|
Previous
More about non-logical connectives |
If Wishes Were Horses: The Lojban Connective System
The Lojban Reference Grammar |
Next
Logical and non-logical connectives within mekso |
In addition to the non-logical connectives of selma'o JOI explained in Sections 14 and 15, there are three other connectives which can appear in joiks: ``bi'i'', ``bi'o'', and ``mi'i'', all of selma'o BIhI. The first two cmavo are used to specify intervals: abstract objects defined by two endpoints. The cmavo ``bi'i'' is correct if the endpoints are independent of order, whereas ``bi'o'' or ``sebi'o'' are used when order matters.
An example of ``bi'i'' in sumti connection:
16.1) mi ca sanli
la drezdn. bi'i la frankfurt.
I [present] stand-on-surface
Dresden [interval] Frankfurt.
I am standing between Dresden and Frankfurt.
In Example 16.1, it is all the same
whether I am standing between Dresden and Frankfurt or between
Frankfurt and Dresden, so ``bi'i'' is the appropriate interval
connective. The sumti ``la drezdn. bi'i la frankfurt.'' falls
into the x2 place of ``sanli'', which is the surface I stand
on; the interval specifies that surface by its limits.
(Obviously, I am not standing on the whole of the interval; the
x2 place of ``sanli'' specifies a surface which is typically
larger in extent than just the size of the stander's feet.)
16.2) mi cadzu ca
la pacac. bi'o la recac.
I walk simultaneous-with
First-hour [ordered-interval] Second-hour.
I walk from one o'clock to two o'clock.
In Example 16.2, on the other hand, it is
essential that ``la pacac.'' comes before ``la recac.'';
otherwise we have an 11-hour (or 23-hour) interval rather than
a one-hour interval. In this use of an interval, the whole
interval is probably intended, or at least most of it.
Example 16.2 is equivalent to:
16.3) mi cadzu ca
la recac. sebi'o la pacac.
I walk simultaneous-with
Second-hour [reverse] [ordered] First-hour.
English cannot readily express ``sebi'o'', but its meaning can be understood by reversing the two sumti.
The third cmavo of selma'o BIhI, namely ``mi'i'', expresses an interval seen from a different viewpoint: not a pair of endpoints, but a center point and a distance. For example:
16.4) le jbama pu daspo la .uacintyn.
mi'i lo minli be li muno
the bomb [past] destroys Washington
[center] what-is measured-in-miles by 50.
The bomb destroyed Washington and fifty miles around.
Here we have an interval whose center is Washington and whose distance, or radius, is fifty miles.
In Example 16.1, is it possible that I am standing in Dresden (or Frankfurt) itself? Yes. The connectives of selma'o BIhI are ambiguous about whether the endpoints themselves are included in or excluded from the interval. Two auxiliary cmavo ``ga'o'' and ``ke'i'' (of cmavo GAhO) are used to indicate the status of the endpoints: ``ga'o'' means that the endpoint is included, ``ke'i'' that it is excluded:
16.5) mi ca sanli la drezdn.
ga'o bi'i ga'o la frankfurt.
I [present] stand Dresden
[inclusive] [interval] [inclusive] Frankfurt.
I am standing between Dresden and Frankfurt,
inclusive of both.
16.6) mi ca sanli la drezdn.
ga'o bi'i ke'i la frankfurt.
I [present] stand Dresden
[inclusive] [interval] [exclusive] Frankfurt.
I am standing between Dresden (inclusive)
and Frankfurt (exclusive).
16.7) mi ca sanli la drezdn.
ke'i bi'i ga'o la frankfurt.
I [present] stand Dresden
[exclusive] [interval] [inclusive] Frankfurt.
I am standing between Dresden (exclusive)
and Frankfurt (inclusive).
16.8) mi ca sanli la drezdn.
ke'i bi'i ke'i la frankfurt.
I [present] stand Dresden
[exclusive] [interval] [exclusive] Frankfurt.
I am standing between Dresden and Frankfurt,
exclusive of both.
As these examples should make clear, the GAhO cmavo that
applies to a given endpoint is the one that stands physically
adjacent to it: the left-hand endpoint is referred to by the
first GAhO, and the right-hand endpoint by the second GAhO. It
is ungrammatical to have just one GAhO.
(Etymologically, ``ga'o'' is derived from ``ganlo'', which means ``closed'', and ``ke'i'' from ``kalri'', which means ``open''. In mathematics, inclusive intervals are referred to as closed intervals, and exclusive intervals as open ones.)
BIhI joiks are grammatical anywhere that other joiks are, including in tanru connection and (as ijoiks) between sentences. No meanings have been found for these uses.
Negated intervals, marked with a ``-nai'' following the BIhI cmavo, indicate an interval that includes everything but what is between the endpoints (with respect to some understood scale):
16.9) do dicra .e'a mi ca la daucac. bi'onai la gaicac.
You disturb (allowed) me at 10 not-from ... to 12
You can contact me except from 10 to 12.
The complete syntax of joiks is:
Example 14.3 in forethought becomes:
16.10) joigi la djan. gi la .alis. bevri le pipno
[Together] John and Alice carry the piano.
The first ``gi'' is part of the joigik; the second ``gi'' is the regular gik that separates the two things being connected in all forethought forms.
Example 16.6 can be expressed in forethought as:
16.11) mi ca sanli ke'i bi'i ga'o
gi la drezdn.
gi la frankfurt.
I [present] stand
[exclusive] between [inclusive] Dresden
and Frankfurt.
I am standing between Dresden (exclusive)
and Frankfurt (inclusive).
In forethought, unfortunately, the GAhOs become physically
separated from the endpoints, but the same rule applies: the
first GAhO refers to the first endpoint.
|
Previous
More about non-logical connectives |
If Wishes Were Horses: The Lojban Connective System
The Lojban Reference Grammar |
Next
Logical and non-logical connectives within mekso |