Quantization (linguistics)

In formal semantics, a predicate is quantized if it being true of an entity requires that it is not true of any proper subparts of that entity. For example, if something is an "apple", then no proper subpart of that thing is an "apple". If something is "water", then many of its subparts will also be "water". Hence, the predicate "apple" is quantized, while "water" is not.[1][2]

Formally, a quantization predicate QUA can be defined as follows, where  U {\displaystyle U} is the universe of discourse,  F {\displaystyle F} is a variable over sets, and  p {\displaystyle p} is a mereological part structure on  U {\displaystyle U} with  < p {\displaystyle <_{p}} the mereological part-of relation:[1][2]

( ∀ F ⊆ U p ) ( Q U A ( F ) ⟺ ( ∀ x , y ) ( F ( x ) ∧ F ( y ) ⇒ ¬ x < p y ) ) {\displaystyle (\forall F\subseteq U_{p})(QUA(F)\iff (\forall x,y)(F(x)\wedge F(y)\Rightarrow \neg x<_{p}y))}

Quantization was first proposed by Manfred Krifka as part of his mereological approach to the semantics of nominals. It has since been applied to other phenomena such as telicity.

## See also

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* Fewer vs. less
* Mass noun
* Mereology
* Telicity
* Cumulativity (linguistics)

## References

[edit]

1. ^ a b Champollion, Lucas; Krifka, Manfred (2016). "Mereology". In Aloni, Maria; Dekker, Paul (eds.). The Cambridge Handbook of Formal Semantics. Cambridge University Press. pp. 369–388\. doi:10.1017/CBO9781139236157.014. ISBN 9781139236157.
2. ^ a b Krifka, Manfred (1989). "Nominal reference, temporal constitution, and quantification in event semantics". In Bartsch, Renate; van Benthem, Johan; van Emde Boas, Peter (eds.). Semantics and Contextual Expressions. Foris. pp. 75–115.

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Formal semantics (natural language)

Central concepts|

* Compositionality
* Denotation
* Entailment
* Extension
* Generalized quantifier
* Intension
* Logical form
* Presupposition
* Proposition
* Reference
* Scope
* Speech act
* Syntax–semantics interface
* Truth conditions

Topics|

| Areas|

* Anaphora
* Ambiguity
* Binding
* Conditionals
* Definiteness
* Disjunction
* Evidentiality
* Focus
* Indexicality
* Lexical semantics
* Modality
* Negation
* Propositional attitudes
* Tense–aspect–mood
* Quantification
* Vagueness

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Phenomena|

* Antecedent-contained deletion
* Cataphora
* Coercion
* Conservativity
* Counterfactuals
* Crossover effects
* Cumulativity
* De dicto and de re
* De se
* Deontic modality
* Discourse relations
* Donkey anaphora
* Epistemic modality
* Exhaustivity
* Faultless disagreement
* Free choice inferences
* Givenness
* Homogeneity (linguistics)
* Hurford disjunction
* Inalienable possession
* Intersective modification
* Logophoricity
* Mirativity
* Modal subordination
* Opaque contexts
* Performatives
* Polarity items
* Privative adjectives
* Quantificational variability effect
* Responsive predicate
* Rising declaratives
* Scalar implicature
* Sloppy identity
* Subsective modification
* Subtrigging
* Telicity
* Temperature paradox
* Veridicality

Formalism|

| Formal systems|

* Alternative semantics
* Categorial grammar
* Combinatory categorial grammar
* Discourse representation theory (DRT)
* Dynamic semantics
* Generative grammar
* Glue semantics
* Inquisitive semantics
* Intensional logic
* Lambda calculus
* Mereology
* Montague grammar
* Segmented discourse representation theory (SDRT)
* Situation semantics
* Supervaluationism
* Type theory
* TTR

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Concepts|

* Autonomy of syntax
* Context set
* Continuation
* Conversational scoreboard
* Downward entailing
* Existential closure
* Function application
* Meaning postulate
* Monads
* Plural quantification
* Possible world
* Quantifier raising
* Quantization
* Question under discussion
* Semantic parsing
* Squiggle operator
* Strawson entailment
* Strict conditional
* Type shifter
* Universal grinder

See also|

* Cognitive semantics
* Computational semantics
* Distributional semantics
* Formal grammar
* Inferentialism
* Logic translation
* Linguistics wars
* Philosophy of language
* Pragmatics
* Semantics of logic

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