14. A few notes on variables

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

What does Example 14.1 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 the 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 Chapter 14) such as the ``.ije'' in Example 14.1. 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 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 Chapter 19, 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:

14.2)    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 14.2 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.