\input zb-basic
\input zb-ioport
\iteman{io-port 01136650}
\itemau{Banerjee, Mohua}
\itemti{Rough sets and 3-valued Lukasiewicz logic.}
\itemso{Ann. Soc. Math. Pol., Ser. IV, Fundam. Inf. 31, No.3-4, 213-220 (1997).}
\itemab
A relationship between rough logic, $\cal RL$ [see {\it M. Banerjee} and {\it M. K. Chakraborty}, Ann. Soc. Math. Pol., Ser. IV, Fundam. Inf. 28, No. 3-4, 211-221 (1996; Zbl 0864.03041)], and 3-valued Lukasiewicz logic, $\cal L3$, is established. Let $\vdash_{RL}$ (resp., $\vdash_{L3}$) denote the consequence relation in $\cal RL$ (resp., $\cal L3$). It holds via some translations that for a set of formulas $\Gamma$ and a formula $\alpha$, $\Gamma\vdash_{RL}\alpha$ iff $\Gamma \vdash_{L3}\alpha$. The existence of an embedding of $\cal RL$ into the modal system S5 is also shown.
\itemrv{Anna Gomoli\'nska (Bialystok)}
\itemcc{}
\itemut{rough sets; rough logic; 3-valued Lukasiewicz logic}
\itemli{}
\end