Distributivity in Formal Semantics

Abstract

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?

The representation and processing of distributivity and collectivity: ambiguity vs. underspecification

“…5 For a good formal explanation why we assume this contrast between lexical predicates as in (8), which do not require the D operator, and phrases/syntactically-complex predicates, which do, see Champollion (2019) and references therein. To be sure, it does not follow that all multi-word expressions require the D operator for their distributive reading, since it is possible that deriving the meaning of some multi-word expressions is not necessarily syntactically mediated.…”

“…That is, since the distributivity is fully located on the verb only, no D operator is needed. See Dotlačil and Brasoveanu Glossa: a journal of general linguistics DOI: 10.5334/g jgl.1131 Champollion (2019) and references therein for a more detailed discussion of lexical and phrasal distributivity.…”

Plurals and Mereology

“…This would be an intermediate reading between the collective reading and the distributive one. Accounting for readings of this kind raises a number of issues which, though interesting, will be set aside for the purposes of our discussion (see especially Gillon [20], Lasersohn [36], Schwarzschild [72], Landman [33], and Champollion [10]).…”

“…That is, the translation of a natural language argument should be validated by the model theory if and only if the argument itself is logically valid. 10 As presented here, the model theory aims to account for logical entailments, such as those presented in our discussion of cumulative reference and distributivity (Section 2.1). By relying on meaning postulates (Carnap [7]), this framework is also able to capture other kinds of entailment involving expressions with related meanings.…”

“…It is easy to see how this translation captures intuitive inferences such as the following: (10) Annie is one of the students atom(a) ∧ a ≤ σ x. * student(x) Annie is a student → student(a)…”