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Reflect on Sience not Frog Legs (Was: AGI will relieve the community)

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Hi,

Now this might come as a shock for this french
philosopher, who had that much problems with
Tennant's logical system called TROLL LOGIC.

Or was it core logic. Don't remember anymore:

 > Representation based comparison does seem to
 > work well on everything I’ve tested, e.g.,
 > “Monkey test” for transitivity and anti-symmetry
 > with repeat counts of 10,000,000.

Well there is balance between testing and proving
in computer science. You could say there is balance
between Inductive and Deductive science.

https://de.wikipedia.org/wiki/Induktion_(Philosophie)

You don’t need to test transitivity. You can
prove it! Mathematicians usually simply say
if < is a total order, then <′ is a total order:

     Theorem on Order Homomorphism

     Proof:
     Given rep:R→H, then define x<′y:⟺rep(x)<rep(y).
     If rep is injective, then <′ is transitive
     and anti-symmetric.

     Assume towards a contradiction that <′ is not
     anti-symmetric. Then we would have x,y such
     that x<′y∧x≠y∧¬x<′y. By definition of <′ and
     injectivity of rep we would have rep(x)<rep(y)
     ∧rep(x)≠rep(y)∧¬rep(x)<rep(y). A contradiction
     with < being anti-symmetric.

     Assume towards a contradiction that <′ is
     not transitive. Then we would have x,y,z such
     that x<′y∧y<′z∧¬x<′z. By definition of <′ we
     would have rep(x)<rep(y)∧rep(y)<rep(z)∧
     ¬rep(x)<rep(z). A contradiction with <
     being transitive.

     Q.E.D.

Bye

Mild Shock schrieb:
> 
> On the bright side, 500 more posts and we
> will have 2030. But then there will be a
> lready Artificial General intelligence (AGI),
> which will answer all your questions in a blink.
> Relieving the community from all pain and headaches.
> 
> We say that the hour of discovery cannot be
> forecast, but when we say this, we imagine
> that the hour is placed in an obscure and
> distant future. Never occurs to us that it has
> any relation to today. This day, or any day,
> could be the event.
> 
> Sometimes discovery comes in circles, shows
> us the dark hand of completely forgetting we
> each must eventually clasp. Nothing is more
> difficult than the loss of past knowledge,
> especially when it is our own end
> and AGI takes over.
> 
> ~~ Eulogy in Final Destination, Flight 180 Crash
> 
> Mild Shock schrieb:
>> Hi,
>>
>> Lee Naish’s idea for an infinite tree syntax:
>>
>> /* Lee Naish’s idea */
>> naish(X, Y) :-
>>     naish([], X, Y).
>>
>> naish(S, X, Y) :- compound(X),
>>     member(Z-Y, S), X == Z, !.
>> naish(S, X, Y) :- compound(X), !,
>>     length(S, N),
>>     X =.. [F|L],
>>     maplist(naish([X-'$IDX'(N)|S]), L, R),
>>     Y =.. [F|R].
>> naish(_, X, X).
>>
>> Now define a compare:
>>
>> naish_compare(C, X, Y) :-
>>     naish(X, A),
>>     naish(Y, B),
>>     compare(C, A, B).
>>
>> Works fine on this example:
>>
>> ?- X = s(s(1,Y),0), Y = s(s(1,X),1),
>>     naish_compare(C, X, Y).
>> C = (>).
>>
>> The residual problem is, that it is extremly slow. Much slower
>> than the native compare/3 which doesn’t use a stack, but a Union
>> Find structure. So conceptually total order and natural order
>>
>> compare/3 are easy, the hard part is making them ultra fast!
>>
>> Bye
> 

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Thread

The Million Dollar question of Prolog Mild Shock <janburse@fastmail.fm> - 2025-08-23 14:54 +0200
  AGI will relieve the community (Was: The Million Dollar question of Prolog) Mild Shock <janburse@fastmail.fm> - 2025-08-25 15:11 +0200
    Reflect on Sience not Frog Legs (Was: AGI will relieve the community) Mild Shock <janburse@fastmail.fm> - 2025-08-25 22:55 +0200
      Switching Gears: From Lee Naish to Peter Deutsch (Was: Reflect on Sience not Frog Legs) Mild Shock <janburse@fastmail.fm> - 2025-08-26 11:24 +0200
        Not for pratical use, only for educational use (Re: Switching Gears: From Lee Naish to Peter Deutsch) Mild Shock <janburse@fastmail.fm> - 2025-08-26 11:32 +0200
  Do Prologs Dream of Canonical Sheep? (Was: The Million Dollar question of Prolog) Mild Shock <janburse@fastmail.fm> - 2025-09-05 12:10 +0100
    Electing "conductor" Prolog variables (Was: Do Prologs Dream of Canonical Sheep?) Mild Shock <janburse@fastmail.fm> - 2025-09-05 12:13 +0100

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