[lojban] Re: priority of se and na/nai in logical connectives

[namor <eldrikdo@gmail.com>]

Am Mittwoch 11 Juni 2008 16:53:45 schrieb Jorge Llambías:
> 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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