Finite structural axiomatization of every finite-valued propositional calculus

Studia Logica 39 (1):1 - 4 (1980)
In [2] A. Wroski proved that there is a strongly finite consequence C which is not finitely based i.e. for every consequence C + determined by a finite set of standard rules C C +. In this paper it will be proved that for every strongly finite consequence C there is a consequence C + determined by a finite set of structural rules such that C(Ø)=C +(Ø) and = (where , are consequences obtained by adding to the rules of C, C + respectively the rule of substitution). Moreover it will be shown that under certain assumptions C=C +.
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