Algebraic semantics for modal logic with propositional quantifiers

Algebraic semantics for modal logic with propositional quantifiers interpret formulas not just as true or false at some possible states, but directly as elements in a Boolean algebra, understood as an algebra of propositions. This general perspective allows us to study modal logics with propositional quantifiers that standard relational semantics based on states (possible worlds) cannot even define. In this talk, I will showcase the use of algebraic semantics in identifying conceptually significant modal logics with propositional quantifiers and also in proving mathematical/computational properties of such logics.