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Identity in Mares-Goldblatt Models for Quantified Relevant Logic

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Abstract

Mares and Goldblatt (The Journal of Symbolic Logic, 71(01), 163–187, 2006) provided an alternative frame semantics for two quantified extensions of the relevant logic R. In this paper, I show how to extend the Mares-Goldblatt frames to accommodate identity. Simpler frames are provided for two zero-order logics en route to the full logic in order to clarify what is needed for identity and substitution, as opposed to quantification. I close with a comparison of this work with the Fine-Mares models for relevant logics with identity and a discussion of constant and variable domains.

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Acknowledgements

I would like to thank Greg Restall, Ed Mares, Lloyd Humberstone, Shay Logan, Dave Ripley, Rohan French, and audience members of the Melbourne Logic Seminar and the Australasian Association for Logic conference 2018 for discussion and feedback. This research was supported by the Australian Research Council, Discovery Grant DP150103801.

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  1. Institute of Philosophy, Slovak Academy of Sciences, Klemensova 19, 813 64, Bratislava, Slovak Republic

    Shawn Standefer

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Standefer, S. Identity in Mares-Goldblatt Models for Quantified Relevant Logic. J Philos Logic 50, 1389–1415 (2021). https://doi.org/10.1007/s10992-021-09603-x

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