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Rough sets and 3-valued Lukasiewicz logic. (English) Zbl 0895.03007

A relationship between rough logic, \(\mathcal RL\) [see M. Banerjee and 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, \(\mathcal L3\), is established. Let \(\vdash_{RL}\) (resp., \(\vdash_{L3}\)) denote the consequence relation in \(\mathcal RL\) (resp., \(\mathcal L3\)). 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 \(\mathcal RL\) into the modal system S5 is also shown.

MSC:

03B50 Many-valued logic
03B60 Other nonclassical logic
03B45 Modal logic (including the logic of norms)

Citations:

Zbl 0864.03041
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