Underfilling

To underfill a verb is to provide it with fewer arguments than there are slots in its definition.

Using a transitive verb as though it were intransitive (Huogaı jí da.) or using an intransitive verb as though it were nullary (Loe ꝡo!) are both examples of underfilling.

The common consensus is that this is allowed, but it's not so clear what exactly it means, and how it comes to mean that.

In logic or mathematics, there's no sensible way to "underfill" a relation. "Twelve is divisible by three" makes sense, but "Twelve is divisible" does not. So when we turn "I hear it" into "I hear", what is really going on?

Theories of underfilling

Verb families

One explanation is that, for example, huogaı is actually a "verb family" of three verbs in a trenchcoat:

huogaı₂: ___ hears ___.
huogaı₁: ___ hears.
huogaı₀: Some hearing happens.

Depending on how many arguments we provide, huogaı selects a completely different lexical item.

This is tidy, but it doesn't gives us a predictable rule for what the intransitive version of a transitive verb means. In English, "I know" means "I know it" but "I eat" means "I eat something". Should this distinction be mindlessly carried over into Toaq if we define dua₁ and chuq₁ as above?

Implicit arguments

Another explanation is that when we underfill huogaı, the remaining slots are filled with some implicit argument. But which? All of sá raı, báq raı, ké raı, and a "vague definite reference" / pronoun seem to make sense in different situations.

Disallowing underfilling

An extreme idea is to ban sentences like Huogaı jí, forcing the speaker to say something explicit and specific like Huogaı jí sá or Huogaı jí hóq. This is semantically watertight but annoying.

Other contexts

Determiners

Even saying something like sá chuq invokes our theory of underfilling, as chuq does not have an object. So, does it mean "someone who eats it", or "someone who eats something"? Or does it simply involve the intransitive chuq₁? For words with two slots, this can be solved by using object incorporation.

Subclauses

Underfilling is typically not possible in a subclause:

 *Laheq, ꝡä moı jí, ꝡä jıq jí.
(Attempted:) That I think, entails that I exist.

The verb moı is transitive. Given how self-termination works / because subclauses are "greedy", ꝡä jıq jí ends up being the object of moı, not of laheq. Thus, this sentence actually means "That I think about that I exist, entails (it/something)."

We can use the prefix hạo, which turns verbs intransitive by applying whatever theory of underfilling we subscribe to:

Laheq, ꝡä hạomoı jí, ꝡä jıq jí.
That I think, entails that I exist.

In other (quasi-)logical languages

In Lojban, underfilling is extremely common and undisputably part of the language. A big number of root words ("gismu") contain 4-5 object places, so you almost have to underfill in most cases, unless you don't want your sentences full of zo'e (explicit object place skipper). There are particles (fa fe fi fo fu, all in word class FA) that skip to a specific slot.

fa	fe	fi	fo	fu
1	2	3	4	5

Example: Let's assume there is a predicate klama that has 5 object places and you want to fill the 4th slot with Ѭ. Without the FA class particles you would have to say "klama zo'e zo'e zo'e Ѭ" which is just silly. You can use these particles to say "klama fo Ѭ" instead.

In (New) Ithkuil, there is a case system that functions like object slots. The reference grammar just refers to them as case, even though you can say they are very close to being a weird kind of object slot. Underfilling is also always necessary to even speak the language, due to every verb technically being able to take 68 arguments (cases).