Semiconic idempotent logic I: Structure and local deduction theorems

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Semiconic idempotent logic I: Structure and local deduction theorems

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

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

Name of the periodical

Annals of Pure and Applied Logic

ISSN

0168-0072

e-ISSN

1873-2461

Volume of the periodical

175

Issue of the periodical within the volume

7

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

30

Pages from-to

103443

UT code for WoS article

001225971600001

EID of the result in the Scopus database

2-s2.0-85189447897