Re: [lojban] Multiple-variable abstractions (WAS: Re: Reasoning by analogy)

[Jacob Thomas Errington <jake@mail.jerrington.me>]

On 2021-01-06 14:13, scope845hlang343jbo@icebubble.org wrote:

> An example of a sentence exhibiting that ambiguity might be {ko'a ce'o
> ko'e ckaji loka porsi}.  Would that mean {ko'a ce'o ko'e porsi} or {ko'a
> porsi ko'e}?  It would be ambiguous.
>
> A way to resolve such ambiguity might be to treat {lo ka broda} as a
> solitary sumti (not a sequence) when the {ka} phrase doesn't contain
> {ce'u}, but as a sequence when it contains multiple {ce'u}.  Such a rule
> could become unwieldy when the property contains many arguments, i.e.
> {lo ka ce'u broda ce'u ce'u ce'u ...}.  So, I might propose the
> following rule:
>
>    (1) The property is interpreted as a sequence when two or more {ce'u}
>        are explicity expressed within it.
>
>    (2) Otherwise (when there are zero or one {ce'u}), it is interpreted
>        as a solitary sumti (as opposed to a sequence).
>
>    (3) Any unexpressed places following the second {ce'u}, if any, are
>        assumed to be {ce'u}.
Rule 3 only really works in simple abstractions; how does one deal with 
situations like {lo ka ce'u broda lo pendo be ce'u}?
> This rule would introduce two questions: (A) How would one speak about a
> sequence with just one element?, and (B) How would one differentiate
> between properties with different numbers of arguments (arities)?
>
> If I say {ko'a ce'o zi'o ckaji lo ka ce'u porsi}, I'm speaking about a
> sequence containing one element, {ko'a}, but I'm not saying that {ko'a
> porsi}.  On the other hand, if I say {ko'a ckaji loka ce'u ce'u porsi},
> then it'd be true that {ko'a porsi}; it'd be the sequence {lo porsi ce'o
> lo se porsi be ri}.  The problem of specifying a sequence with just one
> element (A) is a challenged posed by Lojban's infix syntax, not by
> abstractors like {ka}.
I think a pretty reasonable interpretation of {ko'a ce'o zi'o} is a 
1-tuple. Reminds me of Python's syntax (x,) for a 1-tuple.
> Issue (B), however, does not suggest any easy solutions.  Would {lo ka
> ce'u broda ce'u} be a property with two arguments, or a property with
> more than two arguments, such as {lo ka ce'u broda ce'u ce'u} or {lo ka
> ce'u broda ce'u ce'u ce'u}, with the trailing {ce'u} unexpressed?  It
> might be possible to quantify the number of arguments.
>
> A ternary property, {lo ka ce'u broda ce'u ce'u}, could be expressed as
> something like {lo ci ka broda} or {lo cimei ka broda}.  However, the
> tanru form would introduce the semantic ambiguity inherent in tanru.
> And the form with an inner quantifier might run afoul of Lojban's normal
> interpertation of quantifiers.
I'm not in favour of introducing an exception to the interpretation of 
inner quantifiers to be able to specify the number of arguments, 
especially when we're just cooking up new interpretations without 
consulting any existing usage. Right now, there is no situation where 
the number of arguments to a ka-abstraction is completely unclear. The 
overt {ce'u} in a ka abstraction each represent separate sumti places 
without any implicit tuple unpacking.
> This could be solved, however, by treating quantified abstractions as
> "magic", kind of like the way quantified variables of selma'o GOhA are
> treated magically in the terms of a prenex (preceeding {zo'u}).  I.e.,
> {ro bu'a zo'u broda} doesn't mean the same thing as {roda zo'u broda},
> because {ro bu'a zo'u} is magic.  So, if we consider {lo su'o ka} magic,
> could we use this mechanism to speak about multi-variable properties?

I don't agree that the existence of a wart in the language is a good 
justification for the introduction of new warts. Not to mention that 
following the shift in the last ten years to understand ka-abstractions 
as reified selbri, there isn't really any reason to use {bu'a} except 
maybe a slightly cleaner syntax. Ignoring syntax cleanliness, why say

  .i ro bu'a zo'u da bu'a

when you could say

  .i ro da poi selkai (zi'o) zo'u de da ckaji


I think that tuple unpacking / pattern matching is interesting, which is 
why I already solved this exact problem by leveraging the experimental 
cmavo {ce'ai}.

The way {ce'ai} works in general is that each sumti appearing in it is 
understood as a binder. We concocted {ce'ai} back in ~2013 when 
discussing how to reuse {ce'u} within a ka-abstraction. Here's a 
contrived example:

  without ce'ai: {.i mi ckaji lo ka ce'u goi ko'a batci ko'a}
  with ce'ai: {.i mi ckaji lo ka ko'a ce'ai ko'a ko'a batci}

The idea is to have something specifically for introducing ce'u-like 
bound variables, similar to the way {da} works in {zo'u}. My pattern 
matching idea extends the original definition of {ce'ai} to allow more 
complex sumti to appear in the {ce'ai}-clause, understanding them as 
patterns. For example:

  {ko'a ce'o ko'e ckaji lo ka X ce'o Y ce'ai X broda Y} interprets to 
{ko'a broda ko'e}

(I'm writing capital letters to stand for the equivalent BY cmavo.)

It's also aligned with usual programming language theory because we use 
the introduction form for tuples {ce'o} as a means of deconstructing the 
tuple.

Personally, I see many pros, and very few cons. In fact, the only con I 
can see is the use of an experimental cmavo. But using an experimental 
cmavo for something that's admittedly a niche application seems right on 
brand to me.

.i mi'e la tsani mu'o

P.S. are you a member of roljbogu'e discord server?


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