Abstraction paper, draft 1.0

[cowan@snark.thyrsus.com (John Cowan)]

On Lojban Abstraction
Draft 1.0


1. The Syntax Of Abstraction

The purpose of the feature of Lojban known as "abstraction" is to provide
a means for taking whole bridi and packaging them up, as it were, into
simple selbri.  Syntactically, abstractions are very simple and uniform;
semantically, they are rich and complex, with few features in common
between one variety of abstraction and another. We will begin by discussing
syntax without regard to semantics; as a result, the notion of abstraction
may seem unmotivated at first.  Bear with this difficulty until Section 2.

An abstraction selbri is formed by taking a full bridi and preceding it
by any cmavo of selma'o NU.  There are twelve such cmavo; they are known
as "abstractors".  The bridi is closed by the elidable terminator "kei",
of selma'o KEI.  Thus, to change the bridi

1.1)	mi klama le zarci
	I go-to the store

into an abstraction using "nu", one of the members of selma'o NU, we
change it into

1.2)	nu mi klama le zarci [kei]
	an-event-of my going-to the store

The bridi may be a simple selbri, or it may have associated sumti, as
here.  It is important to beware of eliding "kei" improperly, as
many of the common uses of abstraction selbri involve following them
with words that may appear to be part of the abstraction if "kei"
has been elided.

The grammatical use of an abstraction selbri is exactly the same as
that of a simple brivla.  In particular, abstraction selbri may be
used in tanru:

1.3)	la djan. cu nu sonci kei djica
	John is-an-event-of being-a-soldier type-of desirer.
	John wants to be a soldier.

and also in descriptions with "le":

1.4)	la djan. cu djica le nu sonci [kei]
	John desires the event-of being-a-soldier.

We will most often use descriptions containing abstraction either at the
end of a bridi, or just before the selbri with its "cu"; in either of
these circumstances, "kei" can normally be elided.

The place structure of an abstraction selbri depends on the particular
abstractor, and will be explained individually in the following sections.

Note: In glosses of bridi within abstractions, the grammatical form
used in the English changes.  Thus, in the gloss of Example 1.2 we see
"my going-to the store" rather than "I go-to the store"; likewise,
in the glosses of Examples 1.3 and 1.4 we see "being-a-soldier"
rather than "is-a-soldier".  This procedure reflects the desire for
more readable glosses, and does not indicate any change in the Lojban
form.  A bridi is a bridi, and undergoes no change when it is used as
part of an abstraction selbri.


2. Event Abstraction:  "nu"

The examples in Section 1 made use of "nu" as the abstractor, and it is
certainly the most common abstractor in Lojban text.  Its purpose is
to capture the event or state of the bridi considered as a whole.
Do not confuse the "le" description built on a "nu" abstraction with
ordinary descriptions based on "le" alone.  The following sumti are
quite distinct:

2.1)	le klama
	the comer, that which comes

2.2)	le se klama
	the destination

2.3)	le te klama
	the origin

2.4)	le ve klama
	the route

2.5)	le xe klama
	the means of transportation

2.6)	le nu klama
	the event of coming

Examples 2.1-2.5 are descriptions that isolate the five individual sumti
places of the selbri "klama".  Example 2.6 describes something associated
with the bridi as a whole: the event of it.

In Lojban, the term "event" is divorced from its ordinary English sense of
something that happens over a short period of time. The description:

2.7)	le nu mi sipna
	the event-of my breathing

is an event which lasts for the whole of my life (under normal circumstances).
On the other hand,

2.8)	le nu la djan. cinba la djein.
	the event-of John kissing Jane

is relatively brief by comparison (again, under normal circumstances).

We can see from Examples 2.6-2.8 that ellipsis of sumti is valid in the bridi
of abstraction selbri, just as in main bridi.  Any sumti may be ellipsized
if the listener will be able to figure out what the proper value of it is.
It is extremely common for "nu" abstractions to have the x1 place ellipsized:

2.9)	mi nelci le nu limna
	I like the event-of swimming.
	I like swimming.

is elliptical, and most probably means:

2.10)	mi nelci le nu mi limna
	I like the event-of I swim.

In the proper context, of course, Example 2.9 could refer to the event of
somebody else swimming.

