Proving unprovability in some normal modal logics

Bulletin of the Section of Logic 20 (1):23-29 (1991)
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Abstract
This note considers deductive systems for the operator a of unprovability in some particular propositional normal modal logics. We give thus complete syntactic characterization of these logics in the sense of Lukasiewicz: for every formula  either `  or a  (but not both) is derivable. In particular, purely syntactic decision procedure is provided for the logics under considerations.
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