Modal logic and modal semantics are primarily concerned with the notions of necessity, possibility and related concepts. Their development may in retrospect be seen to have proceeded in several stages. C.I. Lewis [90] on intuitive considerations proposed formal systems of modal propositional logic (MPL) extending standard propositional logic (PL) to include an operator "◊" for possibility and defining the necessity operator as "-◊-", later abbreviated as "□". Alternative notations in common use are "M" and "N".