Proposal: Generalized terbri Notation

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This is a nitpicky proposal concerning a general notational convention for labelling 'generalized terbri' in Lojban definition presentations.

Background/Current State

The definitions of gismu and zi'evla are typically presented as something similar to "x1 is/does [core idea of word] to x2 with x3". The number of 'xi's varies and the exact wording in English/relation between them may vary too. Each of these variables are really representative of terbri (although there is a large problem with conflation of terbri with sumti in discussions of such definitions) in the brivla. There are usually less than five terbri in gismu ("jutsi" is an example of a gismu with arbitrarily many terbri, though).

lujvo are presented in quite a similar fashion. However, sometimes, the symbols which label the terbri are presented as "ya = zb", where 'a' and 'b' are positive integers, "y" stands in for a brief string of letters which represents one veljvo (and may or may not be exactly "x") and "z" does likewise for another word; "ya" refers to the ath terbri of the veljvo represented by "y" and likewise for "zb" by exchange; the equality means that the sumti supplied to this terbri of the lujvo is also supplied to the indicated terbri of the indicated veljvo and, in fact, the latter terbri (plural) are always mutually aligned in referent. There may or may not be any mention of "x1" vel sim.

Connectives have no standard symbolic representation except possibly for a single character, such as "&" for possibly "joi" or "je". Members of selma'o BIhI might be particularly onerous to express in a standard/typical/convention manner - especially with a single symbol if that is desired. In any case, there is no currently employed notation in Lojban definitions/descriptions which specifies analogs of terbri in the context of connectives.

Operators in mekso (officially, constituting and being constituted by exactly selma'o VUhU, but other selma'o of mekso operators may be and have been experimentally proposed) denote the operator by culturally common notation (such as "+" for "su'i") with each operand (technically: 'operand conceptual-slot') being denoted by a lowercase letter in the Latin alphabet in standard alphabetic order starting with "a".

For the sake of this article, all of these 'parameter conceptual-slots' will be called "(generalized) terbri". They will be made more specific by context if necessary.

Let the number of generalized terbri that a word has be called its "arity".


Lack of a Unified Approach

Each gismu and zi'evla, lujvo, and mekso operators have their own conventions for presentation and none match the others. Moreover, connectives do no seem to have any standard convention for this purpose whereas some of the other types of words have multiple conventions.

Cannot Discern terbri Order

This occurs in lujvo but also in mekso operators (see the subsection on cultural reliance for order). As we know, wording can change and this is particularly likely in Lojban, wherein some definitions may be awkward in some natural languages and wherein conversion (permutation of terbri) is extremely common, and even encouraged. If a definition is presented as "p1 = d2 does [action] to p2 = d1", how is one to know which terbri is actually the first, thinking as a Lojban speaker? Are we to rely on presentation order of terbri? What happens if terbri are reused? Or maybe the indices or letters hint at the order... But equality should be reflexive, meaning that the presentation order of variables for a given terbri should be free (so "p1 = d2" is logically/semantically equivalent to "d2 = p1"). And, apart from the issue of cultural reliance, how are we to determine the heirarchical precedence of indices versus symbols when they come into conflict? Would "k2" come before or after "m1", even assuming the standard order of the Latin alphabet? What happens if the variable symbol is actually a string (for example "kla3" has the variable symbol "kla" and the index "3")?

Difficulty in Mentioning the Same terbri Multiple Times

When referencing the same terbri within a given definition - or perhaps even sentence - how does one name it? Can one pull any given variable from the equality list? Or should the whole equality statement be repeated each time? Either option is not particularly pleasing. The first hints at preference or may even break the equality, possibly implying that there is a new terbri in the process. The second option is clunky and leaves no easy way to reference the terbri except by taking the whole word being defined as the terbri name (properly indexed).

Notice that this all leaves room for confusion about which terbri exist and what their ordering is.

No More than Finitely Many Options Exist

For mekso operators, there are only finitely many variables available, even if we allow for varied casing and scripts. Not only is extension/omission difficult (see the relevant subsection), but labelling too many terbri causes the set of available (unassigned) symbols to become depleted.

