一句话：提出将经典余代数逻辑沿 semi-primal 真值代数簇提升为多值逻辑的系统方法，并保持一步完备性与表达性。
本文研究以 semi-primal 代数作为真值度的多值余代数逻辑。作者给出一种系统方法，将定义在布尔代数簇上的 endofunctor 提升到由 semi-primal 代数生成的簇上，并进一步把经典余代数逻辑提升为多值版本。核心结果是这种提升保持（一步）完备性与表达性；对特定 endofunctor 类，还能从经典逻辑的公理化直接得到提升后多值逻辑的公理化。作者将技术应用于经典模态逻辑，展示方法的适用性。
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.
@article{paperbot2743,
title = {Many-valued coalgebraic logic over semi-primal varieties},
author = {Alexander Kurz and Wolfgang Poiger and Bruno Teheux},
journal = {Logical Methods in Computer Science},
volume = {Volume 20, Issue 3},
year = {2024},
doi = {10.46298/lmcs-20(3:6)2024}
}