A Simpler Connective System

This article is part of the Simpler series on simplifying certain aspects of Lojban.
See also: A Simpler Quantifier Logic and A Simpler Morphology [coming soon].

“How does one say “and” in Lojban?”
“Well… it depends, you know.  For sumti, it’s .e.  For tanru and sentences, it’s je. For bridi tails it’s gi’e. And those were just the afterthought connectives. Forethought “and” is ge for everything but tanru, which use gu’e instead. Relative clauses are connected with zi’e.”
“… oh.”

With no less than six ways to say “and” as well as roughly the same number for each of the other logical functions (OR, IFF, WHETHER-OR-NOT) totalling 26, the Lojban connective system can be quite daunting. But despair not, for there is a light at the end of the tunnel.

This post is a reworked version of an article I posted over on Weebly in 2014, called How to substantially simplify the Lojban connective system.

The proposal has received very positive reactions and since the Weebly post wasn’t quite in depth enough and because a simplification of the connective system is one of The Big Things That Will Save Lojban, I decided to write an improved version for the Simpler series.

So, each of the four functions (AND, OR, IFF, WHETHER-OR-NOT) has six connectives that go along with it that are used depending on the things being connected. Except that the relative clause connective zi’e (meaning “and”) has no parallel form for any of the other functions (those forms are simply missing from the language) and there is also no question connective for relative clauses. This means we get 4 * 6 – 3 + 5 = 26 connectives, rather than, say, 5 * 6 = 30, which would have at least been consistent.

These are the logical connectives of Lojban:

.a .e ji .o .u
ga ge ge’i go gu

gi’a gi’e gi’i gi’o gi’u
gu’a gu’e gu’i gu’o gu’u
ja je je’i jo ju
zi’e

But that’s not all. If we look at non-logical connectives as well (things like jo’u and joi), then we’ll find that we can neither make bridi-tail connections nor tanru forethought connections with them. Also, while we do have the option of using them in forethought like ge, we do that by saying JOI gi. Yet another new rule compared to the logical connectives…

We can summarize the situation by saying that the connective system has two major shortcomings:

  1. There are too many connectives.
  2. The paradigm has actual holes. For example, we can’t make non-logical bridi-tail connections, and we can’t make non-logical tanru forethoughts.

Regarding the second point, take a look at this table taken out of The Complete Lojban Language (the official grammar book):

1459456565725

Whoops, wrong image. I actually meant to paste this table. Honest mistake.

construct afterthought
logical
forethought
logical
afterthought
non-logical
forethought
non-logical
bridi ijek* gek ijoik* joigik
sumti ek* gek joik* joigik
bridi-tails gihek* gek joigik
termsets ek* gek joik* joigik
tanru parts jek guhek joik*
operands ek* gek joik* joigik
operators jek guhek joik
tenses/modals jek joik
abstractors jek joik
“An asterisk (*) indicates that tensed connection is permitted. A dash indicates that connection of the specified type is not possible.”

Now that the problems have been clearly identified, let us look at a possible solution.

I will present below a way to reduce the number of afterthought connectives down to a single set of 4 basic ones + 1 question word, by first removing both selma’o A and selma’o GIhA and then letting selma’o JA do all the work, followed by bringing equality to logical and non-logical connectives by removing selma’o GA and selma’o GUhA and replacing them with a universal mechanism.

I will work under the assumption that kujoi is a thing of the past and that lo broda joi lo brode is perfectly correct, so I am not going to address this as part of my discussion of simplifying the connective system.

Eliminating selma’o A

The selma’o of A is the selma’o of sumti connectives (see CLL Chapter 14 Section 6). It is made up of the following cmavo:

.a .e ji .o .u

This selma’o exists because of an old parser restriction of the YACC grammar that requires that everything be parsable with one token of lookahead. However, the now de-facto standard parser camxes uses a PEG, where lookahead is infinite, and where kujoi is no longer a thing. This fact alone undermines selma’o A’s raison d’être.

