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system LPC+Ch; consistency
In his paper [Kybernetika 31, No. 1, 99–106 (1995; Zbl 0857.03042)], E. Turunen says in the corollary on p. 106: “Notice that the third last line on page 195 in [J. K. Mattila, “Modifier logic”, in: J. Kacprzyk (ed.) et al., Fuzzy logic for the management of uncertainty. New York: Wiley. 191–209 (1992)] stating that LPC+Ch calculus is consistent is not correct.” The system LPC+Ch is consistent, which can be seen quite trivially.
[1] Hughes G. E., Cresswell M. J.: An Introduction to Modal Logic. Methuen, London 1968 (reprinted New York 1985) MR 0439586 | Zbl 0205.00503
[2] Mattila J. K.: Modifier logic. In: Fuzzy Logic for the Management of Uncertainty (J. Kacprzyk and L. A. Zadeh, eds.). J. Wiley, New York 1992, pp. 191–209
[3] Mattila J. K.: Modified modus ponens and modal logic. Kybernetika (Supplement) 28 (1992), 28–32 MR 1226047 | Zbl 0861.03011
[4] Turunen E.: Algebraic analysis of LPC+Ch calculus. Kybernetika 31 (1995), 1, 99–106 MR 1324663
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