Saleh Aliyari, Wes: "A Topological approach to some questions in Logic"
Abstract: In this talk we talk about some natural connections between logic and topology
that many non-logicians might know implicitly. After some general examples we consider coalgebras of a the Vietoris functor on the category of Topological spaces and then in the special case of Stone spaces; these are compact, Hausdorff, totally disconnected spaces. The Vietoris functor is the topological version of the power set functor and as such its coalgebras work as Kripke frames for interpreting modal theories. Only the added topological properties provide a frame complete semantics for modal logic. We will prove a characterization theorem for what we call theory maps using basic topology. This gives a way of considering semantics of different logics using a function-based view. Whether this approach is advantageous compared to classical semantics has not yet been explored.