Subject: RECORD:Quantifiers

From: [email-masked]
Date: Fri, 15 Mar 2002 14:50:55 EST

(A summary of the recent discussion, with allowance that some involved may 
not quite agree with some points here.)

1. There are four patterns of quantification in Lojban: {Q broda}, {Q da poi 
broda} and {Q da zo'u ... da broda} and {Q da broda}. The first two belong 
together, the first being an abbreviated form of the second when possible. 
The second two also belong together, the second being an abbreviated form of 
the first when possible. The ultimate basic form of quantification is the 
third form; others are defined in terms of this as abbreviations in complex 
situations.

2. {Q (da poi) broda} with an unmarked Q, presupposes that the set of broda 
has members, is not the empty set. This presupposition can be overridden by 
using a negative quantifier {Q ni'u} (which automatically changes the 
internal quantifier on {lo broda} to {ro ni'u} ) or by returning to the 
explicit forms of unrestricted quantification ("uni-sortal" -- variable 
ranging over everything, not just over brodas).

3. In returning a sentence to basic notation, unmarked Qs are interpreted 
only after all operations have been performed (especially moving negations 
around) and after sentences which are not conjunctions in the ultimate form 
are prefixed with {ge de broda gi} for every {Q (da poi) broda} in the 
sentence. Similarly, {Q ni'u} is interpreted after prefixing {ganai de broda 
gi} to the basic sentence if it is not a conditional.

4. For unmarked Qs in the {Q (da poi) broda} format, all of the usual 
negation moves hold: ro = no... naku = naku mei'ro = naku su'o ... su'o and 
so on for all the regular quantifiers of the Aristotelian set (A = ro, E = 
no, I = su'o, O = me'iro). With negative quantifiers {Q ni'u} the quantifier 
inside a negation will be non-negative and, conversely an unmarked quantifier 
in side a negation will result in a negative quantifer. These latter factors 
are only relevant when and where negative quantifirs are used.