Docs / Semantics / Genericity / NominalMappingParameter
import Linglib.Semantics.Genericity.NominalMappingParameter
The Nominal Mapping Parameter of Chierchia sets what a language's nouns can denote: kinds, so that they are arguments ([+arg]), or properties, so that they are predicates ([+pred]), or either. A setting is the set of denotation types nouns take. The setting and the language's determiners then decide which bare nominals can be arguments. A covert type shift is blocked when a determiner lexicalizes it, the Blocking Principle, and a determiner lexicalizes a shift when it denotes what the shift denotes. An article lexicalizes the definite shifts of its strengths, and a demonstrative, whose deictic presupposition can fail where the definite's does not, lexicalizes none. A [+arg, +pred] language with both articles then admits exactly the bare nominals for which kind formation ∩ is defined, a [+arg, −pred] language every bare nominal, and a [−arg, +pred] language none.
NominalMapping: a setting of the parameter, with the three attested settings argOnly,
argAndPred and predOnly.CovertShift, Determiner.Entry.Lexicalizes, Determiner.Inventory.Blocks: the covert type
shifts, a determiner denoting one, and the Blocking Principle.NominalMapping.LicensesBare: the bare nominals a language admits as arguments.NominalMapping.argAndPred_licensesBare_iff: with ι and ∃ blocked, a [+arg, +pred] language
admits exactly the bare nominals ∩ is defined for.NominalMapping.licensesBare_true_iff: a language admits a bare nominal with a kind iff it is
[+arg].Whether ∩ is defined for a nominal is a proposition down that the consumer supplies, as for
Determiner.Inventory.Available; for Chierchia's ∩ it is Kind.down P ∈ K
(Semantics/Reference/Kind.lean). It depends on the nominal's denotation and not on its number
and countability alone, since a plural property anchored to particular entities has no kind. The
nominal's number is supplied too, since blocking applies only within a determiner's domain.
Kind.down_isSome_of_supClosed and IsAntichain.iota_isGreatest_eq_none decide whether ∩ has a
value for cumulative extensions and for extensions of two or more atoms.
A noun denotes a kind, of type e, or a property, of type ⟨e,t⟩.
Derives DecidableEq, Repr, Fintype.
Used by Genericity.NominalMapping, Genericity.NominalMapping.instMembershipNominalDenotation, Genericity.NominalMapping.instDecidableMemNominalDenotation, Genericity.NominalMapping.mem_argOnly, Genericity.NominalMapping.mem_argAndPred, Genericity.NominalMapping.mem_predOnly
A setting of the Nominal Mapping Parameter is the set of denotation types a language's nouns can
take. The language is [+arg] when .kind is in the setting and [+pred] when .property is; the
empty setting, [−arg, −pred], leaves nouns nothing to denote and is excluded by the paper.
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Used by Genericity.NominalMapping.instMembershipNominalDenotation, Genericity.NominalMapping.instDecidableEq, Genericity.NominalMapping.instDecidableMemNominalDenotation, Genericity.NominalMapping.argOnly, Genericity.NominalMapping.argAndPred, Genericity.NominalMapping.predOnly, Genericity.NominalMapping.CanDenoteKind, Genericity.NominalMapping.instDecidableCanDenoteKind, Genericity.NominalMapping.CanDenoteProperty, Genericity.NominalMapping.instDecidableCanDenoteProperty, Genericity.NominalMapping.LicensesBare, Genericity.NominalMapping.instDecidableLicensesBare, Genericity.NominalMapping.licensesBare_true_iff
Used in Chierchia1998, Guerrini2026, Longobardi2001
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[+arg, −pred]: nouns denote kinds (Mandarin, Japanese).
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Used by Genericity.NominalMapping.mem_argOnly
Used in Chierchia1998
[+arg, +pred]: nouns denote kinds or properties (English, Germanic).
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Used by Genericity.NominalMapping.mem_argAndPred, Genericity.NominalMapping.argAndPred_licensesBare_iff, Genericity.NominalMapping.argAndPred_licensesBare_false_iff
Used in Chierchia1998, Guerrini2026, Longobardi2001
[−arg, +pred]: nouns denote properties (Romance, Greek).
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Used by Genericity.NominalMapping.mem_predOnly
Used in Chierchia1998, Guerrini2026, Longobardi2001
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A nominal can denote a kind outright in a [+arg] language, and otherwise under an overt determiner.
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Used by Genericity.NominalMapping.instDecidableCanDenoteKind
Used in Guerrini2026
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A nominal can denote a property in a [+pred] language.
