Chapter 14: If Wishes Were Horses: The Lojban Connective System
8. Grouping of afterthought connectives
There are several ways in Lojban to render ✥7.5 using afterthought only. The simplest method is to make use of the cmavo “bo” (of selma'o BO). This cmavo has several functions in Lojban, but is always associated with high precedence and short scope. In particular, if “bo” is placed after an ijek, the result is a grammatically distinct kind of ijek which overrides the regular left-grouping rule. Connections marked with “bo” are interpreted before connections not so marked. ✥8.1 is equivalent in meaning to ✥7.8:
✥8.1 mi nelci la djan. .ije mi nelci la martas. .ijabo mi nelci la meris. I like John, and I like Martha or I like Mary.
The English translation feebly indicates with a comma what the Lojban marks far more clearly: the “I like Martha” and “I like Mary” sentences are joined by “.ija” first, before the result is joined to “I like John” by “.ije”.
- Eks can have “bo” attached in exactly the same way, so that ✥8.2 is equivalent in meaning to Example 8.l:
- mi nelci la djan. .e la martas. .abo la meris.
What happens if “bo” is used on both connectives, giving them the same high precedence, as in ✥8.3?
✥8.3 mi nelci la djan. .ebo la martas. .abo la meris.
Does this wind up meaning the same as ✥7.4 and ✥7.6? Not at all. A second rule relating to “bo” is that where several “bo”-marked connectives are used in succession, the normal Lojban left-grouping rule is replaced by a right-grouping rule. As a result, ✥8.3 in fact means the same as Examples 8.1 and 8.2. This rule may be occasionally exploited for special effects, but is tricky to keep straight; in writing intended to be easy to understand, multiple consecutive connectives marked with “bo” should be avoided.
The use of “bo”, therefore, gets tricky in complex connections of more than three sentences. Looking back at the English translations of Examples 7.7 and 7.8, parentheses were used to clarify the grouping. These parentheses have their Lojban equivalents, two sets of them actually. “tu'e” and “tu'u” are used with ijeks, and “ke” and “ke'e” with eks and other connectives to be discussed later. (“ke” and “ke'e” are also used in other roles in the language, but always as grouping markers). Consider the English sentence:
✥8.4 I kiss you and you kiss me, if I love you and you love me.
where the semantics tells us that the instances of “and” are meant to have higher precedence than that of “if”. If we wish to express ✥8.4 in afterthought, we can say:
✥8.5 mi cinba do .ije[bo] do cinba mi .ijanai mi prami do .ijebo do prami mi I kiss you and you kiss me, if I love you and you love me.
marking two of the ijeks with “bo” for high precedence. (The first “bo” is not strictly necessary, because of the left-grouping rule, and is shown here in brackets.)
But it may be clearer to use explicit parenthesis words and say:
✥8.6 tu'e mi cinba do .ije do cinba mi tu'u .ijanai tu'e mi prami do .ije do prami mi [tu'u] ( I kiss you and you kiss me ) if ( I love you and you love me ).
where the “tu'e … tu'u” pairs set off the structure. The cmavo “tu'u” is an elidable terminator, and its second occurrence in ✥8.6 is bracketed, because all terminators may be elided at the end of text.
In addition, parentheses are a general solution: multiple parentheses may be nested inside one another, and additional afterthought material may be added without upsetting the existing structure. Neither of these two advantages apply to “bo” grouping. In general, afterthought constructions trade generality for simplicity.
Because of the left-grouping rule, the first set of “tu'e ... tu'u” parentheses may actually be left off altogether, producing:
✥8.7 mi cinba do .ije do cinba mi .ijanai tu'e mi prami do .ije do prami mi [tu'u] I kiss you and you kiss me if ( I love you and you love me ).
What about parenthesized sumti connection? Consider
✥8.8 I walk to either the market and the house, or the school and the office.
Two pairs of parentheses, analogous to ✥8.6, would seem to be the right approach. However, it is a rule of Lojban grammar that a sumti may not begin with “ke”, so the first set of parentheses must be omitted, producing ✥8.10, which is instead parallel to ✥8.7:
✥8.9 mi dzukla le zarci .e le zdani .a ke le ckule .e le briju [ke'e] I walk-to the market and the house or ( the school and the office ).
If sumti were allowed to begin with “ke”, unavoidable ambiguities would result, so “ke” grouping of sumti is allowed only just after a logical connective. This rule does not apply to “tu'e” grouping of bridi, as ✥8.6 shows.
Now we have enough facilities to handle the problem of ✥7.3: “I am German, rich, and a man — or else none of these.” The following paraphrase has the correct meaning:
✥8.10 [tu'e] mi dotco .ijo mi ricfu [tu'u] .ije tu'e mi dotco .ijo mi nanmu [tu'u] ( I am-German if-and-only-if I am-rich ) and (I am-German if-and-only-if I am-a-man ).
The truth table, when worked out, produces T if and only if all three component sentences are true or all three are false.