Purpose. The way of assignment of exact numerical truth value to any vague predicate sentence remains to be problematic. Methodology. I would like to propose one of the possible ways of estimation for vague sentences: to exploit the supevaluationists' idea of precisification for the interpretation of verity. We can think of the verity of a borderline sentence (the degree to which it is close to definite truth) as the proportion of permissible precisifications on which it is true. Scientific novelty. The proposed construal of degrees, interpreting verities on the basis of a measure over admissible precisifications, allows discrimination among borderline cases that would otherwise (on the standard supervaluationist account) all inhabit the same truth-value gap. My view of vague expressions assumes also that a borderline sentence may affect verity of another borderline sentence. The notion of relative verity reflects an intuitive assumption about possible semantic connections between applications of vague predicates. So-called forcing connection is a non-symmetric, transitive relation, which does not express any temporal or causal dependence between borderline cases; rather, it expresses a logical or semantic relation. I consider different kinds of forcing connection between vague expressions. Conclusion. Using of the notions “relative verity” and “forcing” provides preservation for borderline sentences of certain logical connections, which are postulated by classical logic.