Abstract
Condensed BCK-logic, i.e. the set of BCK-theorems provable by the condensed detachment rule of Carew Meredith, has been shown to be exactly the set of principal types of BCK-λ-terms. In 1993 Sachio Hirokawa gave a characterization of the set of principal types of BCK-λ-terms in β-normal form based on a relevance relation that he defined between the type variables in a type. We define a symmetric notion of this and call it dependence relation. Then, using the notion of β S -reduction introduced by de Groote, we obtain a characterization of the complete set of principal types of BCK-λ-terms.
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Broda, S., Damas, L. (2007). On Principal Types of BCK-λ-Terms. In: Leivant, D., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2007. Lecture Notes in Computer Science, vol 4576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73445-1_9
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DOI: https://doi.org/10.1007/978-3-540-73445-1_9
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