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Lojban

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m (Two personal pronouns mixed)
(→Repeating: Useing combinator W_(2), the deferred version of elementary duplicator W)
Line 32: Line 32:
A little vocabulary:
A little vocabulary:
-
; mi
+
; <code>mi</code>
: I
: I
-
; vecnu
+
; <code>vecnu</code>
: sell
: sell
-
; do
+
; <code>do</code>
: you
: you
-
; ta
+
; <code>ta</code>
: that
: that
Line 45: Line 45:
{| border=5
{| border=5
|+ I sell this to you for some price.
|+ I sell this to you for some price.
-
| mi
+
| <code>mi</code>
-
| rowspan=2 | cu
+
| rowspan=2 | <code>cu</code>
-
| vecnu
+
| <code>vecnu</code>
-
| ta
+
| <code>ta</code>
-
| do
+
| <code>do</code>
-
| zo'e
+
| <code>zo'e</code>
-
| rowspan=2 | vau
+
| rowspan=2 | <code>vau</code>
|-
|-
| <math>x_1</math>
| <math>x_1</math>
Line 60: Line 60:
|}
|}
-
cu and vau are separators (and they are optional).
+
<code>cu</code> and <code>vau</code> 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.
+
<code>zo'e</code> is only a place-keeper: the argument whose place is fiiled in by it is not specified.
== Filipping ==
== Filipping ==
Line 67: Line 67:
{| border=5
{| border=5
|+ That is sold by you to me for some price
|+ That is sold by you to me for some price
-
| ta
+
| <code>ta</code>
-
| rowspan=2 | cu
+
| rowspan=2 | <code>cu</code>
-
| se vecnu
+
| <code>se vecnu</code>
-
| do
+
| <code>do</code>
-
| mi
+
| <code>mi</code>
-
| zo'e
+
| <code>zo'e</code>
-
| rowspan=2 | vau
+
| rowspan=2 | <code>vau</code>
|-
|-
| <math>x_1</math>
| <math>x_1</math>
Line 82: Line 82:
|}
|}
-
Coparing vecnu and se vecnu, it is of taste <math>mathbf C</math> combinator of [[combinatory logic]].
+
Coparing <code>vecnu</code> and <code>se vecnu</code>, it is of taste <math>\mathbf C</math> combinator of [[combinatory logic]].
Comparing structure:
Comparing structure:
{| border=5
{| border=5
! <math>x_1</math>
! <math>x_1</math>
-
| rowspan=3 | cu
+
| rowspan=3 | <code>cu</code>
! predicate
! predicate
! <math>x_2</math>
! <math>x_2</math>
! <math>x_3</math>
! <math>x_3</math>
! <math>x_4</math>
! <math>x_4</math>
-
| rowspan=3 | vau
+
| rowspan=3 | <code>vau</code>
|-
|-
-
| do
+
| <code>do</code>
-
| vecnu
+
| <code>vecnu</code>
-
| ta
+
| <code>ta</code>
-
| rowspan=2 | mi
+
| rowspan=2 | <code>mi</code>
-
| rowspan=2 | zo'e
+
| rowspan=2 | <code>zo'e</code>
|-
|-
-
| ta
+
| <code>ta</code>
-
| se vecnu
+
| <code>se vecnu</code>
-
| mi
+
| <code>mi</code>
|}
|}
== Repeating ==
== 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.
+
Words <code>mi</code>, <code>do</code> correspond to English personal pronouns I (me), you. Lojban has other similar words, e.g. <code>ri</code>. Word <code>ri</code> can be regarded as an argument (of the predicate) which repeats the previous argument.
{| border=5
{| border=5
Line 124: Line 124:
A little vocabulary:
A little vocabulary:
-
; mi
+
; <code>mi</code>
: I
: I
-
; tavla
+
; <code>tavla</code>
: talk
: talk
-
; do
+
; <code>do</code>
: you
: you
-
; la lojban.
+
; <code>la lojban.</code>
: Lojban
: Lojban
Line 137: Line 137:
{| border=5
{| border=5
|+ I talk to you about the Lojban language in Lojban
|+ I talk to you about the Lojban language in Lojban
-
| mi
+
| <code>mi</code>
-
| rowspan=2 | cu
+
| rowspan=2 | <code>cu</code>
-
| tavla
+
| <code>tavla</code>
-
| do
+
| <code>do</code>
-
| la lojban.
+
| <code>la lojban.</code>
-
| la lojban.
+
| <code>la lojban.</code>
-
| rowspan=2 | vau
+
| rowspan=2 | <code>vau</code>
|-
|-
| <math>x_1</math>
| <math>x_1</math>
Line 152: Line 152:
|}
|}
-
The word ri helps us avoiding repeating the argument of predicate in this case:
+
The word <code>ri</code> helps us avoiding repeating the argument of predicate in this case:
-
Mi cu tavla do la lojban. ri vau
+
<code>mi cu tavla do la lojban. ri vau</code>
-
I think, it is more imperative solution, that the <math>\mathbf W</math> combinator of [[combinatory logic]], but in this case, it has the same effect. If Lojban used combinators, I should write:
+
I think, it is more imperative solution, than the <math>\mathbf W</math> combinator of [[combinatory logic]], but in this case, it has the same effect. If Lojban used combinators, I should write (using the elementary duplicator <math>\mathbf W</math>):
-
<math>\mathbf W</math>(Mi cu tavla do) la lojban.
+
<math>\mathbf W</math>(<code>mi cu tavla do</code>) <code>la lojban.</code>
-
<math>\mathbf W</math> could be used for avoiding the many-many reeating zo'e words (of course, if Lojban used combinators):
+
Deferred combinator <math>\mathbf W_{\left(2\right)}</math> helps us even more here:
-
I talk.
+
<code>mi cu</code> (<math>\mathbf W_{\left(2\right)}</math> <code>tavla</code>) <code>do la lojban.</code>
 +
 
