Residuation in finite posets

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F21%3A73609345" target="_blank" >RIV/61989592:15310/21:73609345 - isvavai.cz</a>

Výsledek na webu

<a href="https://arxiv.org/pdf/1910.09009.pdf" target="_blank" >https://arxiv.org/pdf/1910.09009.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/ms-2021-0021" target="_blank" >10.1515/ms-2021-0021</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Residuation in finite posets

Popis výsledku v původním jazyce

When an algebraic logic based on a poset instead of a lattice is investigated then there is a natural problem how to introduce implication to be everywhere defined and satisfying (left) adjointness with conjunction. We have already studied this problem for the logic of quantum mechanics which is based on an orthomodular poset or the logic of quantum effects based on a so-called effect algebra which is only partial and need not be lattice-ordered. For this, we introduced the so-called operator residuation where the values of implication and conjunction need not be elements of the underlying poset, but only certain subsets of it. However, this approach can be generalized for posets satisfying more general conditions. If these posets are even finite, we can focus on maximal or minimal elements of the corresponding subsets and the formulas for the mentioned operators can be essentially simplified. This is shown in the present paper where all theorems are explained by corresponding examples.

Název v anglickém jazyce

Residuation in finite posets

Popis výsledku anglicky

When an algebraic logic based on a poset instead of a lattice is investigated then there is a natural problem how to introduce implication to be everywhere defined and satisfying (left) adjointness with conjunction. We have already studied this problem for the logic of quantum mechanics which is based on an orthomodular poset or the logic of quantum effects based on a so-called effect algebra which is only partial and need not be lattice-ordered. For this, we introduced the so-called operator residuation where the values of implication and conjunction need not be elements of the underlying poset, but only certain subsets of it. However, this approach can be generalized for posets satisfying more general conditions. If these posets are even finite, we can focus on maximal or minimal elements of the corresponding subsets and the formulas for the mentioned operators can be essentially simplified. This is shown in the present paper where all theorems are explained by corresponding examples.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF20-09869L" target="_blank" >GF20-09869L: Ortomodularita z různých pohledů</a><br>

Návaznosti

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

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Mathematica Slovaca

ISSN

0139-9918

e-ISSN

—

Svazek periodika

71

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

SK - Slovenská republika

Počet stran výsledku

14

Strana od-do

"807 "- 820

Kód UT WoS článku

000680658600001

EID výsledku v databázi Scopus

2-s2.0-85107937064