Is it logical to give in? No, especially not if you're a capable government.

Is it illogical that someone would react that way though? Not at all. Here is the logic: "Someone killed people in my country. I like people in my country. I happen to be a leader for my country. I'm responsible for their protection. I should prevent more people dying. Why are they dying? People are killing them. How do I make them stop? Give them what they want? What is it they want (now listening to them)?" etc.

This is why there is a "we will not negotiate with terrorists" rule. If not for that rule I think it'd work pretty well.