Quantization (linguistics)
Encyclopedia
In linguistics
, a quantized expression is such that, whenever it is true of some entity, it is not true of any proper subparts of that entity. 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, "apple" is quantized, while "water" is not. Quantization has proven relevant to the proper characterization of grammatical telicity
(roughly, sentences that present events as bounded/unbounded in time) and the mass/count
distinction for nouns. The notion was first applied to linguistic semantics
by the linguist Manfred Krifka
.
Formally, a quantization predicate QUA can be defined as follows, where
is the universe of discourse, and 
is a variable over sets, and 
is a mereological
part structure
on
with 
the mereological
part-of relation
.
Linguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....
, a quantized expression is such that, whenever it is true of some entity, it is not true of any proper subparts of that entity. 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, "apple" is quantized, while "water" is not. Quantization has proven relevant to the proper characterization of grammatical telicity
Telicity
In linguistics, telicity is the property of a verb or verb phrase that presents an action or event as being complete in some sense...
(roughly, sentences that present events as bounded/unbounded in time) and the mass/count
Mass noun
In linguistics, a mass noun is a noun that refers to some entity as an undifferentiated unit rather than as something with discrete subsets. Non-count nouns are best identified by their syntactic properties, and especially in contrast with count nouns. The semantics of mass nouns are highly...
distinction for nouns. The notion was first applied to linguistic semantics
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
by the linguist Manfred Krifka
Manfred Krifka
Manfred Krifka is director of the Center for General Linguistics at the Humboldt University of Berlin, and editor of the academic journal Theoretical Linguistics.- Bibliography :...
.
Formally, a quantization predicate QUA can be defined as follows, where
is the universe of discourse, and is a variable over sets, and is a mereologicalMereology
In philosophy and mathematical logic, mereology treats parts and the wholes they form...
part structure
Mathematical structure
In mathematics, a structure on a set, or more generally a type, consists of additional mathematical objects that in some manner attach to the set, making it easier to visualize or work with, or endowing the collection with meaning or significance....
on
with the mereologicalMereology
In philosophy and mathematical logic, mereology treats parts and the wholes they form...
part-of relation
Relation (mathematics)
In set theory and logic, a relation is a property that assigns truth values to k-tuples of individuals. Typically, the property describes a possible connection between the components of a k-tuple...
.