Modal logic
Modal logic
From Wikipedia, the free encyclopedia.
Modal logic, or (less commonly) intensional logic is the branch of logic that deals with sentences that are qualified by modalities such as can, could,
might, may, must, possibly, and necessarily, and others. Any logical system making
use of modal operators, such as possibly, or necessarily is thus also called a modal logic. Modal logics are
characterized by semantic intensionality: non-modal logics all have the feature that the truth value of a complex
sentence is determined by the truth values of its sub-sentences. They are thus extensional. In modal logics, by
contrast, this does not hold: both "Bush is president" and "2+2=4" are true, yet "Necessarily, Bush is president" is
false, while "Necessarily, 2+2=4" is true. Necessity and possibility are the most widely discussed
modalities in work on modal logic, and most work on necessity and possibility focuses on the so-called
alethic modalities, but there are other senses of necessity and possibility, and other modalities as well.