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Semantics for Dual and Symmetric Combinatory Calculi

Katalin Bimbó
Journal of Philosophical Logic
Vol. 33, No. 2 (Apr., 2004), pp. 125-153
Published by: Springer
Stable URL: http://www.jstor.org/stable/30226803
Page Count: 29
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Semantics for Dual and Symmetric Combinatory Calculi
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Abstract

We define dual and symmetric combinatory calculi (inequational and equational ones), and prove their consistency. Then, we introduce algebraic and set theoretical relational and operational - semantics, and prove soundness and completeness. We analyze the relationship between these logics, and argue that inequational dual logics are the best suited to model computation.

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