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 eval­u­ate to one of these two val­ues, in the same way that or­di­nary alge­braic ex­pres­sions eval­u­ate to a num­ber.

Also as in alge­braic ex­pres­sions, boolean val­ues can be ma­nipu­lated us­ing cer­tain op­er­a­tors such as \(\land\) (and), \(\lor\) (or), \(\neg\) ([nega­tion), and \(\rightarrow\) (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.


  • Mathematics

    Math­e­mat­ics is the study of num­bers and other ideal ob­jects that can be de­scribed by ax­ioms.