## Chapter 14: If Wishes Were Horses: The Lojban Connective System

### 17. Logical and non-logical connectives within mekso

Lojban has a separate grammar embedded within the main grammar for representing mathematical expressions (or mekso in Lojban) such as “2 + 2”. Mathematical expressions are explained fully in Chapter 18. The basic components of mekso are operands, like “2”, and operators, like “+”. Both of these may be either logically or non-logically connected.

Operands are connected in afterthought with eks and in forethought with geks, just like sumti. Operators, on the other hand, are connected in afterthought with jeks and in forethought with guheks, just like tanru components. (However, jeks and joiks with “bo” are not allowed for operators.) This parallelism is no accident.

In addition, eks with “bo” and with “ke … ke'e” are allowed for grouping logically connected operands, and “ke ... ke'e” is allowed for grouping logically connected operators, although there is no analogue of tanru among the operators.

Only a few examples of each kind of mekso connection will be given. Despite the large number of rules required to support this feature, it is of relatively minor importance in either the mekso or the logical-connective scheme of things. These examples are drawn from Chapter 18, and contain many mekso features not explained in this chapter.

✥17.1 exhibits afterthought logical connection between operands:

✥17.1 vei ci .a vo [ve'o] prenu cu klama le zarci ( three or four ) people go-to the market.

✥17.2 is equivalent in meaning, but uses forethought connection:

✥17.2 vei ga ci gi vo [ve'o] prenu cu klama le zarci ( either 3 or 4 ) people go-to the market.

Note that the mekso in ✥17.1 and ✥17.2 are being used as quantifiers. Lojban requires that any mekso other than a simple number be enclosed in “vei” and “ve'o” parentheses when used as a quantifier. The right parenthesis mark, “ve'o”, is an elidable terminator.

Simple examples of logical connection between operators are hard to come by. A contrived example is:

✥17.3 li re su'i je pi'i re du li vo the-number 2 plus and times 2 equals the-number 4. 2 + 2 ⇔ 4 and 2 x 2 ⇔ 4.

The forethought form of ✥17.3 is:

✥17.4 li re ge su'i gi pi'i re du li vo the-number two both plus and times two equals the-number four. Both 2 + 2 ⇔ 4 and 2 x 2 ⇔ 4.

Non-logical connection with joiks or joigiks is also permitted between operands and between operators. One use for this construct is to connect operands with “bi'i” to create mathematical intervals:

✥17.5 li no ga'o bi'i ke'i pa the-number zero (inclusive) from-to (exclusive) one [0,1) the numbers from zero to one, including zero but not including one

You can also combine two operands with “ce'o”, the sequence connective of selma'o JOI, to make a compound subscript:

✥17.6 xy. boi xi vei by. ce'o dy. [ve'o] “x” sub ( “b” sequence “d” ) $x_{b,d}$

Note that the “boi” in ✥17.5 is not elidable, because the “xi” subscript needs something to attach to.