How does the formal semantics of focus operators handle pragmatic exclusion effects in natural language?

This is an exclusively logical variant of another post of mine that was deleted. Now it Consider the following analogy: Pedro, Carmen, and Ana are very intelligent. Pedro is also very cultured. The latter sentence is grammatical and cannot be refuted, but the way the premise is presented is ambiguous and generates confusion: any reader might assume that only Pedro is cultured among the three. By linking culture solely to Pedro within a structure that groups all three under intelligence, language creates an invisible hierarchy, an effect of focus that conceals the possibilities of Carmen and Ana. Pedro(P), Carmen(C), Ana(A) Intelligent(x) ≡ Ix Cultured(x) ≡ Cx Premises: IP∧IC∧IA CP CP∧CC∧CA ∃xCx ¬CC∧CA F = Restrictive focus operator F(CP)→(CP∧¬CC∧¬CA) Does might this force us to always speak as if we had a logic manual in our hands to avoid misinterpretations? Should natural language be validated from semantic logic (formal semantics of natural language), or should semantic logic, conversely, be validated from natural language?