possibility every function satisfying Axiom 1 and Axiom 3. We call generalized necessity the dual of a generalized possibility. The generalized necessities are related with a very simple and interesting fuzzy logic called necessity logic. In the deduction apparatus of necessity logic the logical axioms are the usual classical tautologies. Also, there is only a fuzzy inference rule extending the usual modus ponens. Such a rule says that if α and α → β are proved at degree λ and μ, respectively, then we can assert β at degree min{λ,μ}. It is easy to see that the theories of such a logic are the generalized necessities and that the completely consistent theories coincide with the necessities (see for example Gerla 2001). See also Fuzzy measure theory Logical possibility Modal logic Probabilistic logic Random-fuzzy variable Transferable belief model Upper and lower probabilities References Dubois, Didier and Prade, Henri, "Possibility Theory, Probability Theory and Multiple-valued Logics: A Clarification", Annals of Mathematics and Artificial Intelligence 32:35–66, 2002. Gerla Giangiacomo, Fuzzy logic: Mathematical Tools for Approximate Reasoning, Kluwer Academic Publishers, Dordrecht 2001. Ladislav J. Kohout, "Theories of Possibility: Meta-Axiomatics and Semantics", Fuzzy Sets and Systems 25:357-367, 1988. Zadeh, Lotfi, "Fuzzy Sets as the Basis for a Theory of Possibility", Fuzzy Sets and Systems 1:3–28, 1978. (Reprinted in Fuzzy Sets and Systems 100 (Supplement): 9–34, 1999.) Brian R. Gaines and Ladislav J. Kohout, "Possible Automata", in Proceedings of the International Symposium on Multiple-Valued Logic, pp. 183-192, Bloomington, Indiana, May 13-16, 1975. Probability theory Fuzzy logic Possibility