Moss' Logic for Ordered Coalgebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F22%3A00483809" target="_blank" >RIV/67985807:_____/22:00483809 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21230/22:00360020 RIV/00216208:11210/22:10369766

Výsledek na webu

<a href="https://dx.doi.org/10.46298/lmcs-18(3:18)2022" target="_blank" >https://dx.doi.org/10.46298/lmcs-18(3:18)2022</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.46298/lmcs-18(3:18)2022" target="_blank" >10.46298/lmcs-18(3:18)2022</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Moss' Logic for Ordered Coalgebras

Popis výsledku v původním jazyce

We present a finitary version of Moss’ coalgebraic logic for T-coalgebras, where T is a locally monotone endofunctor of the category of posets and monotone maps. The logic uses a single cover modality whose arity is given by the least finitary subfunctor of the dual of the coalgebra functor T∂ω, and the semantics of the modality is given by relation lifting. For the semantics to work, T is required to preserve exact squares. For the finitary setting to work, T∂ω is required to preserve finite intersections. We develop a notion of a base for subobjects of TωX. This in particular allows us to talk about the finite poset of subformulas for a given formula. The notion of a base is introduced generally for a category equipped with a suitable factorisation system. We prove that the resulting logic has the Hennessy-Milner property for the notion of similarity based on the notion of relation lifting. We define a sequent proof system for the logic, and prove its completeness.

Název v anglickém jazyce

Moss' Logic for Ordered Coalgebras

Popis výsledku anglicky

We present a finitary version of Moss’ coalgebraic logic for T-coalgebras, where T is a locally monotone endofunctor of the category of posets and monotone maps. The logic uses a single cover modality whose arity is given by the least finitary subfunctor of the dual of the coalgebra functor T∂ω, and the semantics of the modality is given by relation lifting. For the semantics to work, T is required to preserve exact squares. For the finitary setting to work, T∂ω is required to preserve finite intersections. We develop a notion of a base for subobjects of TωX. This in particular allows us to talk about the finite poset of subformulas for a given formula. The notion of a base is introduced generally for a category equipped with a suitable factorisation system. We prove that the resulting logic has the Hennessy-Milner property for the notion of similarity based on the notion of relation lifting. We define a sequent proof system for the logic, and prove its completeness.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Logical Methods in Computer Science

ISSN

1860-5974

e-ISSN

1860-5974

Svazek periodika

18

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

61

Strana od-do

"18:1"-"18:61"

Kód UT WoS článku

000840685400001

EID výsledku v databázi Scopus

2-s2.0-85135602994