A sign of confusion

Ok ... so I have a dilemma.  I got asked to dismount my bicycle a few weeks ago, as I was in a 'No cycling' zone, which I thought was a cycling zone.  When I tried to discuss the lack of logic in the signage with the PCSO's, they got quite hostile and effectively told me that 'rules is rules' and that the matter wasn't open for debate (don't you love it when people try to exert power, rather than enter into sensible discussion?).

Am I the only one struggling with the logic behind the signage?  Allow me to illustrate ... this sign was spotted at Southsea Pier.  It's clear, and I understand it.

The sign forbids dogs on the beach and has a red circle, with a dog inside it, with a red diagonal line through the dog.  It's message is clear ... a picture of a dog with a line through it = no dogs.

However, with my next photograph, the water gets a bit muddy.  The sign has a bicycle inside a red circle.  Following the same logic that was used for the above sign, there's no line through it, so that SHOULD mean that bicycles are permitted, as there's no line through it.

When I attempted to discuss this discrepancy with the PCSO, I was told that it was inside a red circle and that that clearly meant that cycling was prohibited, and that I should know that.

So, using the same logic, I guess the following sign states that doing 20 mph is prohibited.  Doesn't it?

You can see my dilemma.  On one sign, the diagonal line means something is banned, on another, the red border means something is banned, while on still another sign, the red border does not mean something is banned.

It's all clear as mud.  If you were thinking the confusion stopped there, try this one on for size ...

So, we have two cycle lanes, with clear images of bicycles painted on the road surface.  However, then there's a sign of a bicycle with a red border facing the cycle lanes, too?  So, it's a cycle lane where cycling is prohibited?

Congratulations, Portsmouth, on managing to communicate confusing and contradictory messages using internationally recognised symbols meant to make communication clearer.