## Chapter 16: “Who Did You Pass On The Road? Nobody”: Lojban And Logic

### 13. selbri variables

In addition to the variables “da”, “de”, and “di” that we have seen so far, which function as sumti and belong to selma'o KOhA, there are three corresponding variables “bu'a”, “bu'e”, and “bu'i” which function as selbri and belong to selma'o GOhA. These new variables allow existential or universal claims which are about the relationships between objects rather than the objects themselves. We will start with the usual silly examples; the literal translation will represent “bu'a”, “bu'e” and “bu'i” with F, G, and H respectively.

```✥13.1    su'o bu'a zo'u
la djim. bu'a la djan.
For-at-least-one relationship-F :
Jim stands-in-relationship-F to-John.
There's some relationship between Jim and John.```

The translations of ✥13.1 show how unidiomatic selbri variables are in English; Lojban sentences like ✥13.1 need to be totally reworded in English. Furthermore, when a selbri variable appears in the prenex, it is necessary to precede it with a quantifier such as “su'o”; it is ungrammatical to just say “bu'a zo'u”. This rule is necessary because only sumti can appear in the prenex, and “su'o bu'a” is technically a sumti — in fact, an indefinite description like “re nanmu”, since “bu'a” is grammatically equivalent to a brivla like “nanmu”. However, indefinite descriptions involving the bu'a-series cannot be imported from the prenex.

When the prenex is omitted, the preceding number has to be omitted too:

```✥13.2    la djim. bu'a la djan.
Jim stands-in-at-least-one-relationship to-John.```

As a result, if the number before the variable is anything but “su'o”, the prenex is required:

```✥13.3    ro bu'a zo'u
la djim. bu'a la djan.
For-every relationship-F :
Jim stands-in-relationship-F to-John.
Every relationship exists between Jim and John.```

✥13.1 and ✥13.2 are almost certainly true: Jim and John might be brothers, or might live in the same city, or at least have the property of being jointly human. ✥13.3 is palpably false, however; if Jim and John were related by every possible relationship, then they would have to be both brothers and father-and-son, which is impossible.