One Variable Relevant Logics are S5ish

0585531 - ÚI 2025 DE eng J - Článek v odborném periodiku
Ferenz, Nicholas
One Variable Relevant Logics are S5ish.
Journal of Philosophical Logic. Online 22 March 2024 (2024). ISSN 0022-3611
Grant CEP: GA ČR(CZ) GA22-01137S
Institucionální podpora: RVO:67985807
Klíčová slova: First-Order Relevant Logic * Modal Relevant Logic * One-Variable Fragment
Impakt faktor: 1.5, rok: 2022
Způsob publikování: Open access
https://doi.org/10.1007/s10992-024-09753-8

Here I show that the one-variable fragment of several first-order relevant logics corresponds to certain S5ish extensions of the underlying propositional relevant logic. In particular, given a fairly standard translation between modal and one-variable languages and a permuting propositional relevant logic L, a formula A of the one-variable fragment is a theorem of LQ (QL) iff its translation is a theorem of L5 (L.5). The proof is model-theoretic. In one direction, semantics based on the Mares-Goldblatt [15] semantics for quantified L are transformed into ternary (plus two binary) relational semantics for S5-like extensions of L (for a general presentation, see Seki [26, 27]). In the other direction, a valuation is given for the full first-order relevant logic based on L into a model for a suitable S5 extension of L. I also discuss this work’s relation to finding a complete axiomatization of the constant domain, non-general frame ternary relational semantics for which RQ is incomplete [11]
Trvalý link: https://hdl.handle.net/11104/0353225