Foundations Of Cognitive Science

Truth-Value Systems

Assume the existence of a set of primitive terms that can either be true or false.  The truth value of a logical combination of these terms can then be determined from the truth values of the component terms.  This approach is known as using truth-value systems (Lewis & Langford, 1959).  Truth-value systems essentially use truth tables to determine the truth of functions of propositions (i.e. of logical combinations of propositions.  “It is a distinctive feature of this two-valued system that when the property, 0 or 1, of the elements p, q, etc., is given, any function of the elements which is in the system is thereby determined to have the property 0 or the property 1” (Lewis & Langford, 1959, p. 199). 

Truth tables, and the truth-value system that they support, are very powerful.  They can be used to determine whether any complex expression, based on combinations of primitive propositions and primitive logical operations, is true or false (Lewis, 1932).  Indeed, it is this property, and the binary nature of a truth-value system, that inspired Claude Shannon to use such a system to “logically” design systems of switches, which in turn led to the invention of the modern computer (Shannon, 1938).


  1. Lewis, C. I. (1932). Alternative systems of logic. The Monist, 42(4), 481-507.
  2. Lewis, C. I., & Langford, C. H. (1959). Symbolic Logic (2nd ed.). New York.
  3. Shannon, C. E. (1938). A symbolic analysis of relay and switching circuits. Transactions Of The American Institute Of Electrical Engineers, 57, 713-723.

(Added September 2010)