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A Generalization of the Routley-Meyer Semantic Framework

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Abstract

We develop an axiomatic theory of “generalized Routley-Meyer (GRM) logics.” These are first-order logics which are can be characterized by model theories in a certain generalization of Routley-Meyer semantics. We show that all GRM logics are subclassical, have recursively enumerable consequence relations, satisfy the compactness theorem, and satisfy the standard structural rules and conjunction and disjunction introduction/elimination rules. We also show that the GRM logics include classical logic, intuitionistic logic, LP/K3/FDE, and the relevant logics.

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Acknowledgments

I wish to thank David Ripley and an anonymous referee for helpful comments on the paper, and Jc Beall for helpful guidance during the submission and revision process. I wish to thank the University of Connecticut Logic Research Group of spring 2014 for the opportunity to present the paper.

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  1. University of Connecticut, 101 Manchester Hall, 355 Mansfield Rd., Storrs, CT, 06269-1054, USA

    Morgan Thomas

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  1. Morgan Thomas
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Correspondence to Morgan Thomas.

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Thomas, M. A Generalization of the Routley-Meyer Semantic Framework. J Philos Logic 44, 411–427 (2015). https://doi.org/10.1007/s10992-014-9328-4

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  • DOI: https://doi.org/10.1007/s10992-014-9328-4

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