Re: [lojban] Re: Cake, Pie or Ice Cream?

[John E Clifford <kali9putra@yahoo.com>]

But XOR doesn't continue to work with three elements (it's true on line one, 
when all three components are true, for example).  It gives rise to some 
interesting results, I recall, but not the same as "exactly one of".




----- Original Message ----
From: And Rosta <and.rosta@gmail.com>
To: lojban@googlegroups.com
Sent: Sun, January 9, 2011 12:31:45 PM
Subject: Re: [lojban] Re: Cake, Pie or Ice Cream?

Jorge Llambías, On 09/01/2011 14:44:
> On Sun, Jan 9, 2011 at 8:35 AM, Bob LeChevalier, President and Founder
> - LLG<lojbab@lojban.org>  wrote:
>> John E Clifford wrote:
>>
>>> The 'ji' solution to the choice question is very Logjamish; it is easy to
>>> picture JCB cackling with glee over it.  But it raises (not "begs"
>>> gawdammit) some further questions, all of which have been raised before and
>>> probably solved.  But, I don't remember the solutions and they may not be in
>>> the consciousness of many less-than-decades Lojbanists:
>>> 1.  What is the question to which "cream", "sugar, "neither" or "both" are
>>> *answers*, not merely side remarks that happen to do the job answers are
>>> meant to do?
>
> The one I prefer is:
>
>   lo kruji lo sukta zo'u do djica ma
>   "Cream, sugar: you want what?"
>
> The answers "lo kruji", "lo sukta", "noda", "roda". And if you want to
> be less than helpful: "pada", "su'oda", "me'ida", and so on.
[...]
>> We devised a solution, which no one else seems to have mentioned.  That
>> solution was eventually generalized in a different sense, so I am not
>> surprised that it was forgotten.
>>
>> The solution avoided ji altogether, and asked for selection from a set with
>> members specified by lu'i/lu'u.  More complex cases could be specified with
>> multiple set expressions (any 2 of set A) union (any 1 of set B).
>
> You don't spell out the solution. Presumably it was something like:
>
>    do djica ma poi cmima ... ce ... ce ... ce ...
>
> But you don't really need to use sets, you could also say:
>
>    do djica ma poi me ... .a ... .a ... .a ...

Symmetrical connectives reduce logically to quantification over sets.
"A or B (or C)" = "at least one from {A,B(,C)}"
"A and B (and C)" = "each one from {A,B(,C)}"
"A xor B (xor C)" = "exactly one from {A,B(,C)}"

alternatival OR is:

"A alt-or B (alt-or C)" = "which one(s) from {A,B(,C)}"
and for the alternatival exclusive OR:
"A alt-xor B (alt-xor C)" = "which one from {A,B(,C)}"

So I'd argue that "do djica ma poi cmima ... ce ... ce ... ce ..." is logically 
the most basic.

--And.

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