Event descriptions with "le nu" are commonly used to fill the "under
conditions..." places of gismu and lujvo place structures:

2.11)	la lojban. cu frili mi le nu mi tadni [kei]
	Lojban is-easy for-me under-conditions-the event-of I study
	Lojban is easy for me when I study.

(The "when" of the English would also be appropriate for a construction
involving a Lojban tense, but the Lojban sentence says more than that the
studying is concurrent with the ease.)

The place structure of a "nu" abstraction selbri is simply:

	x1 is an event of <the bridi>


3.  Types Of Event Abstractions: "mu'e", "pu'u", "zu'o", "za'i"

Event abstractions with "nu" suffice to express all kinds of events, whether
long, short, unique, repetitive, or whatever.

Lojban also has more finely discriminating machinery for talking about
events, however.  There are four other abstractors of selma'o NU for talking
about four specific types of events.

An event considered as a point in time is called a "point-event", or
sometimes an "achievement".  (This latter word should be divorced, in this
context, from all connotations of success or triumph.)  The abstractor
"mu'e" means "point-event-of":

3.1)	le mu'e la djan. catra la djim. cu zekri
	the point-event-of (John kills Jim) is-a-crime
	John's killing Jim (considered as a point in time) is a crime.

An event considered as extended in time, with a beginning, middle, and
end, is called a "process".  The abstractor "pu'u" means "process-of":

3.2)	le pu'u mi jbena cu cacra li vo
	the process-of (I am-born) is-in-hours the-number four
	I was being born for four hours.

An event considered as extended in time and cyclic or repetitive is called
an "activity".  The abstractor "zu'o" means "activity-of":

3.3)	mi kanlo ri'a le zu'o mi plipe
	I am-healthy because-of the activity-of (I jump)
	I am healthy because I jump.

An event considered as something that is either happening or not happening,
with sharp boundaries, is called a "state".  The abstractor "za'i" means
"state-of":

3.4)	le za'i mi jmive cu ckape do
	the state-of (I am-alive) is-dangerous-to you
	My being alive is dangerous to you.

All of these abstractors could have been replaced by "nu" with some loss
of precision.  Note that Lojban allows the same event to be viewed in
any of these four ways:

	the "state of running" begins when the runner starts
	and ends when the runner stops;

	the "activity of running" consists of the cycle "lift leg,
	step forward, drop leg, lift other leg...";

	the "process of running" puts emphasis on the initial sprint,
	the steady speed, and the final slowdown;

	the "achievement of running" is most alien to English, but
	sees the event of running as a single thing, like
	"Pheidippides' run from Marathon to Athens"
	(the original marathon).

The four event type abstractors have the same place structure as "nu".


4.  Property Abstractions: "ka"

The things described by "le nu" descriptions (or, to put it another way,
the things of which "nu" selbri may correctly be predicated) are only
moderately "abstract".  They are still closely tied to happenings in
space and time.  Properties, however, are much more ethereal.  What is
"the property of being blue", or "the property of being a go-er"?
They are what logic calls "open sentences" or "propositional functions".
If John has a heart, then "the property of having a heart" is something
that is true of John.  In fact,

4.1)	la djan. cu se risna [zo'e]
	John has-as-heart something-unspecified.
	John has a heart.

has the same truth conditions as

4.2)	la djan. cu ckaji le ka se risna [zo'e] [kei]
	John has-the-property the property-of having-as-heart something.
	John has the property of having a heart.

(The English word "have" is tied up in all discussions of Lojban properties:
we are said to "have" properties, but this is not the same sense of
"have" as in "I have money", which is possession.)

Property descriptions, like event descriptions, are often wanted to fill
places in brivla place structures:

4.3)	do cnino mi le ka blanu [kei]
	You are-new to-me in-the-quality-of-the property-of being-blue.
	You are new to me in blueness.

We can also move the property description to the x1 place of Example 4.3,
producing:

4.4)	le ka do blanu [kei] cu cnino mi
	The property-of your blueness is-new to me.

There are several different properties that can be extracted from a bridi,
depending on which place of the bridi is "understood" as being specified
externally.  Thus:

4.5)	ka mi prami [zo'e] [kei]
	a-property-of me loving something-unspecified

is quite different from

4.6)	ka [zo'e] prami mi [kei]
	a-property-of something-unspecified loving me

In particular, sentences like Example 4.7 and Example 4.8 are quite
different in meaning:

4.7)	la djan. cu zmadu la djordj. le ka mi prami
	John exceeds George in-the property-of (I love X)
	I love John more than I love George.