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Used by Genericity.NominalMapping.instDecidableCanDenoteProperty
Used in Guerrini2026
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The covert type shifts are kind formation ∩, the definite ι and the existential ∃ of Chierchia 1998, and the anaphoric definite ι^x of Jenks 2018, which Moroney 2021 makes covert.
Derives DecidableEq, Repr, Fintype.
Used by Determiner.Entry.Lexicalizes, Determiner.Entry.not_lexicalizes_demonstrative, Determiner.Entry.not_lexicalizes_possessive, Determiner.Inventory.Lexicalizes, Determiner.Inventory.Blocks, Determiner.Inventory.Blocks.lexicalizes, Determiner.Inventory.blocks_iff_lexicalizes
Used in Semantics/Genericity/MeaningPreservation, Dayal2004, Moroney2021
A determiner lexicalizes a covert shift when it denotes what the shift denotes on every
restrictor in its domain, Dayal 2004's Blocking Principle. An article lexicalizes ι when one of
its readings is the bare definite on every model, and ι^x when one is the strong article at every
index. A demonstrative would have to equal the shift at every context of utterance and vicinity
relation, and a possessive at every possessor and possession relation, which their presuppositions
prevent (not_lexicalizes_demonstrative, not_lexicalizes_possessive). An indefinite article is
∃, and no determiner is ∩.
The definition is too large to print here; read it in the source.
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Used by Determiner.Entry.lexicalizes_article_iota_iff, Determiner.Entry.lexicalizes_article_iotaAnaphoric_iff, Determiner.Entry.not_lexicalizes_demonstrative, Determiner.Entry.not_lexicalizes_possessive, Determiner.Entry.lexicalizes_iota_iff, Determiner.Entry.lexicalizes_iotaAnaphoric_iff, Determiner.Entry.lexicalizes_exists_iff, Determiner.Entry.not_lexicalizes_down, Determiner.Entry.instDecidablePredCovertShiftLexicalizes, Determiner.Inventory.Lexicalizes, Determiner.Inventory.Blocks, Determiner.Inventory.blocks_iff_lexicalizes
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A demonstrative lexicalizes no covert shift: where no referent has the indexed one in its vicinity, its deictic presupposition fails and the definite's does not.
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A possessive lexicalizes no covert shift: under the empty possession relation it is undefined where the definite is not.
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An inventory lexicalizes a covert shift when one of its determiners does.
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Used by Determiner.Inventory.instDecidablePredCovertShiftLexicalizes, Determiner.Inventory.not_lexicalizes_down, Determiner.Inventory.lexicalizes_exists_iff, Determiner.Inventory.lexicalizes_iota_iff, Determiner.Inventory.lexicalizes_iotaAnaphoric_iff, Determiner.Inventory.Blocks.lexicalizes, Determiner.Inventory.blocks_iff_lexicalizes
Used in Chierchia1998, Dayal2004, Jenks2018, Moroney2021
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The Blocking Principle of Chierchia 1998, (39a) of Dayal 2004: a covert shift is blocked
for a nominal of number num when a determiner whose domain holds such nominals lexicalizes it.
English a selects the singular, so it blocks ∃ for a bare singular and leaves ∃ to a bare plural
or a mass noun. An article marking familiarity alone, as Akan nó, leaves ι to the bare noun, and
a demonstrative blocks nothing.
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Used by Determiner.Inventory.instDecidablePredCovertShiftBlocks, Determiner.Inventory.Blocks.lexicalizes, Determiner.Inventory.not_blocks_down, Determiner.Inventory.blocks_iff_lexicalizes, Genericity.NominalMapping.argAndPred_licensesBare_iff, Genericity.NominalMapping.argAndPred_licensesBare_false_iff
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Where no determiner lexicalizing a shift selects a number, as no definite article in the fragments does, a shift is blocked exactly when it is lexicalized.
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A language with the setting m and the determiners ds admits as an argument a bare
nominal of number num for which ∩ is defined just when down holds: it must be [+arg], and if it
is also [+pred], so that its nouns are predicates, ∩ must be defined for the nominal or ι or ∃ must
be unblocked for its number.
The definition is too large to print here; read it in the source.
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Used by Genericity.NominalMapping.instDecidableLicensesBare, Genericity.NominalMapping.argAndPred_licensesBare_iff, Genericity.NominalMapping.argAndPred_licensesBare_false_iff, Genericity.NominalMapping.licensesBare_true_iff
Used in Chierchia1998
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With ι and ∃ blocked, a [+arg, +pred] language admits exactly the bare nominals ∩ is defined for.
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A language admits a bare nominal with a kind iff it is [+arg].
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