We can safely leave it behind and replace it with selma’o JA. Then the pattern is simply:

<sumti> JA <sumti>

mi je lo xanri pendo be mi
me and my imaginary friend

ra pu cusku «lu mi na temyzi’e li’u» ja su’o simsa
“They said “I have no time” or something like that.”

That’s about all there is to say about this. Wherever you would have used a member of selma’o A before, use the corresponding member of selma’o JA instead. This eliminates selma’o A.

Let’s now turn to —

Eliminating selma’o GIhA

The selma’o of GIhA is the selma’o of bridi-tail connectives (see CLL Chapter 14 Section 9 for an explanation of bridi-tails). These are the members of GIhA:

 gi’a gi’e gi’i gi’o gi’u

Surprisingly, in order to make JA able to join bridi-tails, it is enough to reconceive the cmavo cu as a bridi-tail starter (i.e., every bridi-tail begins with a cu, either explicitly or implicitly via elision), then everything else just naturally falls into place. All JA needs to know is where one bridi-tail ends and another one begins and the cmavo cu will guarantee that we can always mark the beginning of a new bridi tail.

Then, the general pattern becomes:

<bridi-tail> JA <bridi-tail>

This looks exactly like the pattern we saw for connecting sumti… because it is.

Let’s poke at this pattern to see if and how it actually works.

Examples

lo pendo cu prami do je cu djica lo nu do gleki
“Friends love you and want you to be happy.”

The moment je sees the cu to its right it knows that it’s supposed to connect bridi-tails.

Next, a similar case where the first cu is missing:

mi prami do je cu djica lo nu do gleki
“I love you and want you to be happy.”

Even though the first cu is missing, je still knows that it’s supposed to connect bridi-tails because it sees one to its right initiated by cu, so this example poses no problem either.

What if the second cu is missing?

mi prami do je djica lo nu do gleki
“I love you and want you to be happy.”

It… actually works. It works because je wants to connect two units of the same kind. To its left it sees do and to its right it sees djica, a sumti and selbri (or potentially a bridi-tail). As these are not of the same kind, and because the right-hand side unit determines the kind of connection, the do must be part of something else that matches the type of the right-hand side. It could be a selbri, but there is no selbri to the left of je. There is, however, a bridi-tail on both sides.

The first cu is always elidible and there are situations like the one above where even the second cu is elidible. Other situations where cu is always elidible is when the second bridi-tail begins with a preposition (or “tag”) or a member of selma’o NA:

lo tadni cu tatpi je na jundi lo nu lo ctuca cu tavla
The students are tired and do not pay attention to the teacher’s talking.”

mi pu citka je ba cliva
“I ate and will leave.”

With all of these opportunities for elision, be careful not to elide cu when you shouldn’t, as in the following case:

mi citka je viska do
“I eat and see you.”
I eat you and I see you.” 

1311200608936720

You are always on the safe side if you do not elide the cu after je.

Next up is —

Dealing with forethought connectives

To set forethought more clearly apart from afterthought, we will use a new forethought marker that goes in front of the connective, while gi continues to separate the connected arguments just like it always did. Then, as soon as we see that marker we immediately know that we are dealing with a forethought connection, and when we see a bare cmavo of selma’o JA, we know that it must be an afterthought connection. This aids human parsing.

For the same reason selma’o GUhA exists in the official system, we will actually need two markers, one of them specifically for tanru.

We arrive at the following general patterns (one for anything but tanru, and one for tanru):

ga JA <anything> gi <anything>

gu JA <tanru unit> gi <tanru unit>

Examples

ga je lo mlatu gi lo gerku
both cats and dogs

ko ga ja cikre lo karce gi cadzykla lo zvala’i tcadu
Either fix the car or walk to the next town (or both)!”

The connected units can be as complex as desired — they just have to be of the same type.

Tanru forethought connectives must use gu instead:

ta gu je melbi gi ku’i kargydu’e
“That’s both beautiful and however too expensive.”
“That’s beautiful but too expensive.”

