The relationship panel gives you a clear vision of how visibility relationships are working in the picker.

UI overview:

Select an attribute button or its link-controlled picker items, and use the button to set or add them to the graph view.  
The graphing of items is not done automatically via picker selection so you need to manually do it.

The buttons show how the view will lay out the graph nodes.

The button can use to set the visibility operator of the picker item between the value "AND" and "OR".

The button resets the attribute link target value to their current values.

Some tips:

The graph above shows the logic of the visibility control, you just read from left to right to understand what is going on.

Double-click a graphic node in the graph to jump to the item-centric view, same rule applies when you double-click the link graphic node in purple color.

Select the link graphic node in purple color to select all relevant links in the picker view, selecting other graphic nodes will also sync the selection in the picker view.

LMB clicks on an attribute link target value inside [ ] to set a new target value for that picker item.

To set multiple picker item target values, select them and use the toolbar button. .

The viewport hotkey and interaction rule are similar to picker view, like for zoom in / out, etc.