Generalized correspondence analysis for three-valued logics (Q1632053)

This paper extends the correspondence analysis of \textit{B. Kooi} and \textit{A. Tamminga} [Rev. Symb. Log. 5, No. 4, 720--730 (2012; Zbl 1270.03045)] to a larger class of three-valued logics. It generalizes the results from the author and \textit{V. Shangin} [Rev. Symb. Log. 10, No. 4, 756--781 (2017; Zbl 1387.03009)], and from the author [Log. Log. Philos. 26, No. 2, 197--206 (2017; Zbl 1417.03181); Log. Univers. 11, No. 4, 525--532 (2017; Zbl 1385.03032); Log. Log. Philos. 27, No. 1, 53--66 (2018; Zbl 1456.03048); Mosc. Univ. Math. Bull. 73, No. 1, 30--33 (2018; Zbl 1390.03024); Mosc. Univ. Math. Bull. 72, No. 3, 133--136 (2017; Zbl 1396.03048)] regarding deduction systems for three-valued logics. It is shown that the method of correspondence analysis works for the negative fragments of the paraconsistent logic of paradox $\mathbf{LP}$ and the strong Kleene logic $\mathbf{K_3}$ and that this method is also suitable for the negative fragments of Heytings's logic $\mathbf{G_3}$ and its dual $\mathbf{DG_3}$. The power of generalized correspondence analysis is illustrated with examples of $\mathbf{LP}$ and the logics $\mathbf{L3A}$ and $\mathbf{L3B}$ of \textit{J.-Y. Beziau} and \textit{A. Franceschetto} [Springer Proc. Math. Stat. 152, 131--145 (2015; Zbl 1423.03097)].