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Re: [lojban] Mathy person interested in concept, unsure where to begin.

Well, in theory in general, every sentence is derived from a formula.  The question is whether we can automatically derive that formula from the sentence. The best (only?) way to test this is to see whether the formula team 2 derives from a sentence supplied by team 1 is the same formula that team 1 used to derive the sentence in the first place.  A weaker test is to see whether the automatically derived formula corresponds to the intuitive reading of the sentence as provided by proficient speakers who re logically sophisticated, etc.

Sent from my iPad

On Sep 24, 2014, at 14:04, Jorge Llambías <jjllambias@gmail.com> wrote:



On Wed, Sep 24, 2014 at 3:41 PM, 'John E Clifford' via lojban <lojban@googlegroups.com> wrote:
No, the worry is the opposite: whether every sentence of Lojban has a unique (up to equivalence, say) representation in logic which can be automatically derived.  

Right. As I said: 

Logic -> Lojban    trivial
Lojban -> Logic   very much non-trivial
 

Your project is indeed trivial until you throw in all the qualifiers: colloquial, compact, ergonomic (I have no idea what that means for a sentence, but it seems popular these days), unambiguous, etc.

Except for "unambiguous", I agree. The automatic translation from FOPL to Lojban is unambiguous, but usually not colloquial/compact/ergonomic.

 Then we clearly need a full set (whatever tat means -- enough for all the cases we know of or can think of, I suppose) of transformations, not just the "read it as written" (with a few easy additons) version that is trivial.

Right, that's very much a requisite for the Lojban -> Logic direction, and necessary also to achieve colloquial/compact/ergonomic in the Logic -> Lojban part.
 
By way of connecting all this up, the formula derived from a sentence is the same (up to equivalence, of course -- but maybe not even with that condition) as the formula from which the sentence is derived.  That is the test of the logicality of the language.  

The formula derived from the sentence derived from a formula is that same formula. That part is trivial. The problem are the sentences not derived from any formula (or not yet known to be derived from any formula).

mu'o mi'e xorxes

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