# Modal logic

From Glottopedia

**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.