Products of Topological Modal Logics

摘要

This thesis is about logics of space. In it we use various semantic and axiomatic techniques from modal logic and topology to devise a class of increasingly stronger logics of space. The underlying intuition is that in many current academic disciplines spatial intuition and spatial reasoning seem essential. The spectrum includes applied areas such as guiding robots through real three-dimensional space, but also fundamental reasoning about knowledge, processing and updating of information. The thesis makes some initial steps in understanding the structure of space with efficient languages of modal logic, with the ultimate aim of applying them to a wide variety of pure and applied cognitive settings.