From jimc@MATH.UCLA.EDU Wed Mar 1 11:43:25 2000 X-Digest-Num: 380 Message-ID: <44114.380.2116.959273826@eGroups.com> Date: Wed, 1 Mar 2000 11:43:25 -0800 (PST) From: "James F. Carter" Subject: Re: Use and abuse of sets -----BEGIN PGP SIGNED MESSAGE----- On Wed, 1 Mar 2000, Jorge Llambias wrote an extensive reply to a post by lojbab... Since we're stirring the pot about mathematical expressions (MEX), I thought I'd toss in some comments about -gua!spi. I also was not entirely happy with the specialized grammar for MEX. A few small changes from Loglan/Lojban practice allowed an elegant solution. First, following a common mathematical practice, numbers are defined as equivalence classes of equal-count sets, e.g. "the number 2" means "the class of all pairs". The obvious extension is assumed to be feasible for extension rings and fields (e.g. fractions and decimal numbers). Next, mathematical functions are named by predicate words /brivla/ of the usual kind, defined to take such objects as arguments. First place occupants have the property of being in the result set; thus /lo'i/ (veridical set) should be the article used when an argument /sumti/ is made from the expression. "The sum of 2 and 3" is interpreted to mean "the sum of (the class of all pairs) and (the class of all triplets)", which comes out to be "the class of all pentads". Getting this definition to work right takes a little thought in the area of eliminating duplicate members while also not mixing triplets and quads with the pentads, but mathematicians have worked this out. The language's usual syntax for embedded arguments is used when a complex sub-expression occurs as an argument of the containing expression. - -gua!spi has a very simple syntax for embedded arguments. The syntax of Lojban is perfectly useable in this application. Units of measure are defined to multiply the second place argument (a number or other expression) by the unit. They would normally be used in restrictive subordinate clauses. "I weigh 70 kilograms" in Lojban would come out /mi tilju poi kilgrake lo'i mei ze no/. Assuming I haven't botched something in rusty Lojban, the unit of measure is actually semantically valid with current (?) place structures. I'm not presently able to say if this vision of MEX is presently 100% valid usage in Lojban, or if the only thing you need to use it is changes to the (non-baselined) place structures of the math functions. But I offer it as a simple and effective MEX grammar that's coherent with the core grammar of Lojban. For more on -gua!spi see http://www.math.ucla.edu/~jimc/guaspi/guaspi.txt (it's really in TeX, sorry for not having html for you to read). The discussion of MEX is about 80% through. The sample story that follows (550 words), intended to show that -gua!spi can express material from daily life, actually turned out to include a MEX naturally but essentially. James F. Carter Voice 310 825 2897 FAX 310 206 6673 UCLA-Mathnet; 6115 MSA; 405 Hilgard Ave.; Los Angeles, CA, USA 90095-1555 Internet: jimc@math.ucla.edu (finger for PGP key) UUCP:...!{ucsd,ames,ncar,gatech,purdue,rutgers,decvax,uunet}!math.ucla.edu!jimc -----BEGIN PGP SIGNATURE----- Version: 2.6.2 iQCVAwUBOL1y3Q394MqS4/yBAQF4pAP+NitfTG9OqlckiwWNpUOb/M71HXGed4jd PlXLv8pxjxSCxRotWtSikz46EgLh4l7/Qw6AyTEsfX9yVw8zJChlks9ccAhXDHBf TQLVteFHQBPUUDCCCndgLWvg0pyZFT7HasKJfIVaol4RYSHllnsiWCFlPNu7evph G8Mi55NjFyA= =4UUJ -----END PGP SIGNATURE-----