@cite{davidson-gagne-2022} #

Davidson, K. & Gagné, D. (2022). "More is up" for domain restriction in ASL. Semantics & Pragmatics 15, Article 1: 1–52.

Core Argument #

In ASL, vertical height in signing space overtly marks the size of the quantifier domain. When FS(ALL) is signed at neutral height, it quantifies over the contextually supplied domain (e.g., friends who watched the movie). When signed higher, it quantifies over a wider domain (e.g., everyone in the world). This is not a gestural expression of surprise or emphasis — it is a grammatical mechanism that enters through pronominal elements (IX-arc) and composes with quantifiers via a partitive-like restrictor structure.

Key Claims Formalized #

Height = domain size (§5.2): Vertical ordering on loci corresponds to mereological part-hood on domains. Formalized via HeightDDRP as a NestedRestriction, giving all monotonicity theorems free.
Monotonicity contrast (§4): ALL and NONE are ↓MON in the restrictor (smaller domain → easier to satisfy), SOME is ↑MON (larger domain → easier to satisfy). Height affects domain size uniformly, but truth conditions react differently depending on the quantifier's monotonicity.
Height ≠ intensification (§4, after ex. 36): If height were merely emphatic strengthening, then higher SOME should be harder to satisfy (stronger). But higher SOME is easier to satisfy (wider domain for the existential witness). This rules out the emphasis analysis.
Only pronominal structures (§3.3): Bare nouns cannot be height-marked because they lack a pronominal argument position. Height requires IX-arc (overt or incorporated).
Structural parallel to cognitive DDRPs (§5): ASL height (overt, modality-specific) and @cite{ritchie-schiller-2024}'s spatial heuristics (covert, modality-general) are both instances of NestedRestriction — the same abstract nesting structure produces the same formal predictions.

Compositional Grounding #

Truth conditions derive from every_restricted / some_restricted / no_restricted (DomainRestriction.lean), which wrap every_sem / some_sem / no_sem (Quantifier.lean) with a height-indexed domain predicate. Nesting theorems derive from DDRP.every_nesting / DDRP.some_nesting / DDRP.no_nesting, connecting height ordering to restrictor monotonicity.

Not formalized here #

Directional verbs (§3): verb height marking analyzed as pronominal incorporation. The semantic contribution is the same height-indexed domain restriction; the morphological incorporation mechanism is left to @cite{ahn-kocab-davidson-2026} (which postdates this paper and CAN reference it).
Comparison with irgendein (§5.4): @cite{davidson-gagne-2022} argue that ASL height-based domain widening is structurally different from German irgend- (@cite{kratzer-shimoyama-2002}): height is on pronouns (not determiners), gradient (not binary), and restricted to pronominal structures. Documented here but not formalized as a cross-fragment theorem.
Cross-linguistic parallels (§6.2): JSL (ex. 54: chest→cheek→forehead for class→school→prefecture) and Nicaraguan Sign Language (ex. 55: TODO-mid vs TODO-high for local vs national scope) show the same pattern. Placeholder theorems are sorry-marked for future fragment work.

The running example from @cite{davidson-gagne-2022} §1:

Context: "Last night I watched a movie with my friends about vampires.
Afterwards I went to bed and I dreamt that..."

FS(ALL)-neutral BECOME VAMPIRE → 'All of my friends became vampires'
FS(ALL)-high BECOME VAMPIRE → 'All of the people in the world became vampires'