>> These techniques were invented from the field of AI, but that does not mean they remain in the field of AI.
Like I say above, it is pretty uncontroversial that these approaches are part of the field of AI research. You can consult wikipedia or e.g. the calls for papers from major AI conferences, AAAI and IJCAI, if in doubt.
So I have to ask again, why do you say these approaches are are not in the field of AI research? According to whom? And based on what?
I would please like an answer to the above question.
Further, I can certainly point you to successes of symbolic AI, which you say don't exist. For one thing, the entire fields of automated theorem proving, planning, search, game playing, knowledge representation and reasoning, etc. that you say are "not AI", but are like I say still active and still state of the art in their respective tasks. These are certainly successful- they have produced systems and techniques that still work best than any alternative and actually quite well.
For examples of specific systems that were successful in their time, see Logic Theorist [1] that proved 38 of the first 52 theorems in Principia Mathematica; Chinook [2], the first computer program to win a world championship against humans (in checkers/draughts); Deep Blue [3], the first AI system to defeat a human grandmaster (Garry Kasparov) in chess; MYCIN [4] the first AI system to outperform human experts in disease diagnosis (specifically, diagnosis of infections); and so on.
Of course these systems have been superseded - but they were successes nonetheless. Another reason to learn the history of AI is to become aware of those systems- they, indeed, were "there".
Again I have to ask you- where does your knowledge of AI come from? When you make such strong statements about what works and what doesn't, what failed and what succeeded, are you sure you are well informed? Do you draw your knowledge from primary sources, or are you trusting the opinions of others who claim to be experts- but may not be (like in the article above)?
>> How would you tackle this with ILP?
Below I've defined the problem in the format expected by Louise [5]:
?- list_mil_problem(ordered/3).
Positive examples
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ordered([a],[b,c],[d,e,f]).
Negative examples
-----------------
[]
Background knowledge
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shorter/2:
shorter(A,B):-length(A,C),length(B,D),C ?- learn(ordered/3).
ordered(A,B,C):-shorter(A,B),shorter(B,C).
true.
Like I say, this is a trivial problem, not least because its solution is easy to figure out and the background knowledge and metarules are trivial to define by hand. Louise can also perform predicate invention to define new background knowledge (kind of like inventing new features) and also new metarules. That is to say, Louise can learn the shorter/2 and length/2 programs, also from very few examples- and then reuse them as background knowledge. But showing how to do that would make for a larger example. I'm happy to oblige if you are curious.
I should point out that there exists no neural net approach that can learn the same (or a similar) program from a single positive example- not least because neural nets cannot make use of background knowledge (i.e. a library of programs from which to build other programs).
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[1] https://en.wikipedia.org/wiki/Logic_Theorist
[2] https://en.wikipedia.org/wiki/Chinook_(computer_program)
[3] https://en.wikipedia.org/wiki/Deep_Blue_versus_Garry_Kasparo...