## 16.2. Existential claims, prenexes, and variables

Let us consider, to begin with, a sentence that is not in the dialogue:

Example 16.7.

Something sees me.

There are two plausible Lojban translations of Example 16.7. The simpler one is:

Example 16.8.

 [zo'e] viska mi Something-unspecified sees me.

The cmavo zo'e indicates that a sumti has been omitted (indeed, even zo'e itself can be omitted in this case, as explained in Section 7.7) and the listener must fill in the correct value from context. In other words, Example 16.8 means You-know-what sees me.

However, Example 16.7 is just as likely to assert simply that there is someone who sees me, in which case a correct translation is:

Example 16.9.

 da zo'u da viska mi There-is-an-X such-that X sees me.

Example 16.9 does not presuppose that the listener knows who sees the speaker, but simply tells the listener that there is someone who sees the speaker. Statements of this kind are called existential claims. (Formally, the one doing the seeing is not restricted to being a person; it could be an animal or – in principle – an inanimate object. We will see in Section 16.4 how to represent such restrictions.)

Example 16.9 has a two-part structure: there is the part da zo'u, called the prenex, and the part da viska mi, the main bridi. Almost any Lojban bridi can be preceded by a prenex, which syntactically is any number of sumti followed by the cmavo zo'u (of selma'o ZOhU). For the moment, the sumti will consist of one or more of the cmavo da, de, and di (of selma'o KOhA), glossed in the literal translations as X, Y, and Z respectively. By analogy to the terminology of symbolic logic, these cmavo are called variables.

Here is an example of a prenex with two variables:

Example 16.10.

 da de zo'u da prami de There-is-an-X there-is-a-Y such that X loves Y.
 Somebody loves somebody.

In Example 16.10, the literal interpretation of the two variables da and de as there-is-an-X and there-is-a-Y tells us that there are two things which stand in the relationship that one loves the other. It might be the case that the supposed two things are really just a single thing that loves itself; nothing in the Lojban version of Example 16.10 rules out that interpretation, which is why the colloquial translation does not say Somebody loves somebody else. The things referred to by different variables may be different or the same. (We use somebody here rather than something for naturalness; lovers and beloveds are usually persons, though the Lojban does not say so.)

It is perfectly all right for the variables to appear more than once in the main bridi:

Example 16.11.

 da zo'u da prami da There-is-an-X such-that X loves X
 Somebody loves himself/herself.

What Example 16.11 claims is fundamentally different from what Example 16.10 claims, because da prami da is not structurally the same as da prami de. However,

Example 16.12.

 de zo'u de prami de There-is-a-Y such-that Y loves Y

means exactly the same thing as Example 16.11; it does not matter which variable is used as long as they are used consistently.

It is not necessary for a variable to be a sumti of the main bridi directly:

Example 16.13.

 da zo'u le da gerku cu viska mi There-is-an-X such-that the of-X dog sees me
 Somebody's dog sees me

is perfectly correct even though the da is used only in a possessive construction. (Possessives are explained in Section 8.7.)

It is very peculiar, however, even if technically grammatical, for the variable not to appear in the main bridi at all:

Example 16.14.

 da zo'u la ralf. gerku There-is-an-X such-that that-named Ralph is-a-dog
 There is something such that Ralph is a dog.

has a variable bound in a prenex whose relevance to the claim of the following bridi is completely unspecified.