 +
<math>\mathbf W</math>-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!)
(Not specified, to whom, about what topic, in what language!)
-
mi cu tavla zo'e zo'e zo'e vau
+
<code>mi cu tavla zo'e zo'e zo'e vau</code>
What could help us in lambda calculus?
What could help us in lambda calculus?
:<math>\lambda f x . f x x x</math>
:<math>\lambda f x . f x x x</math>
-
mi cu (<math>\left(\lambda f x . f x x x\right)</math> tavla) zo'e vau
+
<code>mi cu</code> (<math>\left(\lambda f x . f x x x\right)</math> <code>tavla</code>) <code>zo'e vau</code>
-
In combinatory logic, <math>\mathbf W^2</math> makes that:
+
In [[combinatory logic]], <math>\mathbf W^2</math> makes that:
-
mi cu (<math>\mathbf W^2</math> tavla) zo'e vau
+
<code>mi cu</code> (<math>\mathbf W^2</math> <code>tavla</code>) <code>zo'e vau</code>
Lojban does not use combinators this way, it uses also rather imperative solutions. Despite of that, Lojban makes me think of [[combinatory logic]] and [[Libraries and tools/Linguistics/Applicative universal grammar|applicative universal grammar]].
Lojban does not use combinators this way, it uses also rather imperative solutions. Despite of that, Lojban makes me think of [[combinatory logic]] and [[Libraries and tools/Linguistics/Applicative universal grammar|applicative universal grammar]].

Revision as of 20:39, 7 August 2006

Contents


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 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.

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
x1 predicate x2 x3 x4

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
x1 predicate x2 x3 x4

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
x1 predicate x2 x3 x4

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

x1 cu predicate x2 x3 x4 vau
do vecnu ta mi zo'e
ta se vecnu mi

4 Repeating

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

Somebody talks to sombebody about something in some language
x1 predicate x2 x3 x4

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
x1 predicate x2 x3 x4

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, than 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?

λfx.fxxx

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
Retrieved from "http://www.haskell.org/haskellwiki/Lojban"

Category: Theoretical foundations