Hmmmm... How to catch a Logician...
I would take a single wooden sign and stick it in the middle of a field. The sign would read "There Is A Totally Dangerous Trap Here That Will Trap You." As the Logician walks by he will deduce that the purpose of a trap is to catch your opponent unawares and thus the sign cannot actually be trapped.
However, he will also deduce that there must be a trap somewhere in the vicinity if the sign is to have any purpose whatsoever (as a distraction from the actual trap). And it would be illogical for anyone to expend the energy to put up the sign for no purpose whatsoever.
Having conluded that there is a trap of some sort near him, but that it cannot be next to the sign itself, he will decide that the area around the sign is the safest immediate locale and move toward it. He will go behind the sign and see the back for the first time. The back will read:
"To travel from any point in space to any other point in space one must first cross half the distance (1/2 of whole). Then one must cross half of the remaining distance (1/4 of whole). And then, once again, cross half of the remaining distance (1/8 of whole). This traveling of half distances will continue to infinity, and never reach the whole value of 1. Therefore point B may never be reached by traveling from point A. Which means you can never escape from the area around this sign Logician. Yes, You Logician. MWAHAHAHAHA!!!
The Logician will then sit down and wait for capture. It would be illogical to expend the energy trying to escape when its been mathematically proven as impossible.
HA! Caught in a prison of your own logic! I'm so evil!
More elaborate traps to come. (I'm looking at you Sorrow!)