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Formal semantics has shown that sentence meanings arise by recursively composing lexical meanings, yet much of the literature on semantic universals models either lexicons with fixed signal structures or holistic composition without interpretable lexical parts. We introduce a framework that integrates this fundamental insight of formal semantics in evolutionary modeling, by allowing lexical meanings and a composition function to co-evolve under pressures for conceptual simplicity and communicative accuracy. We apply this framework to the evolution of quantificational meaning. Analyzing the Pareto frontier, we find that the most well-known semantic universal, conservativity, emerges as an efficient system-wide abstraction. The account is sensitive to syntactic structure and helps reconcile tensions between empirical evidence on quantifier learnability and prior evolutionary models. More broadly, the results demonstrate that the picture of sentential meaning developed in formal semantics can be productively combined with evolutionary modeling. The framework offers a template for studying universals that involve global compression within a grammatical category, semantic specialization of syntactic arguments, and the co-evolution of lexical and compositional meaning.