Moss' Logic for Ordered Coalgebras
Result description
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.
Keywords
coalgebraic logiccover modalityrelation liftingordered coalgebrassimilarityHennessy-Milner property
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/68407700:21230/22:00360020 RIV/00216208:11210/22:10369766
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Moss' Logic for Ordered Coalgebras
Original language description
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.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Logical Methods in Computer Science
ISSN
1860-5974
e-ISSN
1860-5974
Volume of the periodical
18
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
61
Pages from-to
"18:1"-"18:61"
UT code for WoS article
000840685400001
EID of the result in the Scopus database
2-s2.0-85135602994
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Year of implementation
2022