Lojban

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 category logic / functional programming point of view, it uses also rather imperative ideas), but it may give hints and analogies, how combinatry 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.

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.

do	cu	vecnu	ta	mi	zo'e	vau
$x_{1}$		predicate	$x_{2}$	$x_{3}$	$x_{4}$

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.

Filipping

That is sold by you to me for some price

ta	cu	se vecnu	do	mi	zo'e	vau
$x_{1}$		predicate	$x_{2}$	$x_{3}$	$x_{4}$

Coparing vecnu and se vecnu, it is of taste $mathbfC$ 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

Repeating

Words mi, do correspond to Enlish personal pronouns I (me), you. Lojban has other simi;ar words, e.g. ri. Word ri can be regarded as an argument (of the prediate) 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
$x_{1}$		predicate	$x_{2}$	$x_{3}$	$x_{4}$

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 more imperative solution, that the $\mathbf {W}$ combinator of combinatory logic, but in this case, it has the same effect. If Lojban used combinators, I should write:

$\mathbf {W}$(Mi cu tavla do) la lojban.

$\mathbf {W}$ could be used for avoiding the many-many reeating 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?

$\lambda fx.fxxx$

mi cu ($\left(\lambda fx.fxxx\right)$ 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.

References

NC:WhLoj

Nicholas, Nick and Cowan, John (ed.): What is Lojban? Logical Language Group, 2003. Available also online.

Moo:LojPer

Todd Moody: Lojban in Perspective

Available from here, part of Lojban's official homepage