Journal of Symbolic Logic

The Church-Rosser property in dual combinatory logic

Katalin Bimbó

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Abstract

Dual combinators emerge from the aim of assigning formulas containing $\leftarrow$ as types to combinators. This paper investigates formally some of the properties of combinatory systems that include both combinators and dual combinators. Although the addition of dual combinators to a combinatory system does not affect the unique decomposition of terms, it turns out that some terms might be redexes in two ways (with a combinator as its head, and with a dual combinator as its head). We prove a general theorem stating that no dual combinatory system possesses the Church-Rosser property. Although the lack of confluence might be problematic in some cases, it is not a problem per se. In particular, we show that no damage is inflicted upon the structurally free logics, the system in which dual combinators first appeared.

Article information

Source
J. Symbolic Logic, Volume 68, Issue 1 (2003), 132-152.

Dates
First available in Project Euclid: 21 February 2003

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1045861508

Digital Object Identifier
doi:10.2178/jsl/1045861508

Mathematical Reviews number (MathSciNet)
MR1959314

Zentralblatt MATH identifier
1045.03017

Citation

Bimbó, Katalin. The Church-Rosser property in dual combinatory logic. J. Symbolic Logic 68 (2003), no. 1, 132--152. doi:10.2178/jsl/1045861508. https://projecteuclid.org/euclid.jsl/1045861508


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