A Semantics for Possibility Theory Based on Likelihoods*

In this paper, a semantic basis for Possibility Theory based on likelihood functions is presented. In some cases, possibilities have been considered as approximations of Shafer plausibility measures. This approximation exchanges exactness of plausibility values for the simplicity of use of possibility values. In this paper, a different direction is followed. Possibility measures are considered as the supremum of a family of likelihood functions. This is an exact interpretation, not an approximation. The minimum rule to combine possibility distributions is justified in this framework under general conditions. Conditions under which other rules can be applied are also studied.