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Valuations: Bi, Tri, and Tetra

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Abstract

This paper considers some issues to do with valuational presentations of consequence relations, and the Galois connections between spaces of valuations and spaces of consequence relations. Some of what we present is known, and some even well-known; but much is new. The aim is a systematic overview of a range of results applicable to nonreflexive and nontransitive logics, as well as more familiar logics. We conclude by considering some connectives suggested by this approach.

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Acknowledgements

The authors would like to thank the Melbourne Logic Group, and two anonymous referees for helpful discussion and comments on this material. This research was partially supported by “Logic and Substructurality”, grant number FFI2017-84805-P, from the Ministerio de Economía, Industria y Competitividad, Government of Spain.

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Authors and Affiliations

  1. Department of Philosophy, University of California, Davis, Davis, CA, 95616, USA

    Rohan French

  2. Philosophy Department, SoPHIS, Building 11, Monash University, VIC, 3800, Australia

    David Ripley

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  1. Rohan French
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Correspondence to Rohan French.

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Presented by Heinrich Wansing

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French, R., Ripley, D. Valuations: Bi, Tri, and Tetra. Stud Logica 107, 1313–1346 (2019). https://doi.org/10.1007/s11225-018-9837-1

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