Consistent posets

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F21%3A73609342" target="_blank" >RIV/61989592:15310/21:73609342 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1007%2Fs00500-021-05906-y" target="_blank" >https://link.springer.com/article/10.1007%2Fs00500-021-05906-y</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00500-021-05906-y" target="_blank" >10.1007/s00500-021-05906-y</a>

Result language

angličtina

Original language name

Consistent posets

Original language description

We introduce so-called consistent posets which are bounded posets with an antitone involution &apos; where the lower cones of x, x &apos; and of y, y &apos; coincide provided that x, y are different from 0, 1 and, moreover, if x, y are different from 0, then their lower cone is different from 0, too. We show that these posets can be represented by means of commutative meet-directoids with an antitone involution satisfying certain identities and implications. In the case of a finite distributive or strongly modular consistent poset, this poset can be converted into a residuated structure and hence it can serve as an algebraic semantics of a certain non-classical logic with unsharp conjunction and implication. Finally we show that the Dedekind-MacNeille completion of a consistent poset is a consistent lattice, i.e., a bounded lattice with an antitone involution satisfying the above-mentioned properties.

Czech name

—

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

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GF20-09869L" target="_blank" >GF20-09869L: The many facets of orthomodularity</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2021

Confidentiality

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

Name of the periodical

SOFT COMPUTING

ISSN

1432-7643

e-ISSN

—

Volume of the periodical

25

Issue of the periodical within the volume

15

Country of publishing house

US - UNITED STATES

Number of pages

8

Pages from-to

"9765 "- 9772

UT code for WoS article

000661788300001

EID of the result in the Scopus database

2-s2.0-85107984124