On Computational Interpretations of the Modal Logic S4 I. Cut Elimination (1996)
| Venue: | Institut fur Logik, Komplexitat und Deduktionssysteme, Universitat |
| Citations: | 8 - 6 self |
BibTeX
@TECHREPORT{Goubault-larrecq96oncomputational,
author = {Jean Goubault-larrecq},
title = {On Computational Interpretations of the Modal Logic S4 I. Cut Elimination},
institution = {Institut fur Logik, Komplexitat und Deduktionssysteme, Universitat},
year = {1996}
}
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Abstract
A language of constructions for minimal logic is the -calculus, where cut-elimination is encoded as fi-reduction. We examine corresponding languages for the minimal version of the modal logic S4, with notions of reduction that encodes cut-elimination for the corresponding sequent system. It turns out that a natural interpretation of the latter constructions is a -calculus extended by an idealized version of Lisp's eval and quote constructs. In this first part, we analyze how cut-elimination works in the standard sequent system for minimal S4, and where problems arise. Bierman and De Paiva's proposal is a natural language of constructions for this logic, but their calculus lacks a few rules that are essential to eliminate all cuts. The S4 - calculus, namely Bierman and De Paiva's proposal extended with all needed rules, is confluent. There is a polynomial-time algorithm to compute principal typings of given terms, or answer that the given terms are not typable. The typed S4-calculus te...
