Fuzzy bi-Gödel modal logic and its paraconsistent relatives
Marta Bílková,
Sabine Frittella,
Daniil Kozhemiachenko
Abstract:We present an axiomatization of the fuzzy bi-Gödel modal logic ${\textbf{K}\textsf{biG}}^{\textsf{f}}$ formulated in the language containing $\triangle $ (Baaz Delta operator) and treating $-\!-\!< $ (co-implication) as the defined connective. We also consider two paraconsistent relatives of ${\textbf{K}\textsf{biG}}^{\textsf{f}}$ — $\textbf{K}\textsf{G}^{2\pm \textsf{f}}$ and $\textsf{G}^{2\pm \textsf{f}}_{\blacksquare ,\blacklozenge }$. These logics are defined on fuzzy frames with two valuations $e_{… Show more
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