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Quantization (linguistics)

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Informal semantics, apredicate isquantized if it being true of an entity requires that it isnot 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, aquantization predicateQUA can be defined as follows, whereU{\displaystyle U} is theuniverse of discourse,F{\displaystyle F} is a variable oversets, andp{\displaystyle p} is amereological partstructure onU{\displaystyle U} with<p{\displaystyle <_{p}} themereological part-ofrelation:[1][2]

(FUp)(QUA(F)(x,y)(F(x)F(y)¬x<py)){\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 byManfred Krifka as part of hismereological approach to the semantics of nominals. It has since been applied to other phenomena such astelicity.

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References

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  1. ^abChampollion, Lucas; Krifka, Manfred (2016). "Mereology". InAloni, Maria; Dekker, Paul (eds.).The Cambridge Handbook of Formal Semantics. Cambridge University Press. pp. 369–388.doi:10.1017/CBO9781139236157.014.ISBN 9781139236157.
  2. ^abKrifka, 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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