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Published in:
2013 | OriginalPaper | Chapter
Characterizing Subset Spaces as Bi-topological Structures
Author : Bernhard Heinemann
Published in: Logic for Programming, Artificial Intelligence, and Reasoning
Publisher: Springer Berlin Heidelberg
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Subset spaces constitute a relatively new semantics for bi-modal logic. This semantics admits, in particular, a modern, computer science oriented view of the classic interpretation of the basic modalities in topological spaces à la McKinsey and Tarski. In this paper, we look at the relationship of both semantics from an opposite perspective as it were, by asking for a consideration of subset spaces in terms of topology and topological modal logic, respectively. Indeed, we shall finally obtain a corresponding characterization result. A third semantics of modal logic, namely the standard relational one, and the associated first-order structures, will play an important part in doing so as well.