Refutation systems in modal logic

Studia Logica 53 (2):299 - 324 (1994)
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Complete deductive systems are constructed for the non-valid (refutable) formulae and sequents of some propositional modal logics. Thus, complete syntactic characterizations in the sense of Lukasiewicz are established for these logics and, in particular, purely syntactic decision procedures for them are obtained. The paper also contains some historical remarks and a general discussion on refutation systems.
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A Companion to Modal Logic.E. Hughes, G. & Cresswell, M. J.

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