4.8)	la djan. cu zmadu la djordj. le ka prami mi
	John exceeds George in the property of (X loves me).
	John loves me more than George loves me.

The "X" used in the glosses of Examples 4.7-4.8 as a place-holder cannot
be represented only by ellipsis in Lojban, because ellipsis means that
the hearer must be able to fill in the appropriate sumti, as mentioned
in Section 2.  Instead, a convention (the motivation for which is
explained elsewhere) is employed when an explicit sumti is wanted.
A hitherto unused pro-sumti (of selma'o KOhA) is chosen from the series
"da", "de", "di".  If all three of these are already in use, subscripting
with "xi" is employed to provide a unique pro-sumti.  Therefore, an
explicit equivalent of Example 4.7, with no ellipsis, is:

4.9)	la djan. cu zmadu la djordj. le ka mi prami da
	John exceeds George in-the property-of (I love X).

and of Example 4.8 is:

4.10)	la djan. cu zmadu la djordj. le ka da prami mi
	John exceeds George in-the property-of (X loves me).

This convention allows disambiguation of cases like:

4.11)	le ka [zo'e] dunda le xirma [zo'e] [kei]
	the property-of giving the horse

into

4.12)	le ka da dunda le xirma [zo'e] [kei]
	the property-of (X is-a-giver of-the horse to someone-unspecified)
	the property of being a giver of the horse

which is the most natural interpretation of Example 4.11, versus

4.13)	le ka [zo'e] dunda le xirma da [kei]
	the property-of (someone-unspecified is-a-giver of-the horse to X)
	the property of being one to whom the horse is given

which is also a possible interpretation.

The place structure of "ka" abstraction selbri is:

	x1 is a property of <the bridi>


5. Amount Abstractions:  "ni"

Amount abstractions are far more limited than event or property abstractions.
They really make sense only if the selbri of the abstracted bridi is
subject to measurement of some sort.  Thus we can speak of:

5.1)	le ni le pixra cu blanu [kei]
	the amount-of (the picture being-blue)
	the amount of blueness in the picture

because "blueness" could be measured with a colorimeter or a similar
device.  However,

5.2)	le ni la djein. cu mamta [kei]
	the amount-of (Jane being-a-mother)
	the amount of Jane's mother-ness (?)
	the amount of mother-ness in Jane (?)

makes very little sense in either Lojban or English.  We simply do not
have any sort of measurement scale for being a mother.

Semantically, a sumti with "le ni" is a number; however, it cannot be
treated grammatically as a quantifier in Lojban unless prefixed by the
mathematical cmavo "mo'e":

5.3)	li pa vu'u mo'e le ni le pixra cu blanu [kei]
	the-number 1 minus the-operand the amount-of (the picture being-blue)
	1 - B, where B = blueness of the picture

Mathematical Lojban is beyond the scope of this paper, and is explained
more fully elsewhere.

There are contexts where either property or amount abstractions make sense,
and in such constructions, amount abstractions can make use of the same
convention with "da", "de", or "di" as property abstractors.  Thus,

5.4)	le pixra cu cenba le ka [da] blanu [kei]
	the picture varies in-the property-of (X is blue)
	The picture varies in being blue.
	The picture varies in blueness.

is not the same as

5.5)	le pixra cu cenba le ni [da] blanu [kei]
	the picture varies in-the amount-of (X is blue)
	The picture varies in how blue it is.
	The picture varies in blueness.

Example 5.4 conveys that the blueness comes and goes, whereas Example
5.5 conveys that its quantity changes over time.

Whenever we talk of measurement of an amount, there is some sort of
scale, and so the place structure of "ni" abstraction selbri is:

	x1 is the amount of <the bridi> on scale x2


6. Truth-Value Abstraction:  "jei"

The "blueness of the picture" discussed in Section 5 refers to the measurable
amount of blue pigment (or other source of blueness), not to the purity,
actuality, or probability that blueness is present.  That abstraction is
expressed in Lojban using "jei", which is closely related semantically
to "ni".  In the simplest cases, "le jei" produces not a number but a
truth value:

6.1)	le jei li re su'i re du li vo [kei]
	the truth-value-of the-number 2 + 2 = the-number 4
	whether 2 + 2 is 4

is equivalent to "truth", and

6.2)	le jei li re su'i re du li mu [kei]
	the truth-value-of the-number 2 + 2 = the-number 5
	whether 2 + 2 is 5

is equivalent to "falsehood".

