Modules over quantaloids: Applications to the isomorphism problem in algebraic logic and pi-institutions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F17%3A00506928" target="_blank" >RIV/67985807:_____/17:00506928 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jpaa.2016.05.012" target="_blank" >http://dx.doi.org/10.1016/j.jpaa.2016.05.012</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jpaa.2016.05.012" target="_blank" >10.1016/j.jpaa.2016.05.012</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Modules over quantaloids: Applications to the isomorphism problem in algebraic logic and pi-institutions

Popis výsledku v původním jazyce

We solve the isomorphism problem in the context of abstract algebraic logic and of π-institutions, namely the problem of when the notions of syntactic and semantic equivalence among logics coincide. The problem is solved in the general setting of categories of modules over quantaloids. We introduce closure operators on modules over quantaloids and their associated morphisms. We show that, up to isomorphism, epis are morphisms associated with closure operators. The notions of (semi-)interpretability and (semi-)representability are introduced and studied. We introduce cyclic modules, and provide a characterization for cyclic projective modules as those having a g-variable. Finally, we explain how every π-institution induces a module over a quantaloid, and thus the theory of modules over quantaloids can be considered as an abstraction of the theory of π-institutions.

Název v anglickém jazyce

Modules over quantaloids: Applications to the isomorphism problem in algebraic logic and pi-institutions

Popis výsledku anglicky

We solve the isomorphism problem in the context of abstract algebraic logic and of π-institutions, namely the problem of when the notions of syntactic and semantic equivalence among logics coincide. The problem is solved in the general setting of categories of modules over quantaloids. We introduce closure operators on modules over quantaloids and their associated morphisms. We show that, up to isomorphism, epis are morphisms associated with closure operators. The notions of (semi-)interpretability and (semi-)representability are introduced and studied. We introduce cyclic modules, and provide a characterization for cyclic projective modules as those having a g-variable. Finally, we explain how every π-institution induces a module over a quantaloid, and thus the theory of modules over quantaloids can be considered as an abstraction of the theory of π-institutions.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GAP202%2F10%2F1826" target="_blank" >GAP202/10/1826: Matematická fuzzy logika v informatice</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Journal of Pure and Applied Algebra

ISSN

0022-4049

e-ISSN

—

Svazek periodika

221

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

24

Strana od-do

1-24

Kód UT WoS článku

000384864100001

EID výsledku v databázi Scopus

2-s2.0-84977630894