通过扭转结构得到的Kleene代数的模态扩展
A Modal Expansion of Kleene Algebras via Twist Structures
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中文总结 AI 辅助
本文将Jalali的Kleene三元组理论扩展至模态语境，引入模态Kleene代数与三元组并建立范畴等价，还研究中心化情形并建立模态Kleene三元组的拓扑对偶性。
中文摘要 AI 辅助
Jalali提出的Kleene三元组通过扭转积为任意Kleene代数提供了一种表示方式。我们引入了模态Kleene代数与模态Kleene三元组，并建立了对应范畴间的范畴等价关系，将Jalali的对偶性扩展到模态语境中。我们研究了中心化情形，表明带蕴含的Kleene代数可通过将蕴含视为一族模态算子在该框架内自然描述，最终为模态Kleene三元组建立了拓扑对偶性。
英文摘要
Kleene triples, introduced by Jalali, provide a representation of arbitrary Kleene algebras in terms of twist-products. We introduce modal Kleene algebras and modal Kleene triples, and establish a categorical equivalence between the corresponding categories, extending Jalali's duality to the modal setting. We study the centered case and show that Kleene algebras with implication can be naturally described within this framework by viewing implication as a family of modal operators. Finally, we develop a topological duality for modal Kleene triples.
