On Thu, Jul 16, 2015 at 1:23 AM, guskant <gusni...@gmail.com> wrote:For the same reason, I prefer the interpretation of "all true or all false" for {go} and "one and only one of them is true" for {gonai} to the interpretation of grouping of binary connectives.One problem with that interpretation for "gonai" is that it doesn't go well with "go ... ginai ... gi ..." and such. The natural Lojbanic interpretation is for "nai" to negate the following connectand. So "gonai A gi B gi C" would be true when A differs in truth value from B and from C."One and only one of them" is more useful, but hard to reconcile with the general pattern.mu'o mi'e xorxes
On Thu, Jul 16, 2015 at 7:30 AM, Alex Burka <dur...@gmail.com> wrote:So, to the question of that {gu} and {go} mean with more than 2 arguments, we kind of find ourselves with tradeoff between logic and ease of use.First I get nervous extending them to >2-ary at all, since it becomes harder to reason about the negations ({gonai X gi Y} is XOR, but {gonai X gi Y gi Z} is not, it's something strange instead -- and nobody can do truth tables in their head, even fluent speakers).The interpretations you list are undoubtedly useful (particularly the "which one out of these X alternatives"-connective is often asked for,"Which one(s) of the following" would be "ge'i ... gi ... gi ... gi ... ", right?though there is a workable solution using {moi}). But they do not correspond to the mathematical interpretation. For example, n-ary XOR is supposed to be true when an odd number of the arguments are true, which is not obvious (or often useful in speech). Changing this can cause difficulties with composition, for example logical transformations like De Morgans' laws will not work.The negation of "ga ... gi ... gi ..." is still "ge nai ... gi nai ... gi nai ..." and viceversa. And "go ... gi ... gi ..." should be equivalent to "go nai ... gi nai ... gi nai ... ", but that means "go nai" can't mean "one and only one of the following".