Many-Valued Coalgebraic Logic: From Boolean Algebras to Primal Varieties

algebraic semantics; coalgebraic modal logic; many-valued logic; presenting functors; primal algebras; Algebraic semantic; Coalgebraic; Coalgebraic logic; Coalgebraic modal logic; Functors; Many-valued logic; Modal logic; Presenting functor; Truth degree

Abstract :

[en] We study many-valued coalgebraic logics with primal algebras of truth-degrees. We describe a way to lift algebraic semantics of classical coalgebraic logics, given by an endofunctor on the variety of Boolean algebras, to this many-valued setting, and we show that many important properties of the original logic are inherited by its lifting. Then, we deal with the problem of obtaining a concrete axiomatic presentation of the variety of algebras for this lifted logic, given that we know one for the original one. We solve this problem for a class of presentations which behaves well with respect to a lattice structure on the algebra of truth-degrees.

Disciplines :

Computer science

Author, co-author :

Kurz, Alexander; Fowler School of Engineering, Chapman University, Orange, United States

POIGER, Wolfgang ; 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: From Boolean Algebras to Primal Varieties

Publication date :

September 2023

Event name :

CALCO 2023

Event place :

Bloomington, Usa

Event date :

19-06-2023 => 21-06-2023

Audience :

International

Main work title :

10th Conference on Algebra and Coalgebra in Computer Science, CALCO 2023

Editor :

Baldan, Paolo

Publisher :

Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

ISBN/EAN :

978-3-9597728-7-7

Pages :

Peer reviewed :

Peer reviewed

Funding text :

Supported by the Luxembourg National Research Fund under the project PRIDE17/12246620/GPS.

Available on ORBilu :

since 04 October 2023

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