cyclic negation
   HOME

TheInfoList



OR:

In
many-valued logic Many-valued logic (also multi- or multiple-valued logic) refers to a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., "true" and "false ...
with
linearly ordered In mathematics, a total or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation \leq on some set X, which satisfies the following for all a, b and c in X: # a \leq a ( reflexive) ...
truth value In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Computing In some pro ...
s, cyclic negation is a unary truth function that takes a truth value ''n'' and returns ''n'' − 1 as value if ''n'' is not the lowest value; otherwise it returns the highest value. For example, let the set of truth values be , let ~ denote negation, and let ''p'' be a variable ranging over truth values. For these choices, if p = 0 then ~p = 2; and if p = 1 then ~p = 0. Cyclic negation was originally introduced by the logician and mathematician
Emil Post Emil Leon Post (; February 11, 1897 – April 21, 1954) was an American mathematician and logician. He is best known for his work in the field that eventually became known as computability theory. Life Post was born in Augustów, Suwałki Gove ...
.


References

*. See in particula
pp. 188–189
Mathematical logic {{Mathlogic-stub