Many-valued coalgebraic logic over semi-primal varieties

Kurz, Alexander; POIGER, Wolfgang; TEHEUX, Bruno

doi:10.46298/lmcs-20(3:6)2024

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Many-valued coalgebraic logic over semi-primal varieties

Kurz, Alexander; POIGER, Wolfgang; TEHEUX, Bruno

2024 • In Logical Methods in Computer Science, 20 (3), p. 6:1-6:32

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https://hdl.handle.net/10993/61639

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10.46298/lmcs-20(3:6)2024

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Keywords :

coalgebraic logic; many-valued logic; modal logic; semi-primal algebra; one-step completeness; expressivity

Abstract :

[en] We study many-valued coalgebraic logics with semi-primal algebras of truth-degrees. We provide a systematic way to lift endofunctors defined on the variety of Boolean algebras to endofunctors on the variety generated by a semi-primal algebra. We show that this can be extended to a technique to lift classical coalgebraic logics to many-valued ones, and that (one-step) completeness and expressivity are preserved under this lifting. For specific classes of endofunctors, we also describe how to obtain an axiomatization of the lifted many-valued logic directly from an axiomatization of the original classical one. In particular, we apply all of these techniques to classical modal logic.

Disciplines :

Computer science
Mathematics

Author, co-author :

Kurz, Alexander

POIGER, Wolfgang ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)

TEHEUX, Bruno ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)

External co-authors :

yes

Language :

English

Title :

Many-valued coalgebraic logic over semi-primal varieties

Publication date :

17 July 2024

Journal title :

Logical Methods in Computer Science

eISSN :

1860-5974

Publisher :

Centre pour la Communication Scientifique Directe (CCSD)

Volume :

Issue :

Pages :

6:1-6:32

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://lmcs.episciences.org/13948/pdf

FnR Project :

PRIDE17/12246620/GPS

Available on ORBilu :

since 18 July 2024

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