Chapter 5: “Pretty Little Girls' School”: The Structure Of Lojban selbri
6. Logical connection within tanru
The following cmavo are discussed in this section:
je JA tanru logical “and” ja JA tanru logical “or” joi JOI mixed mass “and” gu'e GUhA tanru forethought logical “and” gi GI forethought connection separator
Consider the English phrase “big red dog”. How shall this be rendered as a Lojban tanru? The naive attempt:
✥6.1 barda xunre gerku (big type-of red) type-of dog
will not do, as it means a dog whose redness is big, in whatever way redness might be described as “big”. Nor is
✥6.2 barda xunre bo gerku big type-of (red type-of dog)
much better. After all, the straightforward understanding of the English phrase is that the dog is big as compared with other dogs, not merely as compared with other red dogs. In fact, the bigness and redness are independent properties of the dog, and only obscure rules of English adjective ordering prevent us from saying “red big dog”.
The Lojban approach to this problem is to introduce the cmavo “je”, which is one of the many equivalents of English “and”. A big red dog is one that is both big and red, and we can say:
✥6.3 barda je xunre gerku (big and red) type-of dog
✥6.4 xunre je barda gerku (red and big) type-of dog
is equally satisfactory and means the same thing. As these examples indicate, joining two brivla with “je” makes them a unit for tanru purposes. However, explicit grouping with “bo” or “ke … ke'e” associates brivla more closely than “je” does:
✥6.5 barda je pelxu bo xunre gerku barda je ke pelxu xunre ke'e gerku (big and (yellow type-of red)) dog big yellowish-red dog
With no grouping indicators, we get:
✥6.6 barda je pelxu xunre gerku ((big and yellow) type-of red) type-of dog biggish- and yellowish-red dog
which again raises the question of ✥6.1: what is does “biggish-red” mean?
Unlike “bo” and “ke … ke'e”, “je” is useful as well as merely legal within simple tanru. It may be used to partly resolve the ambiguity of simple tanru:
✥6.7 ta blanu je zdani that is-blue and is-a-house
definitely refers to something which is both blue and is a house, and not to any of the other possible interpretations of simple “blanu zdani”. Furthermore, “blanu zdani” refers to something which is blue in the way that houses are blue; “blanu je zdani” has no such implication — the blueness of a “blanu je zdani” is independent of its houseness.
With the addition of “je”, many more versions of “pretty little girls' school” are made possible: see c5-§16 for a complete list.
A subtle point in the semantics of tanru like ✥6.3 needs special elucidation. There are at least two possible interpretations of:
✥6.8 ta melbi je nixli ckule That is-a-(beautiful and girl) type-of school.
It can be understood as:
✥6.9 That is a girls' school and a beautiful school.
✥6.10 That is a school for things which are both girls and beautiful.
The interpretation specified by ✥6.9 treats the tanru as a sort of abbreviation for:
✥6.11 ta ke melbi ckule ke'e je ke nixli ckule [ke'e] That is-a-( beautiful type-of school ) and ( girl type-of school )
whereas the interpretation specified by ✥6.10 does not. This is a kind of semantic ambiguity for which Lojban does not compel a firm resolution. The way in which the school is said to be of type “beautiful and girl” may entail that it is separately a beautiful school and a girls' school; but the alternative interpretation, that the members of the school are beautiful and girls, is also possible. Still another interpretation is:
✥6.12 That is a school for beautiful things and also for girls.
so while the logical connectives help to resolve the meaning of tanru, they by no means compel a single meaning in and of themselves.
In general, logical connectives within tanru cannot undergo the formal manipulations that are possible with the related logical connectives that exist outside tanru; see Chapter 14 for further details.
The logical connective “je” is only one of the fourteen logical connectives that Lojban provides. Here are a few examples of some of the others:
✥6.13 le bajra cu jinga ja te jinga the runner(s) is/are winner(s) or loser(s). ✥6.14 blanu naja lenku skapi (blue only-if cold) skin skin which is blue only if it is cold ✥6.15 xamgu jo cortu nuntavla (good if-and-only-if short) speech speech which is good if (and only if) it is short ✥6.16 vajni ju pluka nuntavla (important whether-or-not pleasing) event-of-talking speech which is important, whether or not it is pleasing
In ✥6.13, “ja” is grammatically equivalent to “je” but means “or” (more precisely, “and/or”). Likewise, “naja” means “only if” in ✥6.14, “jo” means “if and only if” in ✥6.15, and “ju” means “whether or not” in ✥6.16.
Now consider the following example:
✥6.17 ricfu je blanu jabo crino rich and (blue or green)
which illustrates a new grammatical feature: the use of both “ja” and “bo” between tanru components. The two cmavo combine to form a compound whose meaning is that of “ja” but which groups more closely; “jabo” is to “ja” as plain “bo” is to no cmavo at all. However, both “ja” and “jabo” group less closely than “bo” does:
✥6.18 ricfu je blanu jabo crino bo blanu rich and (blue or green -- blue) rich and (blue or greenish-blue)
An alternative form of ✥6.17 is:
✥6.19 ricfu je ke blanu ja crino [ke'e] rich and ( blue or green )
In addition to the logical connectives, there are also a variety of non-logical connectives, grammatically equivalent to the logical ones. The only one with a well-understood meaning in tanru contexts is “joi”, which is the kind of “and” that denotes a mixture:
✥6.20 ti blanu joi xunre bolci This is-a-(blue and red) ball.
The ball described is neither solely red nor solely blue, but probably striped or in some other way exhibiting a combination of the two colors. ✥6.20 is distinct from:
✥6.21 ti blanu xunre bolci This is a bluish-red ball
which would be a ball whose color is some sort of purple tending toward red, since “xunre” is the more important of the two components. On the other hand,
✥6.22 ti blanu je xunre bolci This is a (blue and red) ball
is probably self-contradictory, seeming to claim that the ball is independently both blu and red at the same time, although some sensible interpretation may exist.
Finally, just as English “and” has the variant form “both ... and”, so “je” between tanru components has the variant form “gu'e … gi”, where “gu'e” is placed before the components and “gi” between them:
✥6.23 gu'e barda gi xunre gerku (both big and red) type-of dog
is equivalent in meaning to ✥6.3. For each logical connective related to “je”, there is a corresponding connective related to “gu'e … gi” in a systematic way.
The portion of a “gu'e … gi” construction before the “gi” is a full selbri, and may use any of the selbri resources including “je” logical connections. After the “gi”, logical connections are taken to be wider in scope than the “gu'e … gi”, which has in effect the same scope as “bo”:
(6.23) gu'e barda je xunre gi gerku ja mlatu (both (big and red) and dog) or cat something which is either big, red, and a dog, or else a cat
leaves “mlatu” outside the “gu'e--gi” construction. The scope of the “gi” arm extends only to a single brivla or to two or more brivla connected with “bo” or “ke--ke'e”.