However, not everything in life (or even in Lojban) is simply true or
false.  There are shades of gray even in truth value, and "jei" is
Lojban's mechanism for indicating the shade of grey intended:

6.3)	mi ba jdice le jei la djordj. cu zekri gasnu [kei]
	I [future] decide the truth-value of George being-a-(crime doer).
	I will decide whether George is a criminal.

Example 6.3 does not imply that George is, or is not, definitely a criminal.
Depending on the legal system I am using, I may make some intermediate
decision.  As a result, "jei" requires an x2 place analogous to that of "ni":

	x1 is the truth value of <the bridi> under epistemology x2


7. Predication/Sentence Abstraction: "du'u"

There are some selbri which demand an entire predication as a sumti; they
make claims about some predication considered as a whole.  Logicians call
these the "propositional attitudes", and they include (in English) things
like knowing, believing, learning, seeing, hearing, and the like.  Consider
the English sentence:

7.1)	I know that Frank is a fool.

How's that in Lojban?  Let us try:

7.2)	mi djuno le nu la frank. cu bebna [kei]
	I know the event of Frank being a fool.

Not quite right.  Events are things which happen; Example 7.2 is
possible, but would mean something like "I know something about Frank's
foolishness."  It is in fact an example of "sumti raising" (see Section
10).  Try again:

7.3)	mi djuno le jei la frank. cu bebna [kei]
	I know the truth-value of Frank being a fool.

Closer.  Example 7.3 says that I know whether or not Frank is a fool, but
doesn't say that he is one, as Example 7.1 does.  To catch that nuance,
we must say:

7.4)	mi djuno le du'u la frank. cu bebna [kei]
	I know the predication that Frank is a fool.

Now we have it.  Note that the implied assertion "Frank is a fool" is
not a property of "le du'u" abstraction, but of "djuno"; we can only
know what is in fact true.  (As a result, "djuno" like "jei" has a place
for epistemology, which specifies how we know.)  Example 7.5 has no
such implied assertion:

7.5)	mi kucli le du'u la frank. cu bebna [kei]
	I am curious about whether Frank is a fool.

and here "du'u" could probably be replaced by "jei" without much change
in meaning.

As a matter of convenience rather than logical necessity, "du'u" has been
given an x2 place, which is a sentence (piece of language) expressing
the bridi:

	x1 is the predication <the bridi>, expressed in sentence x2

and "se du'u" is very useful in filling places of selbri which refer to
speaking, writing, or other linguistic behavior:

7.6)	la djan. cusku le se du'u la djordj. klama le zarci [kei]
	John expresses the sentence-expressing-that George goes-to the store
	John says that George goes to the store.

Example 7.6 differs from

7.7)	la djan cusku lu la djordj. klama le zarci li'u
	John expresses, quote, George goes to the store, unquote.
	John says "George goes to the store".

because Example 7.7 claims that John actually said the quoted words,
whereas Example 7.6 claims only that he said some words or other which were
to the same purpose.


8. Indirect Questions: "kau"

There is an alternative type of sentence involving "du'u" and a selbri
expressing a propositional attitude.  In addition to sentences like

8.1)	I know that John went the store.

we can also say things like

8.2)	I know who went to the store.

This form is called an "indirect question" in English because the embedded
English sentence is a question:  "Who went to the store?"  A person who
says Example 8.2 is claiming to know the answer to this question.  Indirect
questions can occur with many other English verbs as well:  I can wonder, or
doubt, or see, or hear, as well as know who went to the store.

To express indirect questions in Lojban, we use a "le du'u" abstraction,
but rather than using a question word like "who" ("ma" in Lojban), we use
any word that will fit grammatically and mark it with the suffix particle
"kau".  This cmavo belongs to selma'o UI, so grammatically it can appear
anywhere.  The simplest Lojban translation of Example 8.2 is therefore:

8.3)	mi djuno le du'u
		dakau pu klama le zarci
	I know the predication-of
		X [indirect question] [past] going to the store.

