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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

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

10101 - Pure mathematics

Project

<a href="/en/project/GAP202%2F10%2F1826" target="_blank" >GAP202/10/1826: Mathematical Fuzzy Logic in Computer Science</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2017

Confidentiality

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

Name of the periodical

Journal of Pure and Applied Algebra

ISSN

0022-4049

e-ISSN

—

Volume of the periodical

221

Issue of the periodical within the volume

1

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

24

Pages from-to

1-24

UT code for WoS article

000384864100001

EID of the result in the Scopus database

2-s2.0-84977630894