In this paper, a particular extension of the constitutive bi-modal logic for single-agent subset spaces will be provided. That system, which originally was designed for revealing the intrinsic relationship between knowledge and topology, has been developed in several directions in recent years, not least towards a comprehensive knowledge-theoretic formalism. This line is followed here to the extent that subset spaces are supplied with a finite number of functions which shall represent certain knowledge-enabling actions. Due to the corresponding functional modalities, another basic system for subset spaces, topological nexttime logic, comes into play. The resulting merge of logics can, for example, be applied to comparing the different effects of those actions in respect of knowledge. Subsequently, the completeness and the decidabilty of the basic combined system and of a certain extension thereof will be proved.

中文翻译：

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重用拓扑下一次逻辑

在本文中，将提供用于单代理子集空间的本构双模态逻辑的特定扩展。该系统最初是为了揭示知识和拓扑之间的内在关系而设计的，近年来已经在几个方向上发展，尤其是朝着全面的知识理论形式主义发展。这条线在这里遵循到子集空间提供有限数量的功能的程度，这些功能将代表某些知识启用动作。由于相应的功能模态，子集空间的另一个基本系统，拓扑下一次逻辑，开始发挥作用。例如，由此产生的逻辑合并可以应用于比较这些动作在知识方面的不同效果。随后，