In Example 8.3, we have chosen to use "da" as the word marked by "kau".
In fact, any other sumti would have done as well:  "zo'e" or "ma" or
even "la djan.".  Using "la djan." would suggest that it was John who
I knew had gone to the store, however:

8.4)	mi djuno le du'u
		la djan. kau pu klama le zarci
	I know the predication-of
		John [indirect question] [past] going to the store.
	I know who went to the store, namely John.

Using one of the indefinite pro-sumti such as "da", "zo'e", or "ma" does
not suggest any particular value.

It is actually not necessary to use "kau" to express sumti indirect questions;
there is generally a paraphrase of the type:

8.5)	mi djuno fi le pu klama le zarci
	I know about the [past] goer to-the store.
	I know something about the one who went to the store
		(namely, his identity).

because the x3 place of "djuno" is the subject of knowledge, as opposed
to the fact that is known.  But when the questioned point is not a sumti,
but (say) a logical connection, then there is no good alternative to "kau":

8.6)	mi ba viska le du'u
		la djan. jikau la djordj.
		cu zvati le panka
	I [future] see the predication-of
		John [connective indirect question] George
		is-at the park.
	I will see whether John or George (or both) is at the park.
		


9. Minor Abstractions:  "li'i", "si'o", "su'u"

There are three more abstractors in Lojban, all of them little used so far.
The abstractor "li'i" expresses experience:

9.1)	mi na ckaji
		le li'i mi tuple ci da
	I do-not have-as-a-property
		the experience-of my being be-legged-by three somethings.
	I have not experienced having three legs.

Again, the word "have" is pervasive in the English gloss and translation
as the nearest English equivalent of "ckaji", the selbri that relates a
property (in x2) to that which has the property (in x1).

The abstractor "si'o" expresses a mental image, a concept, an idea:

9.2)	mi nelci le si'o la lojban. cu mulno
	I enjoy the concept-of Lojban being-complete.

Finally, the abstractor "su'u" is a vague abstractor, whose meaning must
be grasped from context:

9.3)	ko viska le su'u le ci smacu cu bajra
	you [imperative] see the abstract-nature-of the three mice running
	See how the three mice run!


10. Sumti Raising: "tu'a"

It is sometimes inconvenient, in a situation where an abstract description
is logically required, to express the abstraction.  In English we can
say:

10.1)	I try to open the door.

which in Lojban is:

10.2)	mi troci le nu [mi] gasnu le nu le vorme cu kalri
	I try the event-of (I am-agent-in the event-of (the door is-open)).

which has an abstraction description within an abstraction description.
In English (but not in all other languages), we may also say:

10.3)	I try the door.

where it is understood that what I try is actually not the door itself,
but the act of opening it.  The same simplification can be done in Lojban,
but it must be marked explicitly using a cmavo.  The relevant cmavo is
"tu'a", which belongs to selma'o LAhE.  The Lojban equivalent of Example
10.3 is:

10.4)	mi troci tu'a le vorme
	I try [sumti-raising] the door.

The term "sumti-raising" signifies that a sumti which logically belongs
within an abstraction (or even within an abstraction which is itself
inside an intermediate abstraction) is "raised" to the main bridi level.
This transformation from Example 10.2 to Example 10.4 loses information:
nothing except convention tells us what the abstraction was.

Using "tu'a" is a kind of laziness: it makes speaking easier at the
possible expense of clarity for the listener.  The speaker must be
prepared for the listener to respond something like:

10.5)	tu'a le vorme lu'u ki'a
	[sumti-raising] the door [terminator] [confusion!]

which indicates that "tu'a le vorme" cannot be understood.  (The terminator
for "tu'a" is "lu'u", and is used in Example 10.5 to make clear just what
is being questioned: the sumti-raising, rather than the word "vorme" as such.)
An example of a confusing raised sumti might be:

10.6)	tu'a la djan. cu cafne
	[sumti-raising] John frequently-occurs

This must mean that something which John does occurs frequently: but
without more context there is no way to figure out what.  Note that without
the "tu'a", Example 10.6 would mean that John considered as an event
frequently occurs -- in other words, that John has some sort of on-and-off
existence!  Normally we do not think of people as events in English, but
the x1 place of "cafne" is an event, and if something that does not seem
to be an event is put there, the Lojbanic listener will attempt to construe
it as one.


