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I'm very new to mathematical logic and recently I've encountered with the notion of ASP (answer set programming) when I'm learning classical logic.

My question is that I don't quite get the point why there comes up the notion of ASP and I don't understand the relationship between ASP and classical logic.

More specifically, I'm learning what an answer set program of some propositional signatures looks like and that an answer set (or a stable model) is an interpretation that satisfies a kind of reduction of the answer set program. To me, this seems just like the relationship between a propositional logic sentence and an interpretation (or a truth value assignment) satisfying the sentence (or making the sentence true). I believe there must be some difference between the two problems that I have missed. Any help would be appreciated!

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