Abstract
This article investigates models of axiomatizations related to the semantic conception of truth presented by Kripke (J Philos 72(19):690–716, 1975), the so-called fixed-point semantics. Among the various proof systems devised as a proof-theoretic characterization of the fixed-point semantics, in recent years two alternatives have received particular attention: classical systems (i.e., systems based on classical logic) and nonclassical systems (i.e., systems based on some nonclassical logic). The present article, building on Halbach and Nicolai (J Philos Log 47(2):227–257, 2018), shows that there is a sense in which classical and nonclassical theories (in suitable variants) have the same models.
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Acknowledgements
I would like to thank Martin Fischer, Carlo Nicolai, and Johannes Stern for very helpful discussions on the topic of this article, and two anonymous referee for their valuable comments. This work has been supported partly by the AHRC South, West and Wales Doctoral Training Partnership (SWW DTP), Grant No. AH/L503939/1-DTP1 and partly by the DAAD–Deutscher Akademischer Austauschdienst–German Academic Exchange Service, Grant No. 57552337.
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Castaldo, L. Notes on Models of (Partial) Kripke–Feferman Truth. Stud Logica 111, 83–111 (2023). https://doi.org/10.1007/s11225-022-10016-3
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DOI: https://doi.org/10.1007/s11225-022-10016-3
Keywords
- Theories of truth
- Fixed-point semantics
- Nonstandard models
- Classical and nonclassical logic
- \(\mathrm{KF}\) and PKF