the preternatural intelligence of AI

[dr.mt...@gmail.com]

The rebuild of the site continues.

*  New standard library - adding the calendar program and correcting

                                            a bug with FOR 

*  Fixed THORN - an installation bug fixed and a deep and horrible bug

                              fixed as THORN moves from v 20 to 21.  BTW anybody who tried

                             to install THORN previously and got an error message should

                            try again with the new download.

*  TBoS 5th edition online - high res jpg indexed by chapter, section and

                                                by also aphabetically by index entry

* Shen/tk - as said > 90 pages of doc

The current changes revolve over the Logic Lab where I have revised the

doc.  I also set out to build a new logic compiler because the old one 

was IMO inelegant (though it worked).   The old compiler was a dense 

166 loc and the new one 66 loc; also dense.   The time taken to develop this 

due to AI was cut wrt traditional methods.  

AI is really a boon to me for debugging.  It is has now adapted to me so

well that it is almost telepathic.   I'll give an example.   Deduction rules are

sometimes non-deterministic - they can be legally applied in more than one 

way to give different results though functional programs naturally return only

one result.   Hence this little conversation.

 Me: the problem is non-deterministic d-rules  

ChatGTP: Yes — that is the real architectural problem. 

 Me: there is a very elegant computationally intractable solution  

ChatGTP: Yes — I think I see it.

For a nondeterministic d-rule, take the current hypothesis list and consider all permutations of it. Run the ordinary deterministic compiled rule on each permutation. Every legal choice of matching hypotheses is thereby exposed as a first-match case.

That is exactly what I was thinking.  I don't want to sound harsh, but ... how many human beings could pull my thought out of the air like that?   Its scary in a way in the implications for a lot of white collar work, that something this smart can be around.

Now there was a solution forming in my mind about looking at restricted permutations.  But before I could articulate it ChatGPT beat me to the punch.

ChatGPT: The semantics are elegant; the brute-force realization is not.

But the permutation view tells us exactly what the efficient algorithm should avoid: exploring reorderings that differ only in irrelevant positions. For a rule with schematic hypotheses against a context of size , what matters is not all permutations, but the distinct ordered selections of hypotheses that satisfy the schematic matches. In the worst case that is

P(n,k)=(n−k)!/n!​

rather than n! .

If is small—and most derivation rules have only a few schematic hypotheses—that is a huge improvement. 

That is really really smart.  So I said - OK write the restricted permutation program and it did.

Just amazing really; the intellectual development in one year alone. :O

Mark