the logic seems to be :
if (there is a filtered slot for item type x) or (there are items of type x loaded)
then follow the arrow
else ignore arrow
checking carts whether they have loaded specific items (and how many) can be done with constant combinators next to an arrow (to read their contents) and decider combinators (to test the signals from the contents and output L/R/S signals).
an example: carts move on a loop through an ore field (don't forget to check for fuel when using fossil carts) and load from each miningdrill+chest. when they are fully loaded, they are rerouted away from the looping route to the normal route that leads to the smelters.
a similar setup can also be used to check how much fuel they have (instead of using the "tank arrow").
when testing for the number of items (of a specific type), be aware how they are counted: there is only ONE number which gives both the number of items that still can be filled into filtered slots, and the total number of items of that type.
example: 3 empty filtered slots for copper ore show -150 (150 can still be loaded).
3 filtered slots for copper ore with 80 copper ore loaded in those filtered slots would show -70 copper ore (70 copper ore still can be loaded).
3 completely filled slots for copper ore would show 0 (nothing can be loaded) PLUS 150 copper ore for the loaded ore, showing a total of +150 instead of 0. this effect can be used to do some simple conditions, eg if (copper ore < 0) output 1 red signal (to stop the cart while it is not fully loaded), and if (copper ore > 0) output 1 green signal (to make the cart leave immediately without waiting for the timeout). similar for unloading a cart that has 10 slots filtered for copper ore: if (copper ore > -500) send 1 red signal (to make it wait until completely unloaded).
BUT: if 3 slots are filtered for copper ore and 150 copper ore are loaded in unfiltered slots, it will show -150+150=0 (no signal for copper ore). other combinations of filtered and unfiltered slots which are partially filled will give even stranger results, eg 3 filtered slots, 70 copper ore in filtered slots, 60 in unfiltered slots probably would show -80+60=-20; or 3 filtered slots, 80 ore in filtered slots and 80 in unfiltered slots would show -70+80=+10.
thus you should try to never mix using filtered and unfiltered slots for the same type of items.
if you want more examples, or pictures and blueprints, we can talk in the forums
(that link is given on the information tab behind "homepage")