Question regarding Addition in Prolog

Master / Vertiefung Künstliche Intelligenz
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Question regarding Addition in Prolog
Hey altogether,

I have trouble understanding how ProLog(“I”) can finish additions and wanted to ask if somebody could help me in / explain the following case:

Knowledge-Base:
add(X,Y,Z). [1.]
add(X,zero,X). [2.]
add(X, s(Y), s(Z)) :- add (X,Y,Z). [3.]

Query:
?- add(s(zero), s(zero), W).
Is correct in case add (X, s(Y),s(Z)) when X = s(zero), Y = zero, and W=s(Z) [3.]; Therefore use Tail of the clause
?- add(s(zero), zero, s(Z)).
According to video: Correct in case add (X, zero, X), when X=s(zero) and Z = X [2.]: Therefore this leaves me with the following:
?- add(s(zero), zero, s(s(zero)).

So in my oppinion the Addition would be solved at this moment - I guess it would state “True” now? I also have the Result that W = s(s(zero), but how does that resolve? What happens to the first part of the equitation? I’m sorry if that would be obvious, but I’m just a little confused right now…

Thanks and kind regards.

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This is probably not what you are asking for, but are you sure you want to have the face 1. in your knowledge base? Unless I’m mistaken, it’s basically a fall-through case that let’s true be derived from any add/3 predicate.