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A unified semantics for distributive and non-distributive universal quantifiers across languages.

Nina Haslinger1,2, Alain Noindonmon Hien3, Emil Eva Rosina4

  • 1Department of Linguistics and Philosophy, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 USA.

Natural Language & Linguistic Theory
|September 29, 2025
PubMed
Summary

Universal quantifiers like "every" and "all" have distinct meanings. This study proposes a unified semantic approach, linking quantifier interpretation to predicate properties and complement number, explaining cross-linguistic patterns.

Keywords:
DistributivityMorphosemanticsNon-distributivityNumberUniversal quantification

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Area of Science:

  • Linguistics
  • Semantics
  • Formal Semantics

Background:

  • Universal quantifiers exhibit interpretive differences, with some allowing only distributive meanings (e.g., English 'every') and others permitting non-distributive meanings (e.g., English 'all').
  • Traditional linguistic approaches posit separate lexical entries for distributive and non-distributive quantifiers, failing to explain the correlation between distributivity and complement number.
  • Cross-linguistically, distributive universal quantifiers typically pair with singular complements, while non-distributive quantifiers consistently take plural complements.

Purpose of the Study:

  • To propose a unified lexical meaning for universal quantifiers that derives both distributive and non-distributive interpretations.
  • To explain the cross-linguistic correlation between quantifier distributivity and the number (singular/plural) of its complement.
  • To investigate the role of semantic properties of the restrictor predicate in determining quantifier interpretation.

Main Methods:

  • Developing a single lexical semantic entry for universal quantifiers.
  • Analyzing the semantic contribution of predicate properties (closed under sum vs. quantized) to quantifier interpretation.
  • Examining cross-linguistic data, including languages where the same lexical item varies in interpretation based on complement number.
  • Proposing a morphosyntactic element in distributive forms that restricts semantic combination with predicates of atomic individuals.

Main Results:

  • A single lexical meaning for universal quantifiers can derive non-distributive interpretations when the restrictor predicate is closed under sum and distributive interpretations when it is quantized.
  • The number of the complement is shown to be a consequence of the semantic properties of the restrictor predicate, not an independent grammatical factor.
  • Languages exist where the same universal quantifier expresses distributive or non-distributive meanings contingent on the complement's number.
  • Distributive universal quantifiers in some languages incorporate an additional morphosyntactic element, suggesting structural complexity linked to semantic restrictions.

Conclusions:

  • The study provides a unified semantic account for distributive and non-distributive universal quantification, resolving the traditional dichotomy.
  • The correlation between quantifier distributivity and complement number is derived from the interaction between the quantifier's core meaning and the semantic properties of the restrictor predicate.
  • Semantic properties of the restrictor predicate offer a more robust explanation for quantifier form choice than morphosyntactic number alone.