>> Answer Set Programming (ASP) offers a simple and powerful modeling language to solve combinatorial problems.

I wonder if this isn't the completely wrong way to explain what ASP is for. I'm saying this because until recently I used to think of ASP just like that, a logic programming language that's good for optimisation problems and that is "more declarative" because it implements classical negation (a.k.a. default negation) and not just negation-as-failure as in Prolog (a.k.a. the closed-world assumption).

To be honest, I never though that's particularly interesting. But it turns out that there is a much more interesting motivation for ASP: nomonotonic reasoning, and the ability to represent uncertainty in a purely logical framework, a kind of proof-theoretical framework of reasoning with uncertainty.

This paper is what changed my mind:

Automating commonsense reasoning with ASP and s(CASP)

https://personal.utdallas.edu/~gupta/csr-scasp.pdf

And while I cringe a bit whenever anyone says the words "commonsense reasoning" (because it's typically neither common sense, nor much reasoning; in humans, let alone modelled by machines) the first few sections in the paper are a simple, plain-worded, straight-forward explanation of what ASP is really about that I think will speak to the heart of every logician who has ever looked at Baye's rule, looked at a gigantic, noisy dataset, and couldn't help thinking of the Mogwai and how you should never feed them after midnight lest they turn into Gremlins (like probabilities turn to statistics when you try to instantiate those random variables with actual, you know, numbers).

You can do cool stuff with s(CASP).

See https://swish.swi-prolog.org/p/non-monotonic_ilp.swinb

For an example. The potential hypothesis here are pre generated, but you can imagine an algorithm or adapt an existing one with a tight generalise/specialise loop.

But the scasp finds the two potential rules that cover both positive examples but not the negative example.

i.e.

flies(X,h8):-not penguin(X).

and

flies(X,h17):-bird(X),not penguin(X).

Which is cool.

>> For an example. The potential hypothesis here are pre generated, but you can imagine an algorithm or adapt an existing one with a tight generalise/specialise loop.

Yes! I'm thinking of how to adapt Louise (https://github.com/stassa/louise) to do that. The fact that s(CASP) is basically a Prolog-y version of ASP (with constraints) could make it a very natural sort of modification. Or, of course, there's always Well-Founded Semantics (https://www.swi-prolog.org/pldoc/man?section=WFS).

What's hyp_gen.pl?