Abstract
Substructural logics and their application to logical and semantic paradoxes have been extensively studied. In the paper, we study theories of naïve consequence and truth based on a non-reflexive logic. We start by investigating the semantics and the proof-theory of a system based on schematic rules for object-linguistic consequence. We then develop a fully compositional theory of truth and consequence in our non-reflexive framework.
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Acknowledgements
The authors thank Johannes Stern and two anonymous reviewers for many helpful comments and observations.
Funding
Carlo Nicolai acknowledges the support of the AHRC Grant AH/V015516/1 Properties, Paradox, and Circularity: a Type-Free Account. Both authors acknowledge the support of the staff exchange grant HORIZON-TMA-MSCA-SE no. 101086295 “PLEXUS” by the European Commission. Open access funding provided by Università degli Studi di Torino within the CRUI-CARE Agreement.
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Nicolai, C., Rossi, L. Systems for Non-Reflexive Consequence. Stud Logica 111, 947–977 (2023). https://doi.org/10.1007/s11225-023-10049-2
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DOI: https://doi.org/10.1007/s11225-023-10049-2