One-variable fragments of first-order logics
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F24%3A00585222" target="_blank" >RIV/67985807:_____/24:00585222 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1017/bsl.2024.22" target="_blank" >https://doi.org/10.1017/bsl.2024.22</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/bsl.2024.22" target="_blank" >10.1017/bsl.2024.22</a>
Alternative languages
Result language
angličtina
Original language name
One-variable fragments of first-order logics
Original language description
The one-variable fragment of a first-order logic may be viewed as an “S5-like” modal logic, where the universal and existential quantifiers are replaced by box and diamond modalities, respectively. Axiomatizations of these modal logics have been obtained for special cases — notably, the modal counterparts S5 and MIPC of the one-variable fragments of first-order classical logic and first-order intuitionistic logic, respectively — but a general approach, extending beyond first-order intermediate logics, has been lacking. To this end, a sufficient criterion is given in this paper for the one-variable fragment of a semantically-defined first-order logic — spanning families of intermediate, substructural, many-valued, and modal logics — to admit a certain natural axiomatization. More precisely, an axiomatization is obtained for the one-variable fragment of any first-order logic based on a variety of algebraic structures with a lattice reduct that has thensuperamalgamation property, using a generalized version of a functional representation theorem for monadic Heyting algebras due to Bezhanishvili and Harding. An alternative proof-theoretic strategy for obtaining such axiomatization results is also developed for first-order substructural logics that have a cut-free sequent calculus and admit a certain interpolation property
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
Bulletin of Symbolic Logic
ISSN
1079-8986
e-ISSN
1943-5894
Volume of the periodical
30
Issue of the periodical within the volume
2
Country of publishing house
GB - UNITED KINGDOM
Number of pages
26
Pages from-to
253-278
UT code for WoS article
001358025000006
EID of the result in the Scopus database
2-s2.0-85189700270