term-generic logic. Theoretical Computer Science. 577, pp. 1-24. https://doi.org/10.1016/j.tcs.2015.01.047
TypeArticle
TitleTerm-generic logic
AuthorsPopescu, A. and Roşu, G.
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.

Research GroupFoundations of Computing group
PublisherElsevier B. V.
JournalTheoretical Computer Science
ISSN0304-3975
Publication dates
Print27 Apr 2015
Publication process dates
Deposited23 Apr 2015
Accepted27 Jan 2015
Output statusPublished
Additional information

Available online 4 February 2015

Digital Object Identifier (DOI)https://doi.org/10.1016/j.tcs.2015.01.047
LanguageEnglish
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