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Demo of -gua!spi MEX

                   A Sample of MEX in -gua!spi
             Jim Carter <jimc@math.ucla.edu>, 5/18/90

In Loglan, and now in Lojban, a fairly elaborate syntax was proposed to
express mathematical expressions (MEX).  I have prepared this sample of
MEX in -gua!spi to show one trivial solution, and I am posting it to
the list following <lojbab>'s encouragement to get discussion going.

On analysing the MEX problem I came to the conclusion that the basic
syntax of the language, or a substitute of substantially equal
function, was both necessary and sufficient to express MEX, and hence
when designing -gua!spi I omitted any special MEX syntax, rather than
inventing a separate but equivalent syntax for MEX.  

However, I put some features into the core grammar specifically
anticipating the demands of MEX, such as default articles.  Since the
tones mark where arguments start there is no syntactic need to have any
articles, and hence I caused every case of every primitive word to have
a default article, to be added to the occupying argument if it has none
of its own.  Normally this is "xe" (pronounced "zhe"), corresponding to
Lojban "le", and the feature makes a -gua!spi sentence have noticeably
fewer words than the corresponding Lojban.  Now for MEX, numbers are
defined, as many mathematicians do, as "X1 is a member of the
equivalence class of all sets with N members". For example, a biplane's
wings are a set, which are equivalent in count to the brothers Gemini,
etc. ad infinitum, and this set (class) of sets is "the number two". 
Then the appropriate article for a case for a number, provided by
default on math functions, is "xu" ("all", "lea" in Old Loglan, changed
I think in Lojban), so the case occupant might mean "all pairs".  

What follows is a translation of a short paragraph from a physics
textbook.  It is hard to demonstrate how neat a certain feature is of
-gua!spi to listeners who do not know the language, and so I have
provided three translations:  First, a (nearly) word-for-word
translation, then the original English, and finally a mechanical
translation with phrases marked.  In the latter, [] encloses a sentence
(as in an abstraction), <> encloses a modal or subordinate clause, \\
encloses the anaphoric copy of the restricted phrase (internally
generated), and () encloses the antecedent of any other pronoun.  The
main predicate of each argument has the case number appended ("vo" =
"to" is the predicate of an abstraction).  The translator uses word
order and possessive apostrophes which are often correct in describing
life situations, but which get in the way of the mathematics.

The letterals and equations are written out as if spoken (analogous to
"forty two dollars and seventeen cents"); presumably in a real
mathematics text they would be written as letters.

One form lacking in the paragraph is a good, clear dimensioned
quantity, so I have added a difficult one at the end.  

Perhaps the most useful thing you could do with this passage is to
translate it into Lojban using each of the competing MEX syntaxes, and
particularly, try using the core grammar with no MEX extension.  You may
have to create ad-hoc case specifications, and I don't believe Lojban
has a word for "derivative", which you will have to jury-rig.  There is
enough variety here to give you a broad, if brief, look at the
performance of each candidate.  

\x{^:i !kun   !vn-qci|qky ^vu-zu-jio !se-xo-pse   |vu-gr-tfyn
   !fi-va-ga-xim !dvla-qfle ^fi-ve-fta !tl-co  /fi-plw !dvla-xble 
   ^cmu !psla ^dvla-vzle  }
  {  Quantity energy hot absorbed-by some process anti-infinite
    (named           dQ)     by-rule    nbr.one    sum     dE
    product p      dV }
  { The heat absorbed in an infinitesimal process is given by the first
    law as dQ = dE + p dV.  (Actually d-bar Q; -gua!spi doesn't handle
    unusual letters yet.) }
{[argument energy's2 <hot \energy1\> <cargo/soak/ \energy2\ some
process4 <opposite infinity \process1\>> degree1 <performative name d Q2
\degree1\> plus all d E2 all all p's2 multiply3 all d V3 <standard
ordinal one1 \plus2\>]} %%

\x{^:i |vi-tl-co ^ja /zyn  !xo -kqer       ^dya     !kun   !qci   |qky
   ^kqa |gl-kri       ^fu-cmu    !jvyn   ^gzol /va-ga-xim !cfla-vzle }
  {     First    lets find some expression quotient amount energy hot
   big not increasing product    degrees moles named           cV }
  { Let us first obtain an expression for the molar specific heat cV
    at constant volume. }
{[imperative1 (all your2 (something's) set me3 (something)) discover
some mathematics2 to3 [(mathematics1) quotient2 all to's2 [the big1 <un-
property/increase/ \big1\> energy2 <hot \energy1\>] degree2 all all
kelvin's2 multiply3 all mole3 <performative name c V2 \quotient1\>]
<ordinal one \discover1\>]} %%

