Modal logic

In formal logic, a modal logic is any system of formal logic that attempts to deal with modalities. Traditionally, there are three 'modes' or 'moods' or 'modalities' of the copula to be, namely, possibility, probability, and necessity. Logics for dealing with a number of related terms, such as eventually, formerly, can, could, might, may, must, are by extension also called modal logics, since it turns out that these can be treated in similar ways.

A formal modal logic represents modalities using modal operators. For example, "Jones's murder was a possibility", "Jones was possibly murdered", and "It is possible that Jones was murdered" all contain the notion of possibility. In a modal logic this is represented as an operator, Possibly, attaching to the sentence Jones was murdered.

The basic unary (1-place) modal operators are usually written □ (or L) for Necessarily and ◇ (or M) for Possibly. In a classical modal logic, each can be expressed by the other and negation:

◇P <-> ￢□￢P;
□P <-> ￢◇￢P.
 
Thus it is possible that Jones was murdered if and only if it is not necessary that Jones was not murdered. For the standard formal semantics of the basic modal language, see Kripke semantics.

Reference:
http://en.wikipedia.org/wiki/Modal_logic