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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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Authors and Affiliations

  1. 23 Stratton St. Normandale, Lower Hutt Wellington, New Zealand

    Katalin Bimbó

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  1. Katalin Bimbó
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Bimbó, K. Semantics for Dual and Symmetric Combinatory Calculi. Journal of Philosophical Logic 33, 125–153 (2004). https://doi.org/10.1023/B:LOGI.0000021709.73522.34

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