Re: [lojban] Re: tersmu 0.2

On Sat, Oct 18, 2014 at 3:09 PM, Martin Bays <mbays@sdf.org> wrote:

While, if you'll excuse me reiterating, I would say that given the
profusion of logical connectives and other bridi operators throughout
the language, it's better to give abstract rules which cover many cases
uniformly rather than think in terms of specific rules for each
situation; so in this case I would explain the situation with two rules:
(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.

That's fine, but we still need to identify what "the bridi immediately under construction" is.

> ) or we can say that there are no atomic functions, all functions are
> in fact built out of predicates. In this case, we just need to express
> the function in terms of a predicate, and then apply the rule we
> already have for "ko'a .e ko'e" as a pseudo-argument of an atomic
> predicate.

If I understand correctly, (i) and (ii) also explain these semantics;
the only difference is in whether LAhE introduces a bridi of its own.

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. As I see it, having to know that is tantamount to having a rule for each context.

Hmm... hold on, in {lo tu'o boi re lo mlatu}, we have to parse {re lo
mlatu} first as {re da poi me lo mlatu}. So I don't think any remei are
really involved.

If we assume that {lo [quantifier]} does introduce a sub-bridi, I guess
I'd expect
lo tu'o boi re lo mlatu .a ci lo gerku
-> lo poi'i me re lo mlatu .a ci lo gerku
-> lo poi'i ga me re lo mlatu gi me ci lo gerku
-> lo poi'i ga re da poi me lo mlatu zo'u ke'a me da gi ci da poi me lo
gerku zo'u ke'a me da
(which is a rather bizarre thing to refer to!).

You're right. This is one more argument for cardinal numbers being plural quantifiers rather than singular.

> We cannot claim that the rule for operand-3 always returns true logical
> operands, in the way that we could claim that sumti-6 (almost) always
> returns true logical sumti. "gek operand gik operand-3" is an operand-3,
> for example.

I would say that 'sumti' always returns a term, and so does 'operand',
where "term" is meant in the sense of logic, and where "returning" is
something that only makes sense in the context of the full parsing
algorithm, but is such that e.g. {ko'a .e ko'e} returns what ko'a is
bound to to one branch, while returning what ko'e is bound to to the
other branch - where these "branches" are what are created by the
semantics of logical connectives as in (ii) above. Similarly, {ro da}
returns the variable quantified over by the quantifier it introduces.

What I meant is that "sumti-6" need not contain any quantifiers or connectives operating on a bridi external to sumti-6, whereas the same can't be said for "operand-3". That's assuming that "li pa .a re" is not "li pa .a li re".

> So, I would not want to insist that "mo'e ko'a .e ko'e" is a logical
> operand, and indeed in my example I was not taking it as one. Since
> sumti and operands are logically the same thing, I was just ignoring
> "mo'e" and "li", and the question was whether "ko'a .e ko'e" operates
> on the predicate "sinso" or on the predicate containing the li-clause
> as its argument.

OK; so in other words you're taking {mo'e} to be transparent, i.e. not
to introduce a sub-bridi, but for the production 'mex' to be opaque and
to introduce a sub-bridi corresponding to the predicate "is the result
of applying [operator] to [operands]"?

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?

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"'

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"). Not sure what it could be used for though, since mex only has terms, no formulas.

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.

> Well, I'm not advocating this but we know that "na ku zo'u broda" expresses
> the negation of the proposition expressed by "broda", so it would not be
> out of the question to say that "na ku zo'u tu'e broda .i brode tu'u"
> expresses the negations of both propositions, rather than just the negation
> of their conjunction. 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"?

mu'o mi'e xorxes