Abstract

In this paper, I present a modal system called ∏ (Pi), characterizing it both axiomatically and algebraically, the latter being in terms of structures called π-algebras (pi-algebras). Pi-algebras are a natural generalization of Boolean algebras with operators – a generalization in which equality is replaced by congruence in the characterizing conditions. The resulting system of modal logic is "sub- Lewis", in the sense that it is properly contained in the weakest Lewis system, S1.