Composition Under Distributive Natural Transformations: Or, When Predicate Abstraction is Impossible

Abstract Natural language semanticists have often found it useful to assume that all expressions denote sets of values. The approach is most prominent in the study questions and prosodic focus, but also common work on indefinites, disjunction, negative polarity, scalar implicature. However, popular compositional implementation this idea known face technical obstacles presence object-language binding constructs, including, chiefly, lambda abstraction. problem has been well-described several occasions literature, fact solutions explored. This paper seeks formalize challenge defining an indeterminate semantics for operators, formally establish intuition insurmountable. primary benefit exercise offers abstract characterization what means lift operation from one semantic space another, a notion which may be applied domains having nothing do with alternatives.