[summary: A boolean is a mathematical quantity that can only take on one of two values: "[-true]" or "[-false]". Booleans are to Logic what integers are to [-arithmetic].]
In formal Logic, a boolean variable is a [-variable] that can take on one of only two possible values: "[-true]" or "[-false]". Propositions can then be said to [-evaluation evaluate] to one of these two values, in the same way that ordinary [algebra algebraic] expressions evaluate to a Number.
Also as in algebraic expressions, boolean values can be manipulated using certain operators such as [andoperator $~$\land$~$ (and)], [oroperator $~$\lor$~$ (or)], [negationoperator $~$\neg$~$ ([negation)], and [implicationoperator $~$\rightarrow$~$ (implication)]. This field is called, surprisingly, [-boolean_algebra].
Because booleans can only express absolute truth or falsity, when working with measures of uncertainty you must use other representations, such as Probability.