Some systems adopt logic-based representations but use distributional evidence for predicate disambiguation (Lewis and Steedman, 2013) or to weight probabilistic inference rules Beltagy et al., 2013).
formal semantics captures fundamental aspects of meaning in set-theoretic terms: Entailment, for example, is captured as the inclusion relation between the sets (of the relevant type) denoted by words or other linguistic expressions, e.g., sets of possible worlds that two propositions hold of (Chierchia and McConnell-Ginet, 2000, 299).