Chapter 19: Putting It All Together: Notes on the Structure of Lojban Texts
6. Subscripts: XI
The following cmavo is discussed in this section:
xi XI subscript
The cmavo “xi” (of selma'o XI) indicates that a subscript (a number, a lerfu string, or a parenthesized mekso) follows. Subscripts can be attached to almost any construction and are placed following the construction (or its terminator word, which is generally required). They are useful either to extend the finite cmavo list to infinite length, or to make more refined distinctions than the standard cmavo list permits. The remainder of this section mentions some places where subscripts might naturally be used.
Lojban gismu have at most five places:
✥6.1 mi cu klama le zarci le zdani le dargu le karce I go to-the market from-the house via-the road using-the car.
Consequently, selma'o SE (which operates on a selbri to change the order of its places) and selma'o FA (which provides place number tags for individual sumti) have only enough members to handle up to five places. Conversion of ✥6.1, using “xe” to swap the x1 and x5 places, would produce:
✥6.2 le karce cu xe klama le zarci le zdani le dargu mi The car is-a-transportation-means to-the market from-the house via-the road for-me.
And reordering of the place structures might produce:
✥6.3 fo le dargu fi le zdani fa mi fe le zarci fu le karce cu klama Via the road, from the house, I, to the market, using-the car, go.
Examples 6.1 to 6.3 all mean the same thing. But consider the lujvo “nunkla”, formed by applying the abstraction operator “nu” to “klama”:
✥6.4 la'edi'u cu nunkla mi le zarci le zdani le dargu le karce The-referent-of-the-previous-sentence is-an-event-of-going by-me to-the market from-the house via-the road using-the car.
✥6.4 shows that “nunkla” has six places: the five places of “klama” plus a new one (placed first) for the event itself. Performing transformations similar to that of ✥6.2 requires an additional conversion cmavo that exchanges the x1 and x6 places. The solution is to use any cmavo of SE with a subscript:
✥6.5 le karce cu sexixa nunkla mi le zarci le zdani le dargu la'edi'u The car is-a-transportation-means-in-the-event-of-going by-me to-the market via-the road which-is-referred-to-by-the-last-sentence.
Likewise, a sixth place tag can be created by using any cmavo of FA with a subscript:
✥6.6 fu le dargu fo le zdani fe mi fa la'edi'u fi le zarci faxixa le karce cu klama Via the road, from the house, by me, the-referent-of-the-last-sentence, to the market, using the car, is-an-event-of-going.
Examples 6.4 to 6.6 also all mean the same thing, and each is derived straightforwardly from any of the others, despite the tortured nature of the English glosses. In addition, any other member of SE or FA could be substituted into “sexixa” and “faxixa” without change of meaning: “vexixa” means the same thing as “sexixa”.
Lojban provides two groups of pro-sumti, both belonging to selma'o KOhA. The ko'a-series cmavo are used to refer to explicitly specified sumti to which they have been bound using “goi”. The da-series, on the other hand, are existentially or universally quantified variables. (These concepts are explained more fully in Chapter 16.) There are ten ko'a-series cmavo and 3 da-series cmavo available.
If more are required, any cmavo of the ko'a-series or the da-series can be subscripted:
✥6.7 daxivo X sub 4
is the 4th bound variable of the 1st sequence of the da-series, and
✥6.8 ko'ixipaso something-3 sub 18
is the 18th free variable of the 3rd sequence of the ko'a-series. This convention allows 10 sequences of ko'a-type pro-sumti and 3 sequences of da-type pro-sumti, each with arbitrarily many members. Note that “daxivo” and “dexivo” are considered to be distinct pro-sumti, unlike the situation with “sexixa” and “vexixa” above. Exactly similar treatment can be given to the bu'a-series of selma'o GOhA and to the gismu pro-bridi “broda”, “brode”, “brodi”, “brodo”, and “brodu”.
Subscripts on lerfu words are used in the standard mathematical way to extend the number of variables:
✥6.9 li xy.boixipa du li xy.boixire su'i xy.boixici The-number x-sub-1 equals the-number x-sub-2 plus x-sub-3 $x1 ⇔ x2 + x3$
and can be used to extend the number of pro-sumti as well, since lerfu strings outside mathematical contexts are grammatically and semantically equivalent to pro-sumti of the ko'a-series. (In ✥6.9, note the required terminator “boi” after each “xy.” cmavo; this terminator allows the subscript to be attached without ambiguity.)
Names, which are similar to pro-sumti, can also be subscripted to distinguish two individuals with the same name:
✥6.10 la djan. xipa cusku lu mi'enai do li'u la djan. xire John1 expresses “I-am-not you” to John2.
Subscripts on tenses allow talking about more than one time or place that is described by the same general cmavo. For example, “puxipa” could refer to one point in the past, and “puxire” a second point (earlier or later).
You can place a subscript on the word “ja'a”, the bridi affirmative of selma'o NA, to express so-called fuzzy truths. The usual machinery for fuzzy logic (statements whose truth value is not merely “true” or “false”, but is expressed by a number in the range 0 to 1) in Lojban is the abstractor “jei”:
✥6.11 li pimu jei mi ganra The-number .5 is-the-truth-value-of my being-broad
However, by convention we can attach a subscript to “ja'a” to indicate fuzzy truth (or to “na” if we change the amount):
✥6.12 mi ja'a xipimu ganra I truly-sub-.5 am-broad
Finally, as mentioned in c19-§2, “ni'o” and “no'i” cmavo with matching subscripts mark the start and the continuation of a given topic respectively. Different topics can be assigned to different subscripts.
Other uses of subscripts will doubtless be devised in future.