Products of Topological Modal Logics
Darko Sarenac

Abstract:
This thesis is about logic of space. In it we use various techniques
of modal logic and topology to devise a class of increasingly stronger
logics of space. The underlying intuition is that for lots of
applications spatial intuition and spatial reasoning seem basic. And
this not only in applications such as guiding robots or automated
vehicles through real three-dimensional space, but also for such
diverse applications as 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 an ultimate aim of applying them to cognitive settings.