Editing Possibility theory (section)

==Necessity logic==
We call ''generalized possibility'' every function satisfying Axiom 1 and Axiom 3. We call ''generalized necessity'' the dual of a generalized possibility. The generalized necessities are related to a very simple and interesting fuzzy logic called ''necessity logic''. In the deduction apparatus of necessity logic the logical axioms are the usual classical [[tautology (logic)|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).