[lojban] Re: priority of se and na/nai in logical connectives
namor
> There is no {se} in {iju} or {inaju}, so how does that tell you
> anything about which has priority?
Ah, the example should just show that your third line isn't equal to the
first, because the truth table is different, but as I ignored the 'se' by
seeing only left and right bridi of the connective instead of brodE and
brodA, it doesn't say anything.
> If you add a {se}, it's {inaseju}, which has truth table TTFF, i.e.
> the same as {iseju}, because the negation affects the
> truth-irrelevant side. The fact that {inaseju} is grammatical and
> {isenaju} ungrammatical also indicates that the negation always
> negates the bridi on its side.
Ok, it's easy to remember this way. I think I get it now.
na and nai indeed have higher priority.
But it seems it doesn't work to alter truth tables the way I did.
TTFF =nai> TTFF =se> TFTF (the way I tried to modify the tables) (Here, nai
affects only the logically irrelevant part and is thus ignored)
TTFF =se> TFTF =senai[='na']> FTFT (this way, it works) (Due to the se, the
nai logically becomes a na)
TTFF =nai[='na']> FFTT =se> FTFT ()
Seems it doesn't matter whether 'na'/'nai' or 'se' has higher priority, as
long as na and nai only affect their original bridi.
When working on examples (as you did Jorge) it is probably most convenient to
process 'na'/'nai' first and move the "na" together with the bridi when
applying 'se'.
When working on truth tables (as I did), I think it's easiest to apply
the 'se' on 'na' or 'nai' first, making the former modify the right side and
the latter modify the left side of the connective.
The order in which you actually apply the 'se'- or 'na'/'nai'-changes on the
truth table doesn't matter then.
Example:
broda segi'anai brode
= broda segi'a na brode
= na brode segi'a broda
(= broda gi'a na brode)
[=> TTFT]
Truth Table:
gi'a: TTTF =nai[='na']> TFTT =se> TTFT
Of course, as na/nai binds to broda/brode, you can simply ignore the se.
Thanks for your patient explaining xorxes
--
mu'o mi'e namor
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Pierre Abbat
> Hi, I was told {broda .isejanai brode} wouldn't make any sense since:
>
> broda AND NOT brode == NOT brode AND broda
>
> But the line
> "FTFT U with sentences exchanged and then second negated" from CLL:15:2
> indicates the contrary,
> for the order is the other way around.
> So it would rather be:
>
> broda AND NOT brode != brode AND NOT broda
>
> I also checked this by doing the swapping and then second-negating on a U
> connective myself and it made sense. If, however, I tried doing it the
> other way around it didn't work.
>
> Did I do a mistake or was I told wrong?
{se.a} is the same as {a}. {se} before a logical conjunction makes no
difference unless the conjunction is {u} (or ju, gi'u, etc.).
{na} before a conjunction, and {nai} after it, turn the conjunction into the
same conjunction with one argument negated. If the conjunction has {i}, {na}
comes after {i}, e.g. {inaja}.
To figure out what the grammar says, I'd have to peruse it, which I don't have
time for now. But I ran some sentences through jbofi'e, and {se} is applied
before {na} and {nai}.
Now can you figure out what {teju} and {veju} mean?
Pierre
Jorge Llambías
>
> The order in which you actually apply the 'se'- or 'na'/'nai'-changes on the
> truth table doesn't matter then.
Given a connective with the truth table 1234, where each number can stand
for T or F, {na} will change it to 3412, {nai} will change it to 2143,
and {se} will
change it to 1324. The {na} and {nai} shifts can be applied together
in any order
with respect to each other, in both cases applying na-nai we get 4321. But the
{se} shift must be applied to the truth table before the na/nai shifts.
1234 --> 1234
1234 -nai-> 2143
1234 -na-> 3412
1234 -na-nai-> 4321
1234 -se-> 1324
1234 -se-nai-> 3142
1234 -na-se-> 2413
1234 -na-se-nai-> 4231
The remaining 8 permutations are unreachable, but they wouldn't
produce any new truth table in any case.
> Thanks for your patient explaining xorxes
Thank you, this was interesting as I had never thought about it this way.
mu'o mi'e xorxes
namor
broda AND NOT brode == NOT brode AND broda
But the line
"FTFT U with sentences exchanged and then second negated" from CLL:15:2
indicates the contrary,
for the order is the other way around.
So it would rather be:
broda AND NOT brode != brode AND NOT broda
I also checked this by doing the swapping and then second-negating on a U
connective myself and it made sense. If, however, I tried doing it the other
way around it didn't work.
Did I do a mistake or was I told wrong?
mu'o mi'e nam
Jorge Llambías
> But the line
> "FTFT U with sentences exchanged and then second negated" from CLL:15:2
> indicates the contrary,
> for the order is the other way around.
broda .isejunai brode
= broda .iseju na brode
= na brode .iju broda
i.e. true whenever brode is false (FTFT).
(The wording "U with sentences exchanged and then second negated"
is not very clear. What is "the second"? The original second, or the
second after the exchange? In fact it's the original, brode, as can be
seen from the truth table,)
Similarly:
broda .isejenai brode
= broda .iseje na brode
= na brode .ije broda
(= broda .ije na brode)
(= broda .ijenai brode)
mu'o mi'e xorxes
Jorge Llambías
> Am Mittwoch 11 Juni 2008 01:50:13 schrieb Jorge Llamb�as:
> > broda .isejunai brode
> > = broda .iseju na brode
> > = na brode .iju broda
> >
> > i.e. true whenever brode is false (FTFT).
>
The three lines have the same meaning. The truth table FTFT refers
to the two things connected by {isejunai}, i.e.
broda brode broda.isejunaibrode
T T F
T F T
F T F
F F T
> For the last line, however, this isn't true as far as I understand, as: {na
> brode .iju broda} is FFTT, not FTFT.
The third line is just another way of writing {broda isejunai brode}.
The table FTFT corresponds to the truth values of the whole thing
as a function of those of broda and brode
> Consider a truth table for {na brode .iju broda} or {brode .inaju broda}
> respectively.
> Here, A is the first (brode) and B is the second (broda)
> A B R(esult)
> T T F [(not true) whether or not true]
> T F F [(not true) whether or not false]
> F T T [(not false) whether or not true]
> F F T [(not false) whether or not false]
>
>
> This example, again, suggests se has higher priority than nai.
There is no {se} in {iju} or {inaju}, so how does that tell you
anything about which has priority?
If you add a {se}, it's {inaseju}, which has truth table TTFF, i.e.
the same as {iseju}, because the negation affects the
truth-irrelevant side. The fact that {inaseju} is grammatical and
{isenaju} ungrammatical also indicates that the negation always
negates the bridi on its side.
mu'o mi'e xorxes
namor
> = broda .iseju na brode
> = na brode .iju broda
>
> i.e. true whenever brode is false (FTFT).
For the first line, "i.e. true whenever brode is false (FTFT)" is true.
For the last line, however, this isn't true as far as I understand, as: {na
brode .iju broda} is FFTT, not FTFT.
Consider a truth table for {na brode .iju broda} or {brode .inaju broda}
respectively.
Here, A is the first (brode) and B is the second (broda)
A B R(esult)
T T F [(not true) whether or not true]
T F F [(not true) whether or not false]
F T T [(not false) whether or not true]
F F T [(not false) whether or not false]
This example, again, suggests se has higher priority than nai.
--
mu'o mi'e namor