Up to this point, all we looked at was connections of exactly two things. Official Lojban also permits connecting more than two things… but only indirectly. That is, if you want to say “X and Y and Z” in forethought, you can only do so by saying both “both X and [both Y and Z]”, connecting two things each time for a total of three connected units:

With the official system this becomes:

ge do gi ge mi gi ro drata
both you and both me and everyone else

With simplified connectives it would become:

ga je do gi ga je mi gi ro drata
both you and both me and everyone else

Neither of those is very pretty.

What if gi could just be repeated as often as needed, like this:

ga je do gi mi gi ro drata
both you and me and everyone else

With this, a forethought connection would no longer auto-terminate after the second connected unit. An ambiguity arises:

ga jo’u lo tadni gi mi je lo ctuca cu jmaji
? “The students together with me and the teachers, gather.”

I meant to say that the students gather together with me, and also that the teachers gather, separately from us. But the sentence could also mean that the students gather together with me and the teachers, depending on the precedence of the different connection types. With gi no longer limited to one argument it becomes necessary to be able to explicitly mark the end of a gi chain so that such complex interactions not only remain unambiguous but also become more controllable so we can more easily group things the way we want them (in a PEG there actually would be no ambiguity, but one of the possible readings would simply not be available).

In short: We need a terminator.

In her own experimental grammar, guskant proposed that gi’i be this terminator. This is possible because gi’i is no longer needed as a bridi-tail connective, so it is free to do something else instead. It also has a fitting sound due its similarity to gi, and is thus easier to remember. Therefore, my proposed connective system will copy this approach.

Be sure to check out https://mw.lojban.org/papri/zantufa for more information about guskant’s zantufa parser and for more clever ideas. It was guskant who first showed how to make arbitrary-length gi work.

The problematic example above can now be disambiguated as follows:

ga jo’u lo tadni gi mi gi’i je lo ctuca cu jmaji
“The students together with me, and the teachers, gather.”

ga jo’u lo tadni gi mi je lo ctuca cu jmaji
“The students, together with me and the teachers, gather.”

And all is well again.

This concludes our elimination of various selma’o. Let’s see —

What we are left with

By tossing selma’o A, GA, GUhA, GIhA and ZIhE, the logical connectives got reduced from

.a .e ji .o .u
ga ge ge’i go gu
gi’a gi’e gi’i gi’o gi’u
gu’a gu’e gu’i gu’o gu’u
ja je je’i jo ju
zi’e

to just

ja je ji jo ju

We also kept the helper cmavo gi, and added the terminator gi’i to open up the potential for forethought connections with unlimited arguments. ji is the new universal connective question, restoring balance by replacing the sore thumb that is je’i.

This looks quite impressive, but what do we do with it? Can five connectives really do the work of 26?

Yes.

The following elegant rule is all we need:

Any connective can connect any two things, as long as both things match.

Two things “match” when they are of the same type, e.g. sumti, selbri, sentence, bridi-tail, relative clause, etc. There really are a whole lot of types that can be thus connected, so the payoff is huge.

Here is a list of just some of them.

  • sumti + sumti
  • tanru-unit + tanru-unit
  • sentence + sentence
  • bridi-tail + bridi-tail
  • number string + number string
  • connective + connective
  • abstractor + abstractor
  • sumtcita + sumtcita
  • non-sumti term + non-sumti term
  • termset + termset
  • relative clause + relative clause
  • and others

Every connection type is available both in forethought and in afterthought. Without smoke and mirrors. No trap doors, no exceptions.

The system also removes any difference between logical and non-logical connectives, which means that selma’o JOI as well as VUhU can be merged into selma’o JA, again eliminating two selma’o.

The time has come for a complete rundown, with —

A Fair Comparison — Old versus New

Here is a direct comparison of how the current (i.e., official) system and the proposed system handle all the possible (and impossible) connections.

Old on the left — new on the right. Words in square brackets are elidible terminators. They are only shown where relevant.

