The purpose of this post is to document and summarize a recent change to Toaq’s variable binding syntax. This summary will only cover the new system rather than make a comparison between old and new. The old system is still documented at http://toaq.org/#quantifiers for now.



These are the quantifiers of Toaq:

Toaq Symbol Gloss sa ∃ (existential quantifier) “some”, “there exist”, “there are” tu ∀ (universal quantifier) “any”, “all”, “for all” sıa ¬∃ “no”, “not any” ke ι (iota) “the”, “those …”, “that which …” ja λ lambda quantifier

These quantifiers make up the syntactic class SA (named after the member sa).

Here is a pseudo-grammar of the quantifiers, much simplified and omitting unrelated rules:

argument_phrase <- binding_phrase / bound_phrase binding_phrase <- binding_phrase_1 relative_clause? binding_phrase_1 <- quantifier -tone_phrase bound_phrase <- -tone_phrase

This means that an argument phrase (or noun phrase) is always one of two types:

binding a variable using an already bound variable

Binding a variable is done by using a quantifier before a tone phrase, that is a predicate phrase carrying a falling tone. Such a phrase can optionally be followed by a relative clause, which acts as a restrictor on the domain of the quantifier.

Using an already bound variable is done by using a bare tone phrase.

When binding a variable as described above, the predicate phrase following the quantifier becomes the name of the variable. It can then be re-used within the scope of its quantifier by using the same name with a tone. Relative clauses are not part of the names.

Basic examples

Tỉ sa hảkō da. =

Sa hảkō bı tỉ hákō da.

[∃H : hakō(H)] tı(H).

“There are bears (here/there).”

Ke kủnē bı kảqgāı kúnē sa rảı da.

[ιK : kunē(K)] [∃R : raı(R)] kaqgāı(K,R).

“The dogs, they are seeing something.”

Ke jỉo tïjāo tu tỉeq bı dẻ jío.

[ιJ : jıo(J) ∧ [∀T : tıeq(T)] tıjāo(J,T)] de(J).

“The building that is far away from all roads, it’s beautiful.”

Advanced examples

It is possible to use a tone phrase without the variable having been explicitly bound. In such instances, the variable is treated as having been ke-bound exophorically, i.e., by the current context, the shared knowledge or cultural background of the interlocutors, or similar.

Pronouns are by far the most common example of words that don’t need to be explicitly bound. It is usually clear who the speaker is referring to when saying “I/me” or “you”:

Mảı jí súq.

maı(J, S).

“I love you.”



Both variables (J and S in the logical translation) are bound by the context.

Variables remain bound across sentence boundaries until explicitly re-bound with a new quantifier. This is especially common with ke (“the”), but can also be useful with sa (“some”) and tu (“every”). The following examples demonstrate the resulting logic:

Chỏ jí tu rảı nïe ní kủa da. Jảq dẻ ráı da.

[∀R : raı(R) ∧ nıe(R,N)] cho(J,R). [∀R : raı(R) ∧ nıe(R,N) ∧ cho(J,R)] de(R).

“I like all the things in this room. They are so beautiful.”

“I like all the things in this room. All the things in this room that I like are beautiful.”

Kảqgāı jí sa gủosō da. Nủo gúosō da.

[∃G : guosō(G)] kaqgāı(J,G). [∀R : raı(R) ∧ guosō(R) ∧ kaqgāı(J,R)] nuo(R).

“I see some cows. They (the cows) are asleep.”

“I see some cows. All the cows that I see are asleep.”

Anaphora

Due to the way the binding syntax works, it is very easy to refer back to previously mentioned material. All one has to do is repeat the name of the variable with a tone. However, sometimes the name can be a bit too long, making it impractical to repeat it verbatim. In such cases, using one of the anaphoric predicates is recommended. Here are the most important ones:

Toaq English ho “he/she/they” (3rd person animate) maq “it/they” (3rd person inanimate) hoq “it/that” (3rd person abstract) hoı …

the aforementioned …

Ke sảo ẻlū bı dủa súq chô jí hó.

“As for the big elephant, you know that I like him/her.”

Dẻoq sa gẻo dỉuchē déo da. Pảı hóı kỏaq jí da.

“An old scientist is talking to the children. The aforementioned adult is a friend of mine.”

fin