Negatives in signs

The grammar of warning signs is somewhat challenged by these examples, found within a few metres of each other in Hyde Park.

These icons are clear enough for me. Although, according to international standards, the red circle should be enough, in the UK we've never quite accepted its negative force,. So we tend to add a diagonal line to make sure.

But what I like about this is the additional prohibition: "It is an offence to damage this sign". I want to see that as a pictogram, please – the hand that was feeding the squirrel now attacking the sign with a hammer... all in a red circle with a line through it.

Pragmatically I'm fine with this, but it's a challenge to the sign regs pedant. A red circle generally means no whatever is depicted inside the circle. So this says 'no dogs on leads'... doesn't it?

So we'd need a dog with no lead in the circle... perhaps accompanied by a permissive sign for dogs with leads (generally white on blue).

This one seems to reflect the fact that No Cycling signs don't seem to work - the designer is just having a go at something different to see if it'll work. The black bike in a red circle apparently has come to mean 'cyclists welcome', if the pedestrianised shopping streets of Reading are anything to go by.