Determiner

A determiner is a particle that consumes a predicate phrase and produces a noun phrase.

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

Semantically, these particles tend to correspond to logical quantifiers over a now-bound variable, plus an occurence 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, sa bỉo does three things:

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

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

Determiner particles

Word	Meaning
sa	some X
tu	every X
tushı	each X
tuq	all X
sıa	no X
ke	the X
hoı	the aforementioned X
baq	X in general, X-kind
hı	which X?
ja	λX

Additionally, can be analyzed as a tonal pseudo-determiner that refers to bound variables, or falls back to "implicitly-bound" ke X if there is no earlier binding.

Every, each, all

tu bỉo quantifies over the range of "cups-es". The possible values of bío include not only individual cups, but also groups of cups. A group of cups is also a bỉo, after all.

This can lead to surprising behavior (TODO example), and you want to say tushı instead.

tushı bỉo quantifies over "cups-es that are one", i.e. each individual cup. It's like tu bỉo ru shỉ.

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