Cyclic negation

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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 {0,1,2}, 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.


  • Mares, Edwin (2011), "Negation", in Horsten, Leon; Pettigrew, Richard, The Continuum Companion to Philosophical Logic, Continuum International Publishing, pp. 180–215, ISBN 9781441154231 . See in particular pp. 188–189.