The finite model property for BCK and BCIW

Studia Logica 53 (1):107 - 118 (1994)
Abstract
This paper shows that both implicational logics BCK and BCIW have the finite model property. The proof of the finite model property for BCIW, which is equal to the relevant logic $\text{R}_{\rightarrow}$ , was originally given by the first author in his unpublished paper [6] in 1973. The finite model property for BCK can be obtained by modifying the proof of that for BCIW. Here, both of these proofs will be given in a unified form and the difference between them will be clarified. Further discussions will be given in the last section
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