Distributivity in Formal Semantics

Distributivity in natural language occurs in sentences such as John and Mary (each) took a deep breath, when a predicate that is combined with a plurality-denoting expression is understood as holding of each of the members of that plurality. Language provides ways to express distributivity overtly, with words such as English each, but also covertly, when no one word can be regarded as contributing it. Both overt and covert distributivity occur in a wide variety of constructions. This article reviews and synthesizes influential approaches to distributivity in formal semantics and includes pointers to some more recent approaches. Theories of distributivity can be distinguished on the basis of how they answer a number of interrelated questions: To what extent can distributivity be attributed to what we know about the world, as opposed to the meanings of words or silent operators? What is the relationship between distributivity and plurality? Does distributivity always reach down to the singular individuals in a plurality? If not, under what circumstances is distributivity over subgroups possible, and what is its relation to distributivity over individuals?