Foundations Of Cognitive Science


XOR, also known as "exclusive or", is one of the logic blocks that is defined in Boolean algebra (Boole, 1854). In its modern usage, XOR is defined as a truth function computed over two input variables which themselves can either be true or false. XOR returns as a value of true only if one of the input variables is true and the other is false. If both input variables are true, or if both input variables or false, then XOR returns a value of false.

XOR is important to cognitive science into different respects. First, as part of Boolean algebra is a basic logical operator that is useful in the design and implementation of modern digital computers (Hillis, 1997). Second, XOR was proven by Minsky and Papert (1988) to be a logical function that could not be represented by a perceptron. This proof, also used to show that perceptrons could not detect whether a figure was connected or not, dealt a nearly mortal blow to research on artificial neural networks.


  1. Boole, G. (1854). An investigation of the laws of thought [on which are founded the mathematical theories of logic and probabilities]. London: Walton and Maberley.
  2. Hillis, W. D. (1998). The Pattern on the Stone. New York: Basic Books.
  3. Minsky, M., & Papert, S. (1988). Perceptrons, 3rd Edition. Cambridge, MA: MIT Press.

(Added April 2010)