I have a sentence: "Ann introduces Marie to Jacob.' (I don't know how to do the syntax tree in Latex, I apologize if it looks awful). I need to do three things. First, determine the types associated with every node in the syntax tree. Second, assign the appropriate denotations of the appropriate types to the basic expressions that compose the sentence. Third, compose the denotations of the expressions sequentially to calculate the truth conditions of the sentence as a whole.
I know that "Ann introduces Marie to Jacob" is type T (for 'truth-value'). I know that "Ann" is semantic type E (for 'entity'). So, I know the sister node to "Ann" must be a function that takes E and delivers T: $<e, t>$. Hint: I'm assuming that "to" denotes type $<e,e>$.
However, at this point I'm stuck completing the rest of the question. Does anyone have any tips, suggestions or strategies for getting the rest of the types, denotations and computing the value?