Semiconic idempotent logic I: Structure and local deduction theorems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F24%3A00586504" target="_blank" >RIV/67985807:_____/24:00586504 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.apal.2024.103443" target="_blank" >https://doi.org/10.1016/j.apal.2024.103443</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.apal.2024.103443" target="_blank" >10.1016/j.apal.2024.103443</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Semiconic idempotent logic I: Structure and local deduction theorems

Popis výsledku v původním jazyce

Semiconic idempotent logic is a common generalization of intuitionistic logic, relevance logic with mingle, and semilinear idempotent logic. It is an algebraizable logic and it admits a cut-free hypersequent calculus. We give a structural decomposition of its characteristic algebraic semantics, conic idempotent residuated lattices, showing that each of these is an ordinal sum of simpler partially ordered structures. This ordinal sum is indexed by a totally ordered residuated lattice, which serves as its skeleton and is both a subalgebra and nuclear image. We equationally characterize the totally ordered residuated lattices appearing as such skeletons. Further, we describe both congruence and subalgebra generation in conic idempotent residuated lattices, proving that every variety generated by these enjoys the congruence extension property. In particular, this holds for semilinear idempotent residuated lattices. Based on this analysis, we obtain a local deduction theorem for semiconic idempotent logic, which also specializes to semilinear idempotent logic.

Název v anglickém jazyce

Semiconic idempotent logic I: Structure and local deduction theorems

Popis výsledku anglicky

Semiconic idempotent logic is a common generalization of intuitionistic logic, relevance logic with mingle, and semilinear idempotent logic. It is an algebraizable logic and it admits a cut-free hypersequent calculus. We give a structural decomposition of its characteristic algebraic semantics, conic idempotent residuated lattices, showing that each of these is an ordinal sum of simpler partially ordered structures. This ordinal sum is indexed by a totally ordered residuated lattice, which serves as its skeleton and is both a subalgebra and nuclear image. We equationally characterize the totally ordered residuated lattices appearing as such skeletons. Further, we describe both congruence and subalgebra generation in conic idempotent residuated lattices, proving that every variety generated by these enjoys the congruence extension property. In particular, this holds for semilinear idempotent residuated lattices. Based on this analysis, we obtain a local deduction theorem for semiconic idempotent logic, which also specializes to semilinear idempotent logic.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

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

Annals of Pure and Applied Logic

ISSN

0168-0072

e-ISSN

1873-2461

Svazek periodika

175

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

30

Strana od-do

103443

Kód UT WoS článku

001225971600001

EID výsledku v databázi Scopus

2-s2.0-85189447897