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MTV Logics

Journal of Philosophical Logic volume 51, pages 1477–1519 (2022)Cite this article

Abstract

This essay introduces a novel framework to studying many-valued logics – the movable truth value (or MTV) approach. After setting up the framework, we will show that a vast number of many-valued logics, and in particular many-valued logics that have previously been given very different kinds of semantics, including C, K3, LP, ST, TS, RMfde, and FDE, can all be unified within the MTV-logic approach. This alone is notable, since until now RMfde in particular has resisted attempts to provide it with the same kind of many-valued semantics as the other logics in this list. New proofs of the duality between LP and K3, and of the self-duality of C, ST, TS, and RMfde, are presented. The essay will conclude with a discussion of directions that further research might take.

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Authors and Affiliations

  1. Department of Philosophy, University of Minnesota, 831 Heller Hall, 271 19th Ave. S., Minneapolis, MN, 55455, USA

    Roy T. Cook

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  1. Roy T. Cook
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Correspondence to Roy T. Cook.

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Cook, R.T. MTV Logics. J Philos Logic 51, 1477–1519 (2022). https://doi.org/10.1007/s10992-021-09634-4

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  • DOI: https://doi.org/10.1007/s10992-021-09634-4

Keywords

  • Many-valued logic
  • Duality
  • Negation
  • K3
  • LP
  • ST
  • TS
  • FDE
  • RMfde