Lojban

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1 Introduction
2 Analogies of combinatory logic combinators
3 Filipping
4 Repeating
5 References

1 Introduction

Lojban is a constructed language. “Lojban was not designed primarily to be an international language, however, but rather as a linguistic tool for studying and understanding language. Its linguistic and computer applications make Lojban unique among international languages...” (NC:LojPer, page 15 par 1) -- the entire book is available also online, see the very bottom of the linked page.

It is an artificial language (and, unlike the more a posteriori Esperanto, it is rather of an a priori taste (Moo:LojPer)). It is a human language, capable of expressing everything. Its grammar uses (among others) things taken from mathematical logic, e.g. predicate-like structures. Although its does not make use combinatory logic directly (even, from a combinatory logic / functional programming point of view, it uses also rather imperative ideas), but it may give hints and analogies, how combinatory logic can be useful in linguistics. I like searching Lojban examples illustrating the learned statements when learning about applicative universal grammar.

See its official homepage here.

Wikipedia article on Lojban.

2 Analogies of combinatory logic combinators

The Lojban sentence examples are taken from (NC:WhLoj, Chapter 3. Diagrammed Summary of Lojban Grammar). Sometimes, I modified the sentences slightly, if the combinatory logic analogies made it necessary.

Predicates

Somebody	sells	something	to sombebody	for some price
$x 1$	predicate	$x 2$	$x 3$	$x 4$

A little vocabulary:

mi: I
vecnu: sell
do: you
ta: that

Syntax:

I sell this to you for some price.
`mi`	`cu`	`vecnu`	`ta`	`do`	`zo'e`	`vau`
$x 1$	`cu`	predicate	$x 2$	$x 3$	$x 4$	`vau`

cu and vau are separators (and they are optional). zo'e is only a place-keeper: the argument whose place is fiiled in by it is not specified.

3 Filipping

That is sold by you to me for some price
`ta`	`cu`	`se vecnu`	`do`	`mi`	`zo'e`	`vau`
$x 1$	`cu`	predicate	$x 2$	$x 3$	$x 4$	`vau`

Comparing vecnu and se vecnu, it is of taste $\mathbf C$ combinator of combinatory logic. Comparing structure:

$x 1$	`cu`	predicate	$x 2$	$x 3$	$x 4$	`vau`
`do`		`vecnu`	`ta`	`mi`	`zo'e`
`ta`		`se vecnu`	`mi`	`mi`	`zo'e`

4 Repeating

Words mi, do correspond to English personal pronouns I (me), you. Lojban has other similar words, e.g. ri. Word ri fills in an argument (of the predicate) which repeats the previous argument.

Somebody	talks	to sombebody	about something	in some language
$x 1$	predicate	$x 2$	$x 3$	$x 4$

A little vocabulary:

mi: I
tavla: talk
do: you
la lojban.: Lojban

Syntax:

I talk to you about the Lojban language in Lojban
`mi`	`cu`	`tavla`	`do`	`la lojban.`	`la lojban.`	`vau`
$x 1$	`cu`	predicate	$x 2$	$x 3$	$x 4$	`vau`

The word ri helps us avoiding repeating the argument of predicate in this case:

mi cu tavla do la lojban. ri vau

I think, it is a rather imperative solution, compared to the $\mathbf W$ combinator of combinatory logic, but in this case, it has the same effect. If Lojban used combinators, I should write (using the elementary duplicator $\mathbf W$ ):

$\mathbf W$ (mi cu tavla do) la lojban.

Deferred combinator $\mathbf W_{\left(2\right)}$ helps us even more here:

mi cu ( $\mathbf W_{\left(2\right)}$ tavla) do la lojban.

$\mathbf W$ -sequences could be used also for avoiding the many-many repeating zo'e words (of course, if Lojban used combinators):

I talk.

(Not specified, to whom, about what topic, in what language!)

mi cu tavla zo'e zo'e zo'e vau

What could help us in lambda calculus?

λ f x . f x x x

mi cu ( $\left(\lambda f x . f x x x\right)$ tavla) zo'e vau

In combinatory logic, $\mathbf W^2$ makes that:

mi cu ( $\mathbf W^2$ tavla) zo'e vau

Lojban does not use combinators this way, it uses also rather imperative solutions. Despite of that, Lojban makes me think of combinatory logic and applicative universal grammar.

5 References

NC:WhLoj: Nicholas, Nick and Cowan, John (ed.): What is Lojban? Logical Language Group, 2003. Available also online, see the very bottom of the linked page.
Moo:LojPer: Todd Moody: Lojban in Perspective. Available from here, part of Lojban's official homepage

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Category: Theoretical foundations