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

References

• Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.
• Hughes, G.E. and M.J. Cresswell 1968. An Introduction to Modal Logic, Methuen:London.