Docs / Studies / Studies.Champollion2016b
Champollion, L. (2016). Journal of Semantics, 33(3), 561β622
This file derives the collective readings of noun coordination from the intersective and, on the paper's logical forms. A raised noun is a quantifier over pluralities, and Minimization keeps its minimal witness sets, which for the meet of two raised nouns are the minimal elements of the set product of their generators, the collective and of Heycock and Zamparelli. With Choice Closure above Minimization, a doctor and lawyer met holds of any doctorβlawyer pair and ten men and women got married of ten-person manβwoman mixtures; above no it gives a reading the constraint on its scope excludes. Or is never collective, every gives and and or one reading, and the collective entry overgenerates on conjuncts that are not upward entailing.
Set E and a property of pluralities a Quantifier E. Existential Raising is
a (Quantifier.Det.some) at the type of its argument, Minimization is Minimal, Choice
Raising the Montague lift Quantifier.individual of the chosen member, Distributive Choice
Raising every on the chosen plurality, and Predicate Distributivity π« S \ {β
}.N β β
of Choice Raising
into a hypothesis.MIN(ER(cat)) or MIN(ER(dog)) for the MIN(ER(cat) or ER(dog)) of its prose and
(99b). The two logical forms agree, so the slip is harmless.The split scope of indefinite numerals and Winter's pair semantics are not formalized.
Determiner Fitting (92) applies a determiner of individuals to the union of a property of pluralities and to the union of its meet with the scope.
Used by determinerFitting_some_iff, determinerFitting_no_powerset_iff, determinerFitting_every_pairs_iff, determinerFitting_every_singletons_iff, determinerFitting_some_pairs_iff
Minimization after Existential Raising of a disjunction keeps only singletons, so or is never collective (Β§6.2).
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The composition engine interprets the paper's logical forms, written in labelled brackets, and the theorems below give the truth conditions of each.
The words of the logical forms: two nouns, a predicate of individuals, a relative clause and a verb phrase that are predicates of pluralities, the numerals, and the overt and silent operators, those the paper uses at several types typed by a parameter.
Derives DecidableEq.
Used by lex, raised, crAnd, dcrAnd, plural, closedAbove, fitted, lf24, lf29, lf56, lfLocal, lf60, lf61, lf81, lf83, lf95, lf96, lf97, lf98, lf99, lf99Printed, ClosureBelowNo
The type of an index: 1 and 2 range over choice functions on individuals, the others over
choice functions on pluralities.
Used by holds_lf24, holds_lf29, holds_lf56, holds_lfLocal, holds_lf60, holds_lf61, holds_lf81, holds_lf83, holds_lf95, holds_lf96, holds_lf95_iff_holds_lf96, holds_lf97, holds_lf98, holds_lf99, holds_lf99Printed_iff
The denotations, over two nouns N, N', a predicate V of individuals and predicates R
and S of pluralities: the numerals (70), a (23), no and every at the type Ο of what
they quantify over, the coordinators at a conjoinable type, Determiner Fitting (92), Minimization
(19), Choice Raising (46), Distributive Choice Raising (78), Predicate Distributivity (27), and
Choice Closure over choice functions on Ο, at a property of pluralities (49) and at a sentence
(50).
The definition is too large to print here; read it in the source.
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Used by holds_lf24, holds_lf29, holds_lf56, holds_lfLocal, holds_lf60, holds_lf61, holds_lf81, holds_lf83, holds_lf95, holds_lf96, holds_lf95_iff_holds_lf96, holds_lf97, holds_lf98, holds_lf99, holds_lf99Printed_iff
[[a nounβ] [c [a nounβ]]]: Existential Raising of each noun, coordinated by c.
The definition is too large to print here; read it in the source.
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[[CR tβ] nounβ] [and [[CR tβ] nounβ]].
The definition is too large to print here; read it in the source.
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[[DCR tβ] X] [and [[DCR tβ] Y]].
The definition is too large to print here; read it in the source.
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[ββ [Ξ»β [ββ [Ξ»β [MIN [[CR tβ] nounβ] [and [[CR tβ] nounβ]]]]]]].
The definition is too large to print here; read it in the source.
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[[[DFIT D] X] [PDIST atom]].
Built from ,
The LF (24) of the hydra a man and woman who dated met.
The definition is too large to print here; read it in the source.
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Used by holds_lf24
The LF (29) of a man and woman had a beer.
The definition is too large to print here; read it in the source.
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Used by holds_lf29
The LF (56) of a doctor and lawyer met.
Built from ,
Used by holds_lf56
A doctor and lawyer met with each Choice Closure directly above its Choice Raising.
The definition is too large to print here; read it in the source.
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Used by holds_lfLocal
The LF of (60a) no man and woman have a right β¦, with Choice Closure below no.
Built from ,
Used by holds_lf60, closureBelowNo_lf60
The LF (61), with Choice Closure above no.
The definition is too large to print here; read it in the source.
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Used by holds_lf61, not_closureBelowNo_lf61
The LF (81) of ten men and women got married today.
The definition is too large to print here; read it in the source.
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Used by holds_lf81
The LF (83a) of two Americans and three Russians made an excellent basketball team.
The definition is too large to print here; read it in the source.
Built from
Used by holds_lf83
The LF (95a) of every cat and dog is licensed.
The definition is too large to print here; read it in the source.
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Used by holds_lf95, holds_lf95_iff_holds_lf96
The LF (96a) of every cat or dog is licensed.
The definition is too large to print here; read it in the source.
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Used by holds_lf96, holds_lf95_iff_holds_lf96
The LF (97a) of a cat and dog came running in.
The definition is too large to print here; read it in the source.
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Used by holds_lf97
The LF (98a) of a cat or dog came running in.
The definition is too large to print here; read it in the source.
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Used by holds_lf98
The LF of every cat or dog is licensed described in the prose and in (99b).
The definition is too large to print here; read it in the source.
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Used by holds_lf99, holds_lf99Printed_iff
The LF as (99a) prints it, with Minimization under or.
The definition is too large to print here; read it in the source.
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Used by holds_lf99Printed_iff
No Choice Closure in t takes scope over no, the constraint the paper draws from (59) and
(60).
The definition is too large to print here; read it in the source.
Built from
Used by instDecidablePredTreeUnitWordClosureBelowNo, closureBelowNo_lf60, not_closureBelowNo_lf61
Built from , ,
Built from , ,
With Choice Closure above Minimization, a doctor and lawyer met (56) holds when a doctor and a lawyer met, whatever professions they share (58).
Built from , ,
Built from , ,
Built from , ,
Built from , ,
Built from ,
Built from ,
Ten men and women got married today (81) holds when ten people, at least one man and one woman and nobody else, got married together.
Built from , ,
Built from , ,
Built from , ,
Built from , ,
Every cat and dog is licensed (95) and every cat or dog is licensed (96) agree, the universal half of Bergmann's puzzle.
Built from , , ,
Built from , ,
Built from , ,
Built from , ,
Built from , , ,
When a man and a woman alone smiled, the collective entry of No man and no woman smiled (103a) holds and the intersective one fails.