Given two fuzzy propositions, how to truth-qualify one of them to induce the other one in a semantical equivalence is the first basic issue addressed in this paper. In the most general case, the set of solutions of this converse problem is fully characterized. Two fuzzy subsets of the unit interval ( τ 0 and τ 1, representing linguistic truth values) are introduced that provide best lower and upper approximations when no exact solution can be found: best semantic entailments of propositions are thus derived. In a new approach, the problem is reformulated in terms of fuzzy relation equations, from which results are retrieved and extended. The second part of this paper introduces a truth-possibility index defined from τ 0 and τ 1, that serves pattern-matching purposes, in addition to the usualv possibility and necessity measures. A biomedical application, in which medical knowledge is expressed in a rule form, with ANDed fuzzy propositions in the antecedent, illustrates the aggregation of these measures, for medical diagnosis assistance.