One-variable fragments of first-order logics

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

One-variable fragments of first-order logics

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

One-variable fragments of first-order logics

Popis výsledku anglicky

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

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA22-01137S" target="_blank" >GA22-01137S: Metamatematika substrukturálních modálních logik</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Bulletin of Symbolic Logic

ISSN

1079-8986

e-ISSN

1943-5894

Svazek periodika

30

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

26

Strana od-do

253-278

Kód UT WoS článku

001358025000006

EID výsledku v databázi Scopus

2-s2.0-85189700270