One Variable Relevant Logics are S5ish
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F24%3A00585531" target="_blank" >RIV/67985807:_____/24:00585531 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10992-024-09753-8" target="_blank" >https://doi.org/10.1007/s10992-024-09753-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10992-024-09753-8" target="_blank" >10.1007/s10992-024-09753-8</a>
Alternative languages
Result language
angličtina
Original language name
One Variable Relevant Logics are S5ish
Original language description
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]
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA22-01137S" target="_blank" >GA22-01137S: Metamathematics of substructural modal logics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Philosophical Logic
ISSN
0022-3611
e-ISSN
1573-0433
Volume of the periodical
53
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
23
Pages from-to
909-931
UT code for WoS article
001190188700001
EID of the result in the Scopus database
2-s2.0-85188304602