Plural Semantics

Origin. Link (1983), Landman, Schwarzschild. Pluralities as sums. Collective vs distributive. Mereology for NL. Foundation of plural predication.

Models. Domain includes plural individuals. Mereological structure. Collective and distributive readings. Covers. Plural predication.

Formalism.

Plural domain: D* = closure of D under sum. a ⊕ b: sum of a and b. Atoms and sums. Mereological structure.

Sum operation: ⊕: associative, commutative, idempotent. Join semilattice. a ≤ b iff a ⊕ b = b. Part-of relation.

Plural predicates: *P: pluralized P. *P(x) iff x can be divided into parts each satisfying P. Distributive: applies to atoms. Collective: applies to sum.

Distributive reading: "The students smiled." Each student smiled. ∀x[x ≤ σy.student(y) → smiled(x)]. Predicate distributes.

Collective reading: "The students gathered." The group gathered. gathered(σy.student(y)). Predicate applies to sum.

Covers: Cov(X) = partition-like structure. Intermediate between collective and distributive. "The students lifted three tables." Various cover readings.

σ-operator: σx.P(x) = maximal sum of P's. Definite plural. "The students" = sum of all students. Unique maximal P.

Symbols.

Symbol	Unicode	Meaning
⊕	U+2295	sum
≤	U+2264	part-of
*P	—	pluralized P
σx.P	—	maximal sum

Metatheory. Mereology. Distributivity. Collectivity. Covers.

Applies to. Plural NPs. Distributivity. Reciprocals. Collectivity.

Limitations. Cover complexity. Cumulativity. Event interaction. Cross-linguistic.