Natural deduction for Fitting's four-valued generalizations of Kleene's logics
In [Ann. Soc. Math. Pol., Ser. IV, Fundam. Inf. 20, No. 1--3, 113--131 (1994; Zbl 0804.03016)] \textit{M. Fitting} studied some four-valued generalizations of the three-valued logics introduced by \textit{S. C. Kleene} [Introduction to metamathematics. Amsterdam: North-Holland Publishing Co.; Groningen: P. Noordhoff N. V., (1952; Zbl 0047.00703)]. The aim of the article under review is to present natural deduction systems, as well as completeness theorems, for some of these four-valued logics. In particular \(\mathbf{FDE}^\rightarrow\), \(\mathbf{FDE}^\leftrightarrow\), plus a new logic introduced in the present paper, called \(\mathbf{FDE}^\leftarrow\).
scientific article; zbMATH DE number 6825511
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