From jjllambias@hotmail.com Mon Mar 11 08:55:58 2002 Return-Path: X-Sender: jjllambias@hotmail.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: unknown); 11 Mar 2002 16:55:58 -0000 Received: (qmail 11669 invoked from network); 11 Mar 2002 16:55:16 -0000 Received: from unknown (216.115.97.172) by m9.grp.snv.yahoo.com with QMQP; 11 Mar 2002 16:55:16 -0000 Received: from unknown (HELO hotmail.com) (216.33.241.4) by mta2.grp.snv.yahoo.com with SMTP; 11 Mar 2002 16:55:16 -0000 Received: from mail pickup service by hotmail.com with Microsoft SMTPSVC; Mon, 11 Mar 2002 08:55:16 -0800 Received: from 200.49.74.2 by lw8fd.law8.hotmail.msn.com with HTTP; Mon, 11 Mar 2002 16:55:15 GMT To: lojban@yahoogroups.com Bcc: Subject: Re: [lojban] More about quantifiers Date: Mon, 11 Mar 2002 16:55:15 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Message-ID: X-OriginalArrivalTime: 11 Mar 2002 16:55:16.0262 (UTC) FILETIME=[84D12C60:01C1C91D] From: "Jorge Llambias" X-Originating-IP: [200.49.74.2] X-Yahoo-Group-Post: member; u=6071566 X-Yahoo-Profile: jjllambias2000 la pycyn cusku di'e >Mine, also with a >few modifications, runs as follows: > >A+ ro broda cu brode >A- ro da poi broda cu brode >E+ no broda cu brode >E- no da poi broda cu brode >I+ [suo /lo /su'o lo] broda cu brode >I- (su'o) da poi broda cu brode >O+ me'iro broda cu brode >O- me'iro da poi broda cu brode Here's mine: A+ ro lo su'o broda cu brode A- ro broda cu brode E+ no lo su'o broda cu brode E- no broda cu brode I+ su'o broda cu brode I- naku no lo su'o broda cu brode O+ me'iro broda cu brode O- naku ro lo su'o broda cu brode >The Aristotelian quantifiers are in place, with the right readings, As they will be in any valid system, of course. >the + and >- are clearly marked (Q broda v Q da poi), That's the distinction of your system, yes. Little gain at too high a price, in my opinion. >all the transformations are >entirely regular They follow a rule, no doubt, but some of the relationships will be so hideous as to be unworkable. We have the following relationships among the quantifiers: Contradictories (negation of the whole thing): A- = ~ O+ A+ = ~ O- E- = ~ I+ E+ = ~ I- I- = ~ E+ I+ = ~ E- O- = ~ A+ O+ = ~ A- Complementaries (negation of the predicate): A- = E- ~ A+ = E+ ~ E- = A- ~ E+ = A+ ~ I- = O- ~ I+ = O+ ~ O- = I- ~ O+ = I+ ~ Duals (negation of the complement = complement of the negation): A- = ~ I+ ~ A+ = ~ I- ~ E- = ~ O+ ~ E+ = ~ O- ~ I- = ~ A+ ~ I+ = ~ A- ~ O- = ~ E+ ~ O+ = ~ E- ~ The Aristotelian system (A+,E-,I+,O-) has the contradictories within the system, but it loses the complements and the duals. The "existential" (pc's) system (A+,E+,I+,O+) has the complements within the system, but it loses the contradictories and the duals. The "modern" system (my choice) (A-,E-,I+,O+) keeps contradictories, complements and duals within the system. This has actual implications in the transformation rules for quantifiers. The prenex form by its very nature favours the "modern" system. These transformations will always hold at the prenex level, no matter what we do with the non-prenex forms: roda = naku me'iroda = noda naku = naku su'oda naku noda = naku su'oda = roda naku = naku me'iroda naku su'oda = naku noda = me'iroda naku = naku roda naku me'iroda = naku roda = su'oda naku = naku noda naku Each of the quantifiers can be expressed in terms of each of the others (its contradictory, its complementary and its dual). In the modern system, where the {Q da poi broda cu brode} form is maintained from the prenex form for all four cases (A-,E-,I+,O+), you can still use the very same transformation rules. You can always replace {Q da} by its equivalents. In the Aristotelian or existential systems, this is no longer the case: some of the substitutions will still work (different ones in each system), but most will not work directly, you have to make much more complex manipulations. And the same relationships that work for {Q da} will work for {Q broda} if {Q broda} is the same as {Q da poi broda}. Otherwise, you get into a maze of different rules depending on which level you're working at. For example, if you have {naku su'o broda cu brode}, and you want to express it in terms of {ro}, in my system you just change {su'o broda} to {naku ro broda naku}, and then you are left with {ro broda naku brode}. In pc's system there is no such simple substitution, you have to change the whole form to {ro da poi broda ku'o naku brode}. On the other hand, if you want to change to {me'iro}, you can use the same substitution, {su'o broda} is {me'iro broda naku} in both systems, so in both you get {naku me'iro broda naku brode}. So transformations are entirely regular in any system, yes, but the transformation rules of the modern system are much much simpler than in any other. >and all the forms are unmucky (mainly, to be sure, because >we have hidden the muck, but that is what definitions are meant to do). If there was a need for any of that, maybe I would understand it, but I don't get what the need is. mu'o mi'e xorxes _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp.