BCI-algebras from the point of view of logic

Bulletin of the Section of Logic 12 (3):126-128 (1983)
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Abstract

The following logics are the most noteworthy from the perspective of the calculus of combinators: the Hilbert’s positive implicational logic , the Church’s weak theory of implication , the BCK-logic, and the BCI-logic. Their significance is due to a certain correspondence between combinators and implicational formulas . The first three logics mentioned have been immensely investigated but it was not so in case of the remaining one. The BCI-logics was mentioned by A. N. Prior in the second edition of his Formal Logic of 1962 where it was credited to C. A. Meredith and dated in 1956 . A

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