There isn’t correlation between these inscriptions and implied contents (since he could have put the key and dagger in either box), but there /is/ correlation between {the inscriptions and contents} and the king’s honesty. The king didn’t lie and he wouldn’t have put inscriptions and contents into such an arrangement that would make it true that he lied. This puts a constraint on how he could arrange the inscriptions and contents.
Salient point: why you mention arrangements of inscriptions and contents at all? That is what confuses me. Either the arrangements matter at some point—such as inscribing—in which case there had been a lie when the king labeled an (apparently?) empty box with “This box contains the key.” (not “this box doesn’t contain the dagger”, which would have been true), or not at all, in which case I reiterate my previous question.
There isn’t correlation between these inscriptions and implied contents (since he could have put the key and dagger in either box), but there /is/ correlation between {the inscriptions and contents} and the king’s honesty. The king didn’t lie and he wouldn’t have put inscriptions and contents into such an arrangement that would make it true that he lied. This puts a constraint on how he could arrange the inscriptions and contents.
Salient point: why you mention arrangements of inscriptions and contents at all? That is what confuses me. Either the arrangements matter at some point—such as inscribing—in which case there had been a lie when the king labeled an (apparently?) empty box with “This box contains the key.” (not “this box doesn’t contain the dagger”, which would have been true), or not at all, in which case I reiterate my previous question.