The idea of rights seems to be strongly, if not inextricably, connected to the idea of duties. As far as I remember in philosophy of law this is referred to as "reciprocity". If I must do something, then there must be somebody I owe that action to. Thanks to our legal system, if there's somebody violating my rights by their deeds I can claim my right instead of poking their eyes out or throwing in the towel. I know that this is a very trivial summary, but it's probably enough.
Today I was impudent enough to be riding my bike in the pedestrian zone. I was very slow and very careful. I wouldn't risk getting in trouble by being reckless. A woman I didn't even notice for she was nowhere near me, felt, so I must assume, bothered, for she shouted something about me not being allowed to ride my bike because of the sign that said so.
Now here's my trivial question: If I am not allowed to ride my bike in the pedestrian zone, which is a negative duty, whose right to what did I violate by not causing any trouble while still riding my bike? This might sound silly, but I really don't see it. Do the pedestrians have a right to not see anyone riding a bike? Of course they do have a right to not being hurt by cyclists, but they have that right everywhere, not just in the pedestrian zone, and not only cyclists have the duty to not harm pedestrians, so I don't see of which duty, corresponding to which right, that sign should have reminded me of. I hope there are other answers to this question than a reminder of common sense, the chance of causing or prevention of an accident or rule utilitarianism. Help me out?