[lojban] Re: Question about BO w/mixed logical and non-logical connectives

Le mercredi 8 janvier 2020 05:46:43 UTC, scope845h...@icebubble.org a écrit :

coi rodo,

coi do

I have a couple of (3) questions about {BO} and how it behaves when it
is used in a sumti containing both logical (A) and non-logical (JOI)
connectives and/or tensed logical connections (A+PU+BO, JOI+PU+BO).

(I thought about posting this to the Lojban Beginners' list, but it
didn't seem like a beginners' question. Feel free to re-/cross-post if
you think that appropriate.)

{le xunre .e le crino .e le blanu .e le xekri .e le blabi} means

"(((the red and the green) and the blue) and the black) and the white",
but {BO} increases connective precedence and reverses associativity, so

{le xunre .e le crino .ebo le blanu .ebo le xekri .e le blabi} means

"(the red and (the green and (the blue and the black))) and the white".

This works with non-logical connectives, too, i.e.:

{le xunre joi le crino joibo le blanu joibo le xekri joi le blabi} means

"(the red with (the green with (the blue with the black))) with the white".

That's how {BO} is supposed to work. But what if your sumti contains
BOTH logical and non-logical connectives? Example:

{le xunre .e le crino .e le blanu joi le xekri .e le blabi}

or even:

{le xunre joibo le crino .ebo le blanu .e le xekri joi le blabi}

So, my questions are:

(1) Are the logical connectives (eks, jeks, etc.) and non-logical
connectives (JOI, BIhI, etc.) treated the same when it comes to
pairing-off connected sumti?

Yes.

Or are, for example, the non-logical
connectives given higher precedence than the logical connectives?
(A higher precedence for non-logical connectives would make it
easier to transform a bridi containing the sumti into
logically-connected bridi containing the non-logically-connected
component sumti.)

No.

(2) Is a {BO} attached to a non-logical connective treated identically
to a {BO} attached to a logical connective?

Yes.

Or does, for example,
a {BO} following {JOI} have higher precedence than a {BO} following
{A}?

No.

So I guess the problem comes from the difference between the basis for defining the logical connectives and that for defining the non-logical connectives.

Logical connectives are defined so that the truth value calculation can be performed #[1]. Sumtis connected by logical connectives are expanded to compound formulas. Logical connectives of sumtis without any selbrisni are meaningless because a selbrisni is required to have a truth value.

#[1] ...though the CLL failed in some points. See paradoxes explained by Xorxes and me at URLs below.

https://mw.lojban.org/papri/scope_of_na

https://mw.lojban.org/papri/na_go%27i/en

On the other hand, not all definitions of non-logical connectives are based on the calculation of formulas. Meaning of some non-logical connectives like joi seems to be defined based on sumti. No clear meaning is officially defined for joi used as formula connective, though lojban users may use it in a string and give a meaning to the string as long as it is grammatical.

That difference makes the meaning of mixed use of logical and non-logical connectives unclear.

Lastly, I am confused about the role of {BO} in tensed logical
connections, those of the form {A+PU+BO} or {JOI+PU+BO}. I.e.,

{le xunre .e le crino .ebabo le blanu .ebabo le xekri .ebo le blabi}

or even:

{le xunre .e le crino .ebabo le blanu joi le xekri joibo le blabi}

So, my third and final question:

(3) Does a {BO} required by a tensed connection {A+PU+BO} or {JOI+PU+BO}
(where the {BO} is NOT optional) have the same effect as a {BO} on
an untensed connective (where {BO}s are discretionary)?

Yes.

Or are
tensed logical connectives treated as being {BO}-less?

No.

By my
reading of the grammar, a tensed connection cannot be followed by
two consective {BO}s in a row, i.e. {.apubobo}, to disambiguate the
precedence intended.

Yes, I realize that the pragmatic solution is just to disambiguate any
potentially confusing connections using {KE}..{KEhE} parentheses. But
I'd like to know what the formal rules are for how these different kinds
of connectives interact with each other and with the cmavo {BO}. I
can't find anyplace in the CLL which speaks to this kind of interaction.

Much thanks in bo advance!

A tag like a tense can be inserted between a connective and a BO, but it does not change the behavior of BO. A tag followed by no BO but a sumti or a selbrisni forms a cluster. BO prevents that.

mi'e la guskant mu'o