Geodesic
On the axiomatization of finite-valued logical calculi
Sbornik. Mathematics, Tome 51 (1985) no. 2, pp. 473-491

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The authors propose a general effective method for constructing a predicate calculus complete with respect to $L_n$-general validity in quasi-Hilbert form (i.e. in Hilbert form but using a language extended by finitely many “external metasymbols”) on the basis of an arbitrary many-valued logic. For logics in a fairly large class containing many of the logics studied previously, a general effective method is indicated for constructing a predicate calculus of Hilbert type complete with respect to $L_n$-general validity. The results and methods of the article make it possible to initiate the development of model theory on the basis of an arbitrary finite-valued logic. Bibliography: 25 titles. 
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     title = {On the axiomatization of finite-valued logical calculi},
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O. M. Anshakov; S. V. Rychkov. On the axiomatization of finite-valued logical calculi. Sbornik. Mathematics, Tome 51 (1985) no. 2, pp. 473-491. http://geodesic.mathdoc.fr/item/SM_1985_51_2_a9/