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Abstract:
Modal logic is concerned with the words "necessary" and "possible",
and has been studied extensively by logicians using many different
techniques. One of the most elegant is the approach (due to Tarski in
the 1940s) of interpreting necessity as the interior operation in a
topological space. While this works well for propositional logic
("and", "or", "not", etc.), despite several attempts it has never
been extended in a satisfactory way to the logic of relations and
quantifiers ("for all", "for some"). In this expository talk it is
shown how the topological interpretation can be neatly extended using
recent advances in algebraic logic. The important notion of a "sheaf
of sets" occurs in an unexpected way.
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