* Saturday, 2014-10-18 at 18:21 -0300 - Jorge Llambías <jjllambias@gmail.com>:
> On Sat, Oct 18, 2014 at 3:09 PM, Martin Bays <mbays@sdf.org> wrote:
> > (i) a bridi operator operates on the bridi immediately under
> > construction, i.e. the lowest in the tree;
> > (ii) a logical connective acts as a bridi operator, connecting the
> > two formulae obtained by substituting each connectand in turn
> > for the connected element.
>
> Right, so for each context in which "ko'a .e ko'e" may appear, we need to
> know whether the context introduces a bridi of its own.
Yes. Similarly for contexts in which other logically connected
constructs may appear. So we're not so much discussing how to handle
complex sumti in various contexts, as discussing which constructs
introduce bridi.
> As I see it, having to know that is tantamount to having a rule for
> each context.
Well, a rule for each construct. We need to know how to interpret each
construct in the grammar (obviously!), part of which is determining
whether it introduces a bridi. The handling of logical connectives then
follows by (i) and (ii) above, and similarly for other bridi operators.
> I don't really know how mex work, so I'm only asking questions at this
> point. I would expect that "na'u sinso mo'e ko'a .e mo'e ko'e" within mex
> would work in the same way as "lo sinso be ko'a .e ko'e" outside of mex. I
> take "na'u" to be the mex equivalent of "lo", since it converts a predicate
> into a function. I don't know exactly why the language needs a parallel mex
> sub-language, but if it's going to have one it should at least work as
> closely as possible to how the main language works. If "na'u sinso" does
> not introduce a bridi of its own, why would "lo sinso be", which has the
> same meaning, do?
Right, so we come back to the question of whether the underlying logic
has functions. If we declare that it's purely relational, then all the
constructs which have the form of functions - operators, qualifiers,
non-logical connectives, and I guess also {jo'i} (this list should be
exhaustive) - must actually translate to relations, so it's natural that
they should introduce sub-bridi.
It's certainly true that purely relational logics are easier to reason
about, and that there's no loss in expressivity when eliminating
functions in favour of relations.
But it still feels very counter-intuitive to me that these things which
look like functions shouldn't just be functions.
Maybe it's worth considering utility again briefly, in this rather pure
case of operators. Mex may be an obscure part of the language, but I can
think of examples where having operators be functions gives useful
results; e.g.
li no pi'i mo'e ro namcu du li no
li xy mleca li re .e se ni'i bo ci
(I'm also assuming here that {li} doesn't introduce a bridi.)
The first one is also true with the relational semantics, but I'm not
sure it expresses the same thing (I'd translate it as "the thing which
is 0 times anything is 0", so the fact that such a thing exists becomes
a presupposition rather than a statement). The only examples I can think
of where you even get something that makes sense are ones of this kind
of form.
(Yes, I know, this is a part of the language which hasn't seen much use
anyway, so arguments from utility can't have much force here... but the
situation seems pretty similar with LAhE and JOI and so on.)
> > So this handling of {mo'e ko'a .e ko'e} involves a "new rule"?
>
> Yes, "mo'e" converts a (logical) sumti into a (logical) operand, i.e. it
> doesn't really do anything meaningful since logically a sumti and an
> operand are the same thing. All it does is take a term from the standard
> form of the language and put it in a from that can be used within mex. We
> do need to specify as an additional rule what happens when instead of
> giving it a logical sumti we give it a pseudo-sumti, something that is
> morphologically a sumti but logically something else. Since operands also
> have their corresponding pseudo-operands, it might very well make sense to
> say that "mo'e" also converts pseudo-sumti into their corresponding
> pseudo-operand, i.e. that "mo'e ko'a .e ko'e" is "mo'e ko'a .e mo'e ko'e"'
OK. We get the same results, though, if rather than explicitly
specifying these rules for complex sumti, we just say that {mo'e}
converts a *term* to an operand, and use the usual rules to get terms
out of complex sumti for this to apply to.
> Now "mo'e ro da" would be the way to do quantification within mex (though
> there's no pseudo-operand corresponding to "ro da" in the way that "mo'e
> ko'a .e mo'e ko'e" corresponds to "ko'a .e ko'e").
Right, so here thinking about it as I just described is also helpful
- the resulting operand is just {mo'e da}, and the quantification
happened when we parsed the {ro da}.
> But then the argument for "mo'e" would seem to apply just as well to "li"
> for the reverse direction, in which case "li pa .a re" would have to be "li
> pa .a li re". This unfortunately makes li-clauses break the sumti-6 being
> pure terms rule.
I don't think we should really worry about that rule. It would be neat
if it worked out to be true, but there's plenty in the grammar that
isn't and can't easily be made neat.
> > > The operator "na ku zo'u" is only well defined when
> > > applied to a single proposition. When applied to multiple propositions at
> > > once, who knows how we want it to act. Maybe it should be distributive.
> > I guess it could! Yet another thing to be decided. Do you think it might
> > be a bad idea to decide that it's equivalent to "na ku go broda gi
> > brode"?
>
> Why "go"? That would mean that one of the propositions is true and the
> other false. What would be the generalization to "na ku zo'u tu'e broda .i
> brode .i brodi tu'u"? Or did you mean "ga"?
Sorry, I meant {ge}. (the vowels are in a contiguous line in dvorak...
more of a problem for lojban than for most languages!)
Is there a reason not to declare that {na ku zo'u tu'e broda .i brode}
is equivalent to {na ku zo'u ge broda gi brode}?
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