Simplicial semantics of modal predicate logics

Simplicial semantics for modal and modal predicate logics was introduced by Dmitry Skvortsov in the early 1990s as a maximal Kripke-type semantics. Basic results on this semantics were proved by Skvortsov and Shehtman (1993). In this talk we present a new incompleteness result: there is a continuum of logics (some of which are very simply axiomatized) that are complete in simplicial semantics, but incomplete in Ghilardi's functor semantics. These logics are quantified versions of propositional modal logics above D4.1 (= K4+seriality+McKinsey formula).