\x{^:o -sno              !cy !dvla-vzle }
  { Sufficient-condition zero    dV }
  { Then dV = 0 ...}
{[conjunction \discover1 11+22\ sufficient to2 [d V1 zero]]} %%

\x{^:o -sno              !can !so-vo-dem !jl ^vu-zu-dre-stl  !ci^cu^co
   !fu-psy |zu-plm !vo-dem !dvla-qfle ^dvla-xble }
  { Sufficient-condition change equation    (address    vector 5  2  1)
    simple example  equal      dQ         dE }
  { ...and (5.2.1) reduces simply to dQ = dE.  ("Example" is not very
    good; I need a word for "specifically".}
{[conjunction \sufficient1\ sufficient to2 [to [something1 same2
<object/address/ \same2\ to1 [five1 list all two2 all one3]>] change to2
[(to1) simple2 <set/example/ \simple2\ to1 [d Q1 same d E2]>]]]} %%

\x{^:o -sno              !dem !cfla-vzle |va-ga-zu-xim !zr-dya
   !vxln ^xbil    !qfle ^tfle ^vu-zo-kaw !gl-kri      -kqa
   !fi-zr-dya !vxln ^xbil !xble ^tfle ^vu-zo-kaw !gl-kri    -kqa }
  { Sufficient-condition equal    cV      name-of       quotient
    nu   derivative Q    T       status no-increase   size
    quotient   nu derivative E    T       status no-increase size }
  { Hence one obtains
             1 (dQ)    1 (dE)
       cV == - (--)  = - (--)
             v (dT)V   v (dT)V  
    (v for nu, subscript V means constant volume.  See note below on -kri.}
{[conjunction \sufficient1 22+8\ sufficient to2 [c V1 <performative name
\c V2\ all nu's3 quotient1 all all Q's2 derivative2 T3 <object/state/
\derivative1\ to2 [to1 [(derivative1) big] un- increase]>> same all
nu's3 quotient2 all all E's2 derivative2 T3 <object/state/ \derivative1\
to2 [to1 [(derivative1) big] un- increase]>]]} %%

>From Reif, Fred, "Fundamentals of Statistical and Thermal Physics",
McGraw-Hill, 1965, p. 156, "Specific Heats".  

\x{^:i !vbna-xau       =spa     |vu    -xi     -tiw-fli /fi-kua |dya
   !xdem =co-cy-ku ^bzen }
  {     boat roundtrip to space when (typical) stop fly    fast quotient
   meter  1  0  7   second }
  { When landing the space shuttle's speed is 107 meters per second. }
{[space's2 boat1 and1 (which's1) roundtrip2 (space2) <typical actor/stop/
\and1\ to2 [(and1) fly]> fast <quotient all all one zero seven's2 meter2
\fast1\ all seconds3>]}

---- Appendix on -gua!spi ----

If you're trying to pronounce the examples, tones are:

  /	rising		Starts or sometimes continues higher level phrase
  !	falling		Starts subphrase
  |	down-up		Starts subordinate clause (so does vu, ve, vi, va)
  ^	up-down		Starts another subphrase at the same level
  =	low-even	Compound word going in transitive case, usually X2
  -	high-even	Compound word for abstraction case, or parallel cpd.

Phonemes differing from Lojban are:

  c	ch		CHew
  j	dj		John
  q	sh		SHoe
  w	ng		stroNG
  x	zh		aZure, breZHnev
  y	i (short)	thIck, Idiot
  :	pause		hawai:i (this is a period in Lojban, but periods are
				 too hard to see in handwriting.)
  #	schwa		Among

About kri-status in the sentence with the derivatives: the modal phrase
modifies xbil-derivative, and hence the status is that the derivative
doesn't change size.  In reality it should say that the volume doesn't
change.  But the volume of what?  It's the gas undergoing the
infinitesimal process assumed in the first sentence, but that gas never
appears as an argument, and since I'm trying to demonstrate a point,
I'm not going to "improve" the original English very much.  When you
have a parser-organizer breathing down your neck that will point out
every little inconsistency in your text, you begin to wonder if
ordinary people will ever accept a logical language.