Afterthought
ko’a .e ko’e
broda je broda
broda [vau] gi’e  broda [vau]
ko’a broda .ije  ko’e brode
pu je  ba
NOT POSSIBLE
poi broda  zi’e  poi brode
NOT POSSIBLE
pa  .e  re
su’i je  pi’i
NOT POSSIBLE
 nu ja  du’u
 NOT POSSIBLE
NOT POSSIBLE
ko’a  ji  ko’e
broda  je’i  brode
broda [vau] gi’i brode [vau]
NOT POSSIBLE
ko’a je ko’e
broda je broda
(cu) broda [vau] je cu broda [vau]
ko’a broda .ije  ko’e brode
pu je  ba
pu ko’a je  ba ko’e
poi broda je  poi brode
poi broda ja  poi brode
pa je  re
su’i je  pi’i
je je  ja
nu je  du’u
lo je  le
(cu) broda [vau] joi cu brode [vau]
ko’a ji  ko’e
broda ji  brode
(cu) broda [vau] ji  cu brode [vau]
poi broda ji  poi brode
Forethought
ge ko’a gi ko’e
gu’e broda gi brode
ge broda [vau] gi brode [vau]
ge ko’a broda gi ko’e brode
NOT POSSIBLE
ge pu ko’a gi ba ko’e (camxes only)
NOT POSSIBLE
ge pa gi re
gu’e
su’i gi pi’i
NOT POSSIBLE
NOT POSSIBLE
NOT POSSIBLE
NOT POSSIBLE
joi gi gi (same as ge)
NOT POSSIBLE
ge’i gi (same as ge)
gu’i gi (same as gu’e)
ga je
ko’a gi ko’e [gi’i]
gu je broda gi brode [gi’i]
ga je broda [vau] gi brode [vau] [gi’i]
ga je ko’a broda gi ko’e brode [gi’i]
ga je pu gi ba [gi’i] ko’a
ga je pu ko’a gi ba ko’e [gi’i]
ga je poi broda gi poi brode [gi’i]
ga je pa gi re [gi’i]
ga je su’i gi pi’i [gi’i]
ga je joi gi jo’u [gi’i]
ga je nu gi du’u [gi’i]
ga je lo gi le [gi’i]
ga je gi gi gi [gi’i]
ga joi gi [gi’i] (same as ga je)
gu joi broda gi brode [gi’i]
ga ji gi [gi’i] (same as ga je)
gu ji gi [gi’i] (same as gu je)

Aaaaand — that’s it.

If you are interested in seeing more proposals in a similar spirit you might also like the other posts in the Simpler series: A Simpler Quantifier Logic and A Simpler Morphology [coming soon].

If you have comments or questions leave them below.

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9 thoughts on “A Simpler Connective System

  1. I would to propose a tiny addendum.
    Current lojban has only {ku’a} for ‘intersection’, {johe} for ‘union’ and {joheihi} for ‘symmetrical difference’, as set connectors. Seeing that lojban regularly express logic connectors, I propose to build set connectors in the same way, just add a suffix or something like that to distinguish them. Indeed:
    AUB={x | x ∈ A or x ∈ B}
    A∩B={x | x ∈ A and x ∈ B}
    AΔB={x | x ∈ A xor x ∈ B}
    it’s obvious to see that, instead of irregular forms like {johe}, {joheihi}, and {ku’a}, it’s easier to say, for example, that:
    AUB = A ja’i B
    A∩B = A je’i B
    AΔB = A jo’i nai B
    if {‘i} is the suffix for “set”, as for the gadri {la’i}, {lo’i}, {le’i}
    This system allows things that neither natural languages nor mathematical notations could, creating extra-connectors, like A\B={x | x ∈ A and x ∉ B}= A je’i nai B

    Like

  2. When using a {ga|gu}{JA}–gi–{[gi]…[gi]}– construction, are the JA changed to cycle among truth tables, or are the gi changed as well? (or only the gi changed?) For example, “.i mi cu gu najenai cadzu gi bajra” (I neither walk nor run) or “.i mi cu gu je cadzu naginai bajra” or “.i mi cu gu najenai cadzu naginai bajra”?

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