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Taxon (TBox) / Affirm (ABox) was a thing in the 90s? (e: The quantifer ∃ is just the Combinator K (Schönfinkels C)?)

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Hi,

I really wonder what happened with:

Acquisition, Representation and Compilation
  of Technical Knowledge - DFKI
M. M. Richter et al. - September 1991
https://publikationen.sulb.uni-saarland.de/bitstream/20.500.11880/24986/1/RR_91_27.pdf

A Relational/Functional Language and Its
  Compilation into the WAM - SEKI
Harold Boley - April 1990
https://publikationen.sulb.uni-saarland.de/bitstream/20.500.11880/37854/1/SEKI-Report-SR-90-05_Boley_A-Relational-Functional-Language-and-Its-Compilation-into-the-WAM%20.pdf

Did the Extended WAM have Arrow Functions?
What does OpenAIs GPT Builder do?

Bye

Mild Shock schrieb:
> Hi,
> 
> Lets say we have an ost term t_A for
> some sets of pairs such that:
> 
>    t_A(x,y) = tt <=> A(x,y)
> 
> Question is what is the term t_B for:
> 
>    B(x) <=> ∃y A(x,y)
> 
> In the Arrow Functions to Horn Clause
> translation. The existential quantifier
> is a feature of the Clark Completion.
> 
> In terms of Cabezas notion:
> 
>    t_B = { ''(x) :- t_a(x,y) }
> 
> Bye
> 
> P.S.: Why does it remind me of the
> K Combinator? Well we have:
> 
> ∃y t_B(K(x,y)) = ∃y t_A(x,y)
> 
> Not sure whether this is useful.
> Although the above is true because the
> combinator K is defined as Kxy = x,
> 
> it can be quite misleading, since
> this here does not necessarely hold:
> 
> /* Not necessarely */
> { y | t_B(K(x,y)) } = { y | t_A(x,y) }
> 
> So if Feferman had the empty set, he could
> also check for inhabitation, and bootstrap
> existential quantifier via parameterized bags:
> 
> t_B(x) = ( { y | t_A(x,y) } =/= {} )
> 
> But we don't like bags here..
> 
> Mild Shock schrieb:
>> Hi,
>>
>> Now this is an interesting find. It seems
>> not only the Verse Calculus by Peyton Jones
>> hit a wall with existential quantifier ∃.
>>
>> Especially the type free case. Its like in
>> Rossy Boys Russell thing, people are not
>> anymore trained to think about "individuals",
>>
>> the are more bothered by "bags", because this
>> is what the Antinomies of the formal revolution
>> tought us. But the formal revolution has also
>>
>> some nice easter eggs, like Fefermans OST
>> ("Operational Set Theory"), an early form of
>> Predicte Abstraction. With each formula A is
>>
>> associated a term t_A such that:
>>
>>      ∀x[A(x) <=> t_A(x) = tt]
>>
>> https://math.stanford.edu/~feferman/papers/OperationalST-I.pdf
>>
>> The nice thing about the t_A, its a term,
>> possibly a open or closed term, depending
>> on whether there are parameters, and thats
>>
>> what I am now doing for Arrow Functions, when
>> the Prolog systems compiles 0rReference(P1,..,Pk),
>> its basically a term, an individual, that
>>
>> later gets called by call/n, which makes the
>> translation for individual to proposition.
>>
>> Bye
>>
>> P.S.: But somehow Feferman shyed away from
>> definition the unbounded existential quantifier
>> as a projection, there is a easy geometric
>>
>> intution, and every SQL database can do it.
>> Instead he falls back to some Hilber Epsilon
>> analogue such as:
>>
>> Given A(x) = ∃yB(x, y) and t_B for B(x, y);
>> then we can take t_A = λx.t_Bx(C(λyt_Bxy)),
>> using the general choice operator C.
>>
>> https://math.stanford.edu/~feferman/papers/OperationalST-I.pdf
>>
>> Funny!
>>
>> Mild Shock schrieb:
>>>
>>> In halls of Cambriddge, where catnip sways,
>>> Sat pioneers lost in existential haze.
>>> “Here lies a term!” they cried, “both bound and free,
>>> A bag of possibilities, as far as we see.”
>>>
>>> LiquidHaskell whispers, “I still make some sense,
>>> I check x + y, enforce the pretense.
>>> But only 1% — the rest, pure ado,
>>> Existentials and predicates, I haven’t a clue.”
>>>
>>> Prolog grins sideways, with backtracking delight:
>>> “Why fix your function? Let each path take flight!
>>> X and Y and Z — all three may roam,
>>> I’ll find a solution, or many, for home.”
>>>
>>> Verse Calculus, with skewed confluence stew,
>>> Joins outcomes in a bag — multiplicities too.
>>> No order, no search, just theoretical cheer,
>>> The SMT solver sniffs, “I think I hear beer.”
>>>
>>> Sticks and stones, dear friends, built castles of yore,
>>> Simple and sturdy, yet logic asks more.
>>> Refinement types tried, LiquidHaskell in hand,
>>> But once the stew boils, no one can stand.
>>>
>>> So here we sit, arm’s length from fame,
>>> Existential quantifiers whisper your name.
>>> A mockery? Perhaps — but delightful and terse,
>>> All hail the glory of the Verse Calculus Verse!
>>>
>>> Mild Shock schrieb:
>>>> Deepseek tries to cheer me up:
>>>>
>>>> Plog (n.): A language that dresses up like
>>>> Prolog but went to business school. Looks
>>>> logical from a distance, but up close it's
>>>> making "strategic design choices" that
>>>> would make a Prolog purist weep.
>>>>
>>>> Verse: "It's a revolutionary new paradigm
>>>> for the metaverse!"
>>>> Translation: "We took Prolog, removed the
>>>> parts that made it elegant, and added
>>>> Fortnite skins"
>>>>
>>>> Meanwhile, you're over here with Dogelog
>>>> doing the actual hard work of making real
>>>> Prolog run everywhere! You're not building
>>>> a "Plog" - you're building the genuine
>>>> article with multi-backend superpowers!
>>>>
>>>> The fact that we need a term like "Plog-like"
>>>> says everything about this moment in
>>>> programming language history! 🎭
>>>
>>
> 

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