一句话：用余代数统一框架为命题几何逻辑添加模态，并建立其推导系统、完备性与行为等价理论。
本文借助余代数理论，为命题几何逻辑引入一种统一的模态扩展框架。其模型建立在拓扑空间与连续映射的某个满子范畴上的自函子余代数之上。作者研究此类几何模态逻辑的推导系统、可靠性与完备性，并给出一种方法：将 Set 上的自函子连同谓词提升，提升到拓扑空间范畴，同时保持开谓词提升结构。文章进一步比较所得模型类上的模态等价、行为等价与互模拟，并为相应范畴构造终对象。该工作为几何逻辑与余代数模态逻辑之间建立了基础理论联系。
Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebras for an endofunctor on some full subcategory of the category of topological spaces and continuous functions. We investigate derivation systems, soundness and completeness for such geometric modal logics, and we specify a method of lifting an endofunctor on Set, accompanied by a collection of predicate liftings, to an endofunctor on the category of topological spaces, again accompanied by a collection of (open) predicate liftings. Furthermore, we compare the notions of modal equivalence, behavioural equivalence and bisimulation on the resulting class of models, and we provide a final object for the corresponding category.
@article{paperbot1639,
title = {Coalgebraic Geometric Logic: Basic Theory},
author = {Nick Bezhanishvili and Jim de Groot and Yde Venema},
journal = {Logical Methods in Computer Science},
volume = {Volume 18, Issue 4},
year = {2022},
doi = {10.46298/lmcs-18(4:10)2022}
}