Set Theory and Logic


Refutation of Two Modern Modal Logics: "JYB4" and the Follow-on "AR4"

Authors: Colin James III

We evaluate the four-valued logic systems of J.-Y. Béziau and F. Schang as JYB4 and AR4. JYB4 named the four-valued modal logic Ł4 as Łukasiewicz's nightmare because of the alleged absurdity of (◇p&◇q) → ◇(p&q). A model checking system is then framed based on 0± and 1±. We show (◇p&◇q) → ◇(p&q) is equivalent to (◇p&◇~p) → ◇(p&~p) with (◇p&◇q) = ◇(p&q) as a theorem. AR4 was a doxastic logic follow-on to JYB4. We name these modern modal logic systems as Béziau's nightmare and Schang's nightmare.

Comments: 3 Pages. © Copyright 2018 by Colin James III All rights reserved. Respond to the author by email at: info@ersatz-systems dot com.

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[v1] 2018-11-23 05:59:45

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