The legal answer is that the speed limit BEFORE the intersection is the speed limit THROUGH the intersection. The next question is - what is your speed relative to the speed limit?
If the speed limit is 30 and you are going 40, does that mean it is safe to go 40 through the intersection?
Whoops - Yes is the wrong answer.
Just like the 2 second rule when following another car, driving through an intersection has it's own set of conditions.
First - you are not operating in one direction. You have cars potentially crossing and at the same time cars in your direction and coming at you, possibly making turns. This is like playing 8 dimension chess!
So should you jam on the brakes and get down to the speed limit? NO.
While approaching an intersection, you need 2 buffer zones - one ahead and one behind. If you are to slow down you need to do this in plenty of time for the following car to slow down. Building up this buffer is the key to having the most flexibility in case of a rouge driver.
Now if there is no driver in front of behind, and you are going about the speed limit, your eyes not have to scan the intersection. Are there cars stopped? Might a car make a right turn on red? Are you blocked from other cars by a parked car or truck waiting to turn? If you cannot have a good view of the entire intersection, slowing down is not a bad idea.
The tricks mentioned before, about looking at pedestrian lights for clues if a light will change are still valid, as is the fac that yellow lights will not always give you the time to beat the red if going way under the speed limit.
Check you speed before going through the intersection and be ready to react to all the inputs.
I can see this is not finished yet....