The first inscription says that the inscriptions have the same truth value. If the second one is false then the first one implies that it is false which, in turn, implies that the first one is true. Contradiction. So the premise that “the second inscription is false” is false. So the second inscription is true.
The Jester’s logical inference is right. The point isn’t that the Jester’s logic was wrong—it wasn’t. It’s that the Jester assumed that the locations of the key and the dagger would follow the logic when there really was no good reason to assume so. This is meant to illustrate that making unwarranted assumptions about reality isn’t a good idea.
The first inscription says that the inscriptions have the same truth value. If the second one is false then the first one implies that it is false which, in turn, implies that the first one is true. Contradiction. So the premise that “the second inscription is false” is false. So the second inscription is true.
The Jester’s logical inference is right. The point isn’t that the Jester’s logic was wrong—it wasn’t. It’s that the Jester assumed that the locations of the key and the dagger would follow the logic when there really was no good reason to assume so. This is meant to illustrate that making unwarranted assumptions about reality isn’t a good idea.