Showing papers by "Melvin Fitting published in 1984"

Linear Reasoning in Modal Logic

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A Symmetric Approach to Axiomatizing Quantifiers and Modalities

Abstract: We present an axiomatization of several of the basic modal logics, with the idea of giving the two modal operators □ and ◊ equal weight as far as possible. Then we present a parallel axiomatization of classical quantification theory, working our way up through a sequence of rather curious subsystems. It will be clear at the end that the essential difference between quantifiers and modalities is amusing in a vacuous sort of way. Finally we sketch tableau proof systems for the various logics we have introduced along the way. Also, the “natural” model theory for the subsystems of quantification theory that come up is somewhat curious. In a sense, it amounts to a “stretching out” of the Henkin-style completeness proof, severing the maximal consistent part of the construction quite thoroughly from the part of the construction that takes care of existential-quantifier instances.