This morning has two talks on modal logic: first up was Marcus Kracht with a survey on the development of modal logic; now Steve Awodey is reporting on joint work with Kishida on topological semantics of first-order modal logic. Marcus talked about some interesting results in the mathematics of modal logic, especially general semantics for first-order modal logic. Steve’s talk is old-skool chalkboard math, with pretty drawings. I just learned what sheaf is. He has a beautiful model theory for first-order S4 in terms of sheaves.