Investigation into combinatory systems with dual combinators

Studia Logica 66 (2):285-296 (2000)
Abstract
Combinatory logic is known to be related to substructural logics. Algebraic considerations of the latter, in particular, algebraic considerations of two distinct implications, led to the introduction of dual combinators in Dunn & Meyer 1997. Dual combinators are "mirror images" of the usual combinators and as such do not constitute an interesting subject of investigation by themselves. However, when combined with the usual combinators, the whole system exhibits new features. A dual combinatory system with weak equality typically lacks the Church-Rosser property, and in general it is inconsistent. In many subsystems terms "unexpectedly" turn out to be weakly equivalent. The paper is a preliminary attempt to investigate some of these issues, as well as, briefly compare function application in symmetric -calculus and dual combinatory logic
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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Reprint years 2004
DOI 10.1023/A:1005252431462
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Semantics for Dual and Symmetric Combinatory Calculi.Katalin Bimbó - 2004 - Journal of Philosophical Logic 33 (2):125-153.
The Church-Rosser Property in Dual Combinatory Logic.Katalin Bimbó - 2003 - Journal of Symbolic Logic 68 (1):132-152.
The Church-Rosser Property in Symmetric Combinatory Logic.Katalin Bimbó - 2005 - Journal of Symbolic Logic 70 (2):536 - 556.

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