Structural Completeness in Many-Valued Logics with Rational Constants

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F22%3A00559061" target="_blank" >RIV/67985807:_____/22:00559061 - isvavai.cz</a>

Výsledek na webu

<a href="https://dx.doi.org/10.1215/00294527-2022-0021" target="_blank" >https://dx.doi.org/10.1215/00294527-2022-0021</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1215/00294527-2022-0021" target="_blank" >10.1215/00294527-2022-0021</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Structural Completeness in Many-Valued Logics with Rational Constants

Popis výsledku v původním jazyce

The logics R Ł, RP, and RG have been obtained by expanding Łukasiewicz logic Ł, product logic P, and Gödel–Dummett logic G with rational constants. We study the lattices of extensions and structural completeness of these three expansions, obtaining results that stand in contrast to the known situation in Ł, P, and G. Namely, R Ł is hereditarily structurally complete. RP is algebraized by the variety of rational product algebras that we show to be Q -universal. We provide a base of admissible rules in RP, show their decidability, and characterize passive structural completeness for extensions of RP. Furthermore, structural completeness, hereditary structural completeness, and active structural completeness coincide for extensions of RP , and this is also the case for extensions of RG , where in turn passive structural completeness is characterized by the equivalent algebraic semantics having the joint embedding property. For nontrivial axiomatic extensions of RG , we provide a base of admissible rules. We leave the problem open whether the variety of rational Gödel algebras is Q-universal.

Název v anglickém jazyce

Structural Completeness in Many-Valued Logics with Rational Constants

Popis výsledku anglicky

The logics R Ł, RP, and RG have been obtained by expanding Łukasiewicz logic Ł, product logic P, and Gödel–Dummett logic G with rational constants. We study the lattices of extensions and structural completeness of these three expansions, obtaining results that stand in contrast to the known situation in Ł, P, and G. Namely, R Ł is hereditarily structurally complete. RP is algebraized by the variety of rational product algebras that we show to be Q -universal. We provide a base of admissible rules in RP, show their decidability, and characterize passive structural completeness for extensions of RP. Furthermore, structural completeness, hereditary structural completeness, and active structural completeness coincide for extensions of RP , and this is also the case for extensions of RG , where in turn passive structural completeness is characterized by the equivalent algebraic semantics having the joint embedding property. For nontrivial axiomatic extensions of RG , we provide a base of admissible rules. We leave the problem open whether the variety of rational Gödel algebras is Q-universal.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Notre Dame Journal of Formal Logic

ISSN

0029-4527

e-ISSN

1939-0726

Svazek periodika

63

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

39

Strana od-do

261-299

Kód UT WoS článku

000933209300001

EID výsledku v databázi Scopus

2-s2.0-85137050042