logic
posted by anonymous .
Since the boolean interpretatrion doesn't acknowledge any relationship between categorical propositions but contradiction...if the two statements are related in some other way acknowledged on the square of opposition, such as through the relationship of contrarity, are we able to tell anything about the truth value of one under the boolean interpretation, given the truth value of the other? Is it always undetermined?

I am not sure I understand the question.
However, although you can not say one way or another about a converse or inverse, you certainly can say that the contrapositive has value "true"
eg:
Given:
If a cow, then a mammal
then
If not a mammal, then not a cow 
I don't know if this will be any clearer, but...
I just want to know if you have two categorical propositions that are related in some way on the square of opposition (but who's relationship is not recognized under the Boolean Interpretation), and you know the truth value of one of the statements (either true or false), can you tell anything about the truth value of the other statement under the Boolean Interpretation...