Modal logic

Modal logic is the logic of sentences with modal expressions like necessarily and possibly. These expressions can be added as operators (say N and P) to standard logic:

(i) If phi is a formula, then Nphi is a formula (ii) If phi is a formula, then Pphi is a formula

Sentences like these are interpreted in terms of possible worlds. Nphi is true if phi is true in every possible world; Pphi is true if phi is true in some possible world.

Links
Utrecht Lexicon of Linguistics