Determiner: Difference between revisions

Latest revision as of 22:41, 5 February 2024

A determiner is a particle that consumes a verb form and produces a noun form — specifically, a determiner phrase.

For example: sá “some” is a determiner, bıo “…is a cup” is a predicate phrase, and sá bıo is a noun form meaning “some cup(s).”

Determiner particles

Word	Meaning
	X (bound; see below)
sá	some X
tú	every/each single X
tútu	every group of X-es (see below)
túq	all the Xs together
sía	no X
ní	this/that X
hú	endophoric determiner
ké	exophoric determiner
báq	X in general, X-kind
já	λX, see Property
hí	which X?

Semantics

Formally, grammatical determiners tend to correspond to logical quantifiers over a now-bound variable, plus an occurrence of that variable. For example, the sa determiner corresponds to the $\exists$ quantifier. The tagged predicate phrase doubles both as a domain and a name for the variable.

In short, sá bıo does three things:

introduces an existentially bound variable bío to the clause;
specifies that it refers to a cup (or some cups: see plural logic);
acts in its place in the sentence as an instance of this variable.

Heaq jí sá bıo.
${\color {brown}\underbrace {\exists {\textsf {bio}}:} _{1}}\;{\color {chocolate}\underbrace {{\textrm {Cup}}({\textsf {bio}})\mathop {\wedge } } _{2}}\;{\textrm {Heaq}}({\textsf {ji}},{\color {teal}\underbrace {\textsf {bio}} _{3}})$
I'm holding some cup(s).

Every, each, all

tú bıo quantifies over single cups, i.e. each individual cup. This is often what we want to say, despite not being the "purest" form of for-all quantification in plural logic; after all, groups of several cups are also bıo. The expression tútu bıo quantifies over the range of "cups-es": the possible values of bío then include not only individual cups, but also groups of cups.

You can read tútu bıo nä … as: "for all xx, if xx are some cups…"

túq bıo doesn't make a "for-all" statement. Instead it refers to the single entity "all cups (together)".

@@ Line 1: / Line 1: @@
-Grammatically, a '''quantifier''' is a particle that consumes a predicate phrase and produces a noun phrase.
-For example: {{t|sa}} “some” is a quantifier, {{t|bỉo}} “…is a cup” is a predicate phrase, and {{t|sa bỉo}} is a noun phrase meaning “some cup(s)”.
+A '''determiner''' is a particle that consumes a [[verb form]] and produces a [[noun form]] — specifically, a [[determiner phrase]].
-These particles are called “quantifiers” because they semantically corrsepond to a ''logical'' quantifier over a now-bound variable, plus an occurence of that variable. The consumed predicate phrase doubles both as a ''domain'' and a ''name'' for the variable.
+For example: {{t|sá}} “some” is a determiner, {{t|bıo}} “…is a cup” is a predicate phrase, and {{t|sá bıo}} is a noun form meaning “some cup(s).”
-In short, {{t|sa bỉo}} does three things:
+== Determiner particles ==
-# <span style="color:red">introduces</span> an existentially bound variable {{t|bío}} to the clause;
+{| class="wikitable"
-# <span style="color:orange">specifies</span> that it refers to a cup (or some cups: see [[plural logic]]);
+|-
+! Word !! Meaning
+|-
+| {{done|2}} || X (bound; see below)
+|-
+| {{t|sá}} || some X
+|-
+| {{t|tú}} || every/each single X
+|-
+| {{t|tútu}} || every group of X-es (see below)
+|-
+| {{t|túq}} || all the Xs together
+|-
+| {{t|sía}} || no X
+|-
+| {{t|ní}} || this/that X
+|-
+| {{t|hú}} || endophoric determiner
+|-
+| {{t|ké}} || exophoric determiner
+|-
+| {{t|báq}} || X in general, X-[[kind]]
+|-
+| {{t|já}} || λX, see [[Property]]
+|-
+| {{t|hí}} || which X?
+|}
+== Semantics ==
+Formally, grammatical determiners tend to correspond to logical '''quantifiers''' over a now-bound variable, plus an occurrence of that variable. For example, the {{t|sa}} determiner corresponds to the <math>\exists</math> quantifier. The tagged predicate phrase doubles both as a ''domain'' and a ''name'' for the variable.
+In short, {{t|sá bıo}} does three things:
+# <span style="color:brown">introduces</span> an existentially bound variable {{t|bío}} to the clause;
+# <span style="color:chocolate">specifies</span> that it refers to a cup (or some cups: see [[plural logic]]);
 # acts in its place in the sentence as an <span style="color:teal">instance</span> of this variable.
 <blockquote>
-{{t|Hẻaq jí <u>sa bỉo</u>.}}<br>
+{{t|Heaq jí <u>sá bıo</u>.}}<br>
-<math>{\color{red}\exists \textsf{bio}}: {\color{orange}\textrm{Bio}(\textsf{bio}) \,\wedge} \, \textrm{Heaq}(\textsf{ji}, {\color{teal}\textsf{bio}})</math>
+<math>
+   {\color{brown}     \underbrace{\exists \textsf{bio}:}_{1}}
+\; {\color{chocolate} \underbrace{\textrm{Cup}(\textsf{bio}) \mathop\wedge}_{2}}
+\; \textrm{Heaq}(\textsf{ji},
+    {\color{teal}     \underbrace{\textsf{bio}}_{3}}
+   )
+</math><br>
+I'm holding some cup(s).
 </blockquote>
+=== Every, each, all ===
+{{t|tú bıo}} quantifies over single cups, i.e. each individual cup. This is often what we want to say, despite not being the "purest" form of for-all quantification in [[plural logic]]; after all, ''groups'' of several cups are also {{t|bio}}. The expression {{t|tútu bıo}} quantifies over the range of "cups-es": the possible values of {{t|bío}} then include not only individual cups, but also groups of cups.
+You can read {{t|tútu bıo nä …}} as: "for all ''xx'', if ''xx'' are some cups…"
+{{t|túq bıo}} doesn't make a "for-all" statement. Instead it refers to the single entity "all cups (together)".