Topological reasoning and the logic of knowledge
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Modal logic
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CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
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We prove a new completeness theorem for topologic, a particular system for reasoning about knowledge and topology. In fact, we show that topologic is complete with respect to the Cantor space, i.e., the set of all infinite 0-1-sequences endowed with the initial segment topology. To this end, we make use of the connection between the semantics of topologic and McKinsey and Tarski’s topological interpretation of the modal box operator, as well as of Georgatos’ Normal Form Lemma.