Difficulty in Extension and Omission

For mekso operators, using lowercase letters of the Latin alphabet in order results in the inability to easily extend the notation to an nth term for a specific natural n, for an arbitrary natural n, or for n being infinity - especially if ellision is occuring. Does one say "a, b, c, ..., z" in order to mean any of these? If so, which option? Does 'z' represent the last term (if so, what does "last" mean?) or the twenty-sixth term specifically, or what?

Cultural Reliance on Order

While the Lojban language strives for cultural neutrality, these conventions betray this goal. Sure, the goal is about the language itself and not how its definitions are presented, but it still seems out of place to present mekso definitions using the Latin alphabet with the assumption that the reader knows the standard order thereof. Furthermore, there is nothing special about this order, which makes it morally problematic for alien learners.

Conflict with Cultural Expectations Concerning Meaning

Symbols may conflict with standard cultural conventions for what they mean or how their referrents are denoted, particularly in mekso definitions. Consider a definition which extends to so far as to include a generalized terbri denoted by "f". Normally, in Western mathematics culture, the symbol "f" is almost universally and exclusively reserved for a function. But if the definition is not exceptionally lucky, this terbri very well could be a number (a non-function), in which case the meaning will be confusing and unnatural to such audiences. This problem does not just arise with "f": many Latin and Greek letters have common meanings in mathematics and, especially, physics (wherein they extremely rarely are explicitly defined).

Free Variables Cannot Exist

If I want to make a comment about a definition indicating, for example, that only n of the tebri need to be filled, I will not be able to do so because the symbol "n" will be implicitly reserved for the fourteenth terbri of the word - even if it is currently not defined, its use may lead to confusion (especially if "m" is used), hint at the existence of other terbri, and precludes future extensions of the definition.

Main Proposal

The goal is to create a unified, universal, robust, culturally neutral, very transparent system for notation. There are at least three options.

  1. Little-"x" notation: Pick a single lowercase letter and use it as a marker for all terbri, for example "x". Its index determines which terbri it is; the index is a natural number (an integer strictly greater than 0) and they count by ones without skipping. Any repeat mention of the variable (in which case its index is the same with respect to occurences) indicates not a new terbri but simply that the terbri has the indicated relationship. All new terbri are introduced and named solely by this symbol and the relevant index; equivalent veljvo tebri may be assigned via "=", but they only need be mentioned once. This option is easily back-compatible for gismu and many zi'evla definitions; mekso, lujvo, and connectives would need editing.
  2. Big-"X" notation: Do the same thing but with a capital letter, for example "X". This has the advantage of not singling out a single lowercase letter (which means that it may be used in order to reference veljvo terbri and alphabetic symmetry is maintained). The disadvantage is that this convention has very rarely been used, meaning that most definitions (for all classes of words) currently do not comply with it and will need to be edited.
  3. Wordname notation: Use the word in the name of the terbri. For example, "klama" would be defined thusly: "klama1 is a goer/goes to destination location klama2 [...]". This has the advantage of being clear and independent of context (when referring to the terbri elsewhere, this covention could and is already used); it works perfectly fine with lujvo definitions. The disadvantage is that it is not exactly uniform in appearance (just format) across words, it may not be discernible at a glance, it may cause some confusion for newcomers, it results in a word appearing in its own definition (albeit as a placeholder), and the word can be quite long (making this convention rather inconvenient). Shortening couldnl happen, but unless safeguards are put into place, all of the aforementioned present problems emerge again, but worse.

It is possible that each situation actually has its own solution. This mitigates the achievement of the uniformity goal somewhat, but there would at least be uniformity within classes. For example, all brivla could adopt the little-"x" notation whereas all connectives and mekso operators could use big-"X" notation. This is lai .krtisfranks.'s personal preference.

Caveat: This proposal is primarily designed for English, Spanish, or French in standard Latin transcription. Other languages and other writing systems, of course, may support it.

Issues with the Proposal


Generalizations/Going Further



The following people contributed to this article. All ideas and opinions are theirs. All first-person personal pronouns refer to them.

  • lai .krtisfranks.