Cyclic Negation
In many-valued logic with linearly ordered truth values, 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 particulapp. 188–189 Mathematical logic {{Mathlogic-stub ...
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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") for any proposition. Classical two-valued logic may be extended to ''n''-valued logic for ''n'' greater than 2. Those most popular in the literature are three-valued (e.g., Łukasiewicz's and Kleene's, which accept the values "true", "false", and "unknown"), four-valued, nine-valued, the finite-valued (finitely-many valued) with more than three values, and the infinite-valued (infinitely-many-valued), such as fuzzy logic and probability logic. History It is wrong that the first known classical logician who did not fully accept the law of excluded middle was Aristotle (who, ironically, is also generally considered to be the first classical logician and the "father of wo-valuedlogic"). In fact, Aristotle did not contest the uni ...