16.14. A few notes on variables

A variable may have a quantifier placed in front of it even though it has already been quantified explicitly or implicitly by a previous appearance, as in:

Example 16.108.

ci	da	poi	mlatu	cu	blabi	.ije	re	da	cu	barda
Three	Xs	which-are	cats		are-white,	and	two	Xs		are-big.

What does Example 16.108 mean? The appearance of ci da quantifies da as referring to three things, which are restricted by the relative clause to be cats. When re da appears later, it refers to two of those three things – there is no saying which ones. Further uses of da alone, if there were any, would refer once more to the three cats, so the requantification of da is purely local.

In general, the scope of a prenex that precedes a sentence extends to following sentences that are joined by ijeks (explained in Section 14.4) such as the .ije in Example 16.108. Theoretically, a bare i terminates the scope of the prenex. Informally, however, variables may persist for a while even after an i, as if it were an .ije. Prenexes that precede embedded bridi such as relative clauses and abstractions extend only to the end of the clause, as explained in Section 16.8. A prenex preceding tu'e…tu'u long-scope brackets persists until the tu'u, which may be many sentences or even paragraphs later.

If the variables da, de, and di (or the selbri variables bu'a, bu'e, and bu'i) are insufficient in number for handling a particular problem, the Lojban approach is to add a subscript to any of them. Each possible different combination of a subscript and a variable cmavo counts as a distinct variable in Lojban. Subscripts are explained in full in Section 19.6, but in general consist of the cmavo xi (of selma'o XI) followed by a number, one or more lerfu words forming a single string, or a general mathematical expression enclosed in parentheses.

A quantifier can be prefixed to a variable that has already been bound either in a prenex or earlier in the bridi, thus:

Example 16.109.

ci	da	poi	prenu	cu	se ralju	pa	da
Three	Xs	which	are-persons		are-led-by	one-of	X

Three people are led by one of them.

The pa da in Example 16.109 does not specify the number of things to which da refers, as the preceding ci da does. Instead, it selects one of them for use in this sumti only. The number of referents of da remains three, but a single one (there is no way of knowing which one) is selected to be the leader.