11. Abstract Lujvo

The cmavo of NU can participate in the construction of lujvo of a particularly
simple and well-patterned kind.  Consider that old standard example, "klama":

	x1 comes/goes to x2 from x3 via route x4 by means x5.

The selbri "nu klama [kei]" has only an x1 place, the event-of-going, but
the full five places exist implicitly between "nu" and "kei", since a full
bridi with all sumti may be placed there.  In a lujvo, there is no such
room, and consequently the lujvo "nunklama" ("nun-" is the rafsi for "nu"),
needs to have six places:

	x1 is the event of x2's coming/going to x3 from x4
		via route x5 by means x6.

Here the x1 place of "nunklama" is the x1 place of "nu", and the other
five places have been pushed down by one to occupy x2 through x6.

For those abstractors which have an x2 place as well, the standard
convention is to place this x2 place after, rather than before, the
places of the gismu being abstracted.  The place structure of "nilklama",
the lujvo derived from "ni klama", is the imposing:

	x1 is the amount of x2's coming/going to x3 from x4
		via route x5 by means x6, measured on scale x7.

It is not uncommon for abstractors to participate in the making of more
complex lujvo as well.  For example, "nunsoidji", from "nu sonci kei djica",
which in English is an "event-of being-a-soldier desirer", might have a
place structure something like:

	x1 desires the event of (x2 being a soldier of army x3)
		for purpose x4

This lujvo is quite different from "soidji", a "soldier desirer", whose
place structure could be:

	x1 desires a (soldier of army x2) for purpose x3

A "nunsoidji" might be someone who is about to enlist, whereas a "soidji"
might be a camp-follower.  (These place structures are only devised for
the sake of this example, and are not official.)

Where such an ambiguity of meaning is not likely, however, "nun-" and similar
abstractor rafsi may be omitted:  "kargau" (from "kalri gasnu") is a sensible
lujvo for "opener, one who opens something" (see Example 10.2), and need
not be expressed as "nunkargau".

One use of abstract lujvo is to eliminate the need for explicit "kei" in
tanru:  "nunkalri gasnu" means the same as "nu kalri kei gasnu", but is
shorter.  In addition, many English words ending in "-hood" are represented
with "nun-" lujvo, and other words ending in "-ness" or "-dom" are
represented with "kaz-" lujvo ("kaz-" is the rafsi for "ka"); "kazblanu"
is "blueness".


12. Table Of Abstractors

The following table gives each abstractor, an English gloss for it, a
Lojban gismu which is connected with it (more or less remotely: the
associations between abstractors and gismu are meant more as memory hooks
than for any kind of inference), the rafsi associated with it, and (on
the following line) its place structure.  Some abstractors do not have
rafsi, in which case a rafsi or pair of rafsi associated with the related
gismu may be used instead, by convention; thus "li'i se tuple", the
experience of having a leg, might be expressed in a rafsi as
"lifrysuctyseltuple".  (This lujvo may be thought no better than the
selbri from which it is made, but at least the possibility of making it
exists.)

nu	event of	fasnu		nun
		x1 is an event of <the bridi>
ka	property of	ckaji		kaz
		x1 is a property of <the bridi>
ni	amount of	klani		nil
		x1 is an amount of <the bridi> measured on scale x2
jei	truth-value of	jetnu		jez
		x1 is a truth-value of <the bridi> under epistemology x2
li'i	experience of	lifri		lifrysucty
		x1 is an experience of <the bridi> to experiencer x2
si'o	idea of		sidbo		sidbysucty
		x1 is an idea/concept of <the bridi> in the mind of x2
du'u	predication of	-----		dum
		x1 is the bridi <the bridi> expressed by sentence x2
su'u	abstraction of	sucta		sucty
		x1 is an abstract nature of <the bridi>
za'i	state of	zasti		zastynun
		x1 is a state of <the bridi>
zu'o	activity of	zukte		zuktynun
		x1 is an activity of <the bridi>
pu'u	process of	pruce		prucynun
		x1 is a process of <the bridi>
mu'e	point-event of	mulno		mulnynun
		x1 is a point-event/achievement of <the bridi>

-- 
John Cowan	cowan@snark.thyrsus.com		...!uunet!lock60!snark!cowan
			e'osai ko sarji la lojban.