|
|
| (8 intermediate revisions by 4 users not shown) |
| Line 1: |
Line 1: |
| A '''determiner''' is a particle that consumes a predicate phrase and produces a noun phrase.
| |
|
| |
|
| For example: {{t|sa}} “some” is a determiner, {{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]]. |
|
| |
|
| Semantically, these particles tend to correspond to logical '''quantifiers''' over a now-bound variable, plus an occurence 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.
| | 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:
| |
| # <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>
| |
| <math>
| |
| {\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}}
| |
| )
| |
| </math><br>
| |
| I'm holding some cup(s).
| |
| </blockquote>
| |
|
| |
|
| == Determiner particles == | | == Determiner particles == |
| Line 27: |
Line 9: |
| ! Word !! Meaning | | ! Word !! Meaning |
| |- | | |- |
| | {{t|sa}} || some X | | | {{done|2}} || X (bound; see below) |
| | |- |
| | | {{t|sá}} || some X |
| | |- |
| | | {{t|tú}} || every/each single X |
| |- | | |- |
| | {{t|tu}} || every X | | | {{t|tútu}} || every group of X-es (see below) |
| |- | | |- |
| | {{t|tushı}} || each X | | | {{t|túq}} || all the Xs together |
| |- | | |- |
| | {{t|tuq}} || all X | | | {{t|sía}} || no X |
| |- | | |- |
| | {{t|sıa}} || no X | | | {{t|ní}} || this/that X |
| |- | | |- |
| | {{t|ke}} || the X | | | {{t|hú}} || endophoric determiner |
| |- | | |- |
| | {{t|hoı}} || the aforementioned X | | | {{t|ké}} || exophoric determiner |
| |- | | |- |
| | {{t|baq}} || X in general, X-[[kind]] | | | {{t|báq}} || X in general, X-[[kind]] |
| |- | | |- |
| | {{t|hı}} || which X? | | | {{t|já}} || λX, see [[Property]] |
| |- | | |- |
| | {{t|ja}} || λX | | | {{t|hí}} || which X? |
| |} | | |} |
|
| |
|
| Additionally, {{tone|2}} can be analyzed as a tonal pseudo-determiner that refers to bound variables, or falls back to "implicitly-bound" {{t|ke X}} if there is no earlier binding.
| | == 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. |
|
| |
|
| === Every, each, all ===
| | In short, {{t|sá bıo}} does three things: |
| {{t|tu bỉo}} quantifies over the range of "cups-es". The possible values of {{t|bío}} include not only individual cups, but also groups of cups. A group of cups is also a {{t|bỉo}}, after all. | | # <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. |
|
| |
|
| This can lead to surprising behavior: see below.
| | <blockquote> |
| | {{t|Heaq jí <u>sá bıo</u>.}}<br> |
| | <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> |
|
| |
|
| {{t|tushı bỉo}} quantifies over "cups-es that are one", i.e. '''each''' individual cup. It's like {{t|tu bỉo ru shỉ}}. | | === 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. |
| {{t|tuq bỉo}} doesn't make a "for-all" statement. Instead it refers to the single entity "all cups (together)".
| |
| | |
| === Inappropriate {{t|tu}} ===
| |
| | |
| You might think that {{t|Nẻo tu bỉo sa tỏqfua}} means "every cup is on ''some'' table", where possibly each cup is on its own table. Certainly, presenting sentences such as <math>\forall b, \exists t: N(b,t)</math> and assigning them this interpretation is popular in discussions of ''singular'' predicate logic.
| |
| | |
| But because the plural-logic {{t|tu bỉo}} ranges over all "cups-es", i.e. all groups of cups, it also includes the referent "{{t|bío}} = ''all'' relevant cups together". Consequently, this sentence ends up saying that all cups are on the ''same'' table, namely whichever {{t|sa tỏqfua}} this maximal {{t|bío}} is on.
| |
|
| |
|
| As a concrete demonstration, if there are three cups B1, B2, B3, then {{t|Nẻo tu bỉo sa tỏqfua}} claims all of the following:
| | You can read {{t|tútu bıo nä …}} as: "for all ''xx'', if ''xx'' are some cups…" |
| * There is some table that B1 is on.
| |
| * There is some table that B2 is on.
| |
| * There is some table that B3 is on.
| |
| * There is some table that [B1 {{t|roı}} B2] are on.
| |
| * There is some table that [B1 {{t|roı}} B3] are on.
| |
| * There is some table that [B2 {{t|roı}} B3] are on.
| |
| * There is some table that [B1 {{t|roı}} B2 {{t|roı}} B3] are on. (So they are all on the same table!)
| |
|
| |
|
| You can explicitly quantify over single cups to get the intended meaning: {{t|Nẻo tushı bỉo sa tỏqfua}}.
| | {{t|túq bıo}} doesn't make a "for-all" statement. Instead it refers to the single entity "all cups (together)". |