A Sample of MEX in -gua!spi Jim Carter , 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 '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 > degree1 plus all d E2 all all p's2 multiply3 all d V3 ]} %% \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 energy2 ] degree2 all all kelvin's2 multiply3 all mole3 ] ]} %% \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 ] change to2 [(to1) simple2 ]]]} %% \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 > same all nu's3 quotient2 all all E's2 derivative2 T3 ]]} %% 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) fast ]} ---- 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.