Proving Unprovability in Some Normal Modal Logic
نویسنده
چکیده
The present communication suggests 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 φ either ` φ or a φ (but not both) is derivable. In particular, purely syntactic decision procedure is provided for the logics under considerations. All background in modal logic, necessary for this paper can be found in the initial chapters of [1], [3] or [5]. Henceforth we shall informally read S a φ as “φ is unprovable in S”. All systems presented here will contain the “minimal” a` system L consisting of the axiom:
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Suhrawardi's Modal Syllogisms
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