A quantificational determiner denotes the denotations of its readings.
- instDenotesSetFamily = { denote := fun (d : QuantificationalDeterminer) => (fun (s : Quantifier.Det.Symbol) => s.denote) '' ↑d.readings }
Docs / Semantics / Quantification / Determiner
The readings of a quantificational determiner
import Linglib.Semantics.Quantification.Determiner · namespace QuantificationalDeterminer
A quantificational determiner denotes the readings its entry records, each the global denotation of a determiner symbol, so it has as many readings as symbols it records, and none when its standard is left to context, as with many. Each symbol denotes the global denotation of a tree of numbers, so every reading of every quantificational determiner is conservative, satisfies extension and is closed under isomorphism: what a lexical entry can mean meets the conditions that determiner denotations are claimed to meet.
References
- Barwise & Cooper 1981, Generalized Quantifiers and Natural Language formalized
- Keenan & Stavi 1986, A Semantic Characterization of Natural Language Determiners formalized
- van Benthem 1984, Questions About Quantifiers
- Peters & Westerståhl 2006, Quantifiers in Language and Logic formalized
Declarations
(d : QuantificationalDeterminer) :
Denotes.denote d = (fun (s : Quantifier.Det.Symbol) => s.denote) '' ↑d.readings
{d : QuantificationalDeterminer} {Q : Quantifier.Det.Family} :
Q ∈ Denotes.denote d ↔ ∃ s ∈ d.readings, s.denote = Q
{d : QuantificationalDeterminer} {s : Quantifier.Det.Symbol} (hs : s ∈ d.readings) :
s.denote ∈ Denotes.denote d
{d : QuantificationalDeterminer} {s : Quantifier.Det.Symbol} (h : d.readings = {s}) :
Denotes.denote d = {s.denote}
A quantificational determiner has as many readings as the symbols its entry records.
Every reading of a quantificational determiner is conservative, satisfies extension and is closed under isomorphism.
{d : QuantificationalDeterminer} {Q : Quantifier.Det.Family} (hQ : Q ∈ Denotes.denote d) :
Q.Conservative ∧ Q.Ext ∧ Q.Isom