Potassco: The Answer Set Solving Collection

>> 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).

Thank you. You convinced me to read the paper, and so far I’m loving it.

Thanks, that's a nice example.

>> 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?

ASP has both classical negation and negation-as-failure, but that is not quite why I'd say it is "more declarative". Prolog is capable of performing "imperative" tasks (by this I really mean side effects), while ASP solvers exclusively find stable models (answer sets) that may (or may not) exist for a given logic program. In ASP you can only declare a model with your input, and the output is either one or more stable model(s), or the knowledge that the model was unsatisfiable.

You are right about it being more than just a "modeling language to solve combinatorial problems", I agree that description sells it a bit short. As you pointed out, it is well suited for problems involving non-monotonic reasoning and uncertainty. You can encode reasoning that is more reality-hardened, with logical rules to deal with imperfect information.

Potassco is a wonderful collection of software. I have used clingo recently to prototype some puzzle ideas that I had. After encoding the rules in ASP I could quickly produce a single model through clingo to see if the puzzle design was feasible or not. (I also decided to use clingo to enumerate the solution space, but it turned out to be much bigger than I anticipated and after ten days I terminated the process with just shy of a billion solutions found...)

Since then I have been dreaming of using it to actually power puzzle software, where a single logic program could be used for both puzzle generation and validation. But that's not even the only "power couple" I can think of with respect to clingo/ASP integration. There are a number of hard problems that benefit from the declarative approach and could leverage the power and speed of a solver like clingo. And with libclingo this is now a feasible option to transform your problem into an ASP program, call clingo, then transform the answer set into your solution.