Chapter 16: “Who Did You Pass On The Road? Nobody”: Lojban And Logic
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:
✥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 ✥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 ✥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 c16-§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 ✥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.