1.2. Existential claims, prenexes, and variables

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

Example 1.7. 

Something sees me.


There are two plausible Lojban translations of Example 1.7. The simpler one is:

Example 1.8. 

[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 1.1) and the listener must fill in the correct value from context. In other words, Example 1.8 means You-know-what sees me.

However, Example 1.7 is just as likely to assert simply that there is someone who sees me, in which case a correct translation is:

Example 1.9. 

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

Example 1.9 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 1.1 how to represent such restrictions.)

Example 1.9 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 1.10. 

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 1.10 , 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 1.10 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 1.11. 

da zo'u da prami da
There-is-an-X such-that X loves X

Somebody loves himself/herself.


What Example 1.11 claims is fundamentally different from what Example 1.10 claims, because da prami da is not structurally the same as da prami de. However,

Example 1.12. 

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

means exactly the same thing as Example 1.11 ; 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 1.13. 

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 1.1.)

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

Example 1.14. 

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.