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Modal logic

SEMANTICS: 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.
LIT. Gamut, L.T.F. (1991)
Hughes, G.E. and M.J. Cresswell (1968)