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For example, I have heard of a topological one wherein negation means the interior of the complement (but still would like a reference).

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    The wikipedia entry for intuitionistic logic http://en.wikipedia.org/wiki/Intuitionistic_logic gives some references and in particular has a little bit to say about the topological interpretation you aluded to. See the section "Heyting Algebra Semantics".2010-10-22

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