"Exhaustivity: A Semantic Account of 'Quantity' Implicatures" argues against the Grice/Horn approach to scalar and clausal implicatures, and offers an alternative theory of these implicatures, which derives them based on a semantic operation of exhaustivization. The exhaustivity operator makes reference to the structure of the semantic domain it operates on. It requires the domain to have the structure of a join semilattice. Exhaustivity may operate on the partial order in the domain of singular and plural objects, or the context may provide other structured domains of interpretation, and hence other orders and maximality operations (orders of numbers, ranks, properties, relations etc.). The present theory also provides a principled account of the dependence of scalar implicatures on focal structure, and of scalar implicatures in logically complex sentences ('implicature projection').

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