Suggested answer for Exercise 4
In the sentence John thinks that Jim knows that Mary gave his book to Jane there is a verb think which takes a clause as its argument. In this clause there is a verb know which again takes a clause as an argument. The verb think assigns two thematic roles: an experiencer to the DP John, which occupies the specifier of the vP in the D-structure, and a propositional, which is assigned to the CP in the specifier position of the VP. The DP John has to move to the specifier position of the IP in order to get Case from the finite I head. There is an abstract light verb in the v head which requires the main verb to adjoin to it. The CP is in a Case position but CPs do not need to be assigned Case, moreover, CPs avoid Case positions, so the CP moves rightwards and adjoins to the VP. Inside this