Abstract
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.
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Heinemann, B. (2010). The Cantor Space as a Generic Model of Topologically Presented Knowledge. In: Ablayev, F., Mayr, E.W. (eds) Computer Science – Theory and Applications. CSR 2010. Lecture Notes in Computer Science, vol 6072. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13182-0_16
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DOI: https://doi.org/10.1007/978-3-642-13182-0_16
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