Subject: Re: [lojban] RECORD:Quantifiers

From: "Jorge Llambias" <[email-masked]>
Date: Fri, 15 Mar 2002 20:48:56

la pycyn cusku di'e

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

I will note the points of disagreement for the record.

>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.

I basically agree, but one could add a fifth form,
{Q da poi broda zo'u da broda}. You probably include it
in the second form. Also, taking the third as basic is
somewhat arbitrary. It is also possible to start from the
{poi}-form and define {ro da} as {ro da poi ke'a du ke'a}.
(This is basically what the reference I quoted last time
does.) But this is just an additional comment, no real
disagreement here.

>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).

My system simply does not have this presupposition. In many cases
the set of broda has to be non-empty by conversational implicature,
but that's all. The reason for this is that it simplifies things
enormously, and nothing is lost as far as I can tell.

>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.

I suspect these rules work for Q=ro and Q=su'o, but not for
Q=no and Q=me'iro. Example:

no da poi broda cu brode
-> no da zo'u ge broda gi brode

And that would be it according to the rules. But you would
need to prefix {ge da broda gi} to give it existential import.
Maybe by "ultimate form" you mean ro/su'o forms, right?
In that case, you would go to:

-> ro da zo'u ganai da broda ginai da brode

and then yes, the rules tell you to add {ganai da broda gi}.
So perhaps it should be made explicit that "ultimate forms"
must be in terms of the positive quantifiers.

All these rules in point 3 are not needed in my system.

>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.

This is true in my system as well.

In my system, the complicated rules can be recovered by
marking the universals as {roma'u} and {noma'u}.

mu'o mi'e xorxes

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