The modal intervals theory deals with quantified propositions in AE-form, i.e. universal quantifiers precede existential ones, where variables are quantified over continuous domains and with equality constraints. It allows to manipulate such quantified propositions computing only with bounds of intervals. A simpler formulation of this theory is presented. Thanks to this new framework, a mean-value extension to generalized intervals (intervals whose bounds are not constrained to be ordered) is defined. Its application to the validation of quantified propo- sitions is illustrated