The church-Rosser property in dual combinatory logic

Journal of Symbolic Logic 68 (1):132-152 (2003)
Abstract
Dual combinators emerge from the aim of assigning formulas containing ← 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
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DOI 10.2178/jsl/1045861508
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References found in this work BETA
Combinators and Structurally Free Logic.J. Dunn & R. Meyer - 1997 - Logic Journal of the IGPL 5 (4):505-537.
Two Extensions of the Structurally Free Logic LC.K. Bimbó & J. Dunn - 1998 - Logic Journal of the IGPL 6 (3):403-424.

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Citations of this work BETA
Semantics for Dual and Symmetric Combinatory Calculi.Katalin Bimbó - 2004 - Journal of Philosophical Logic 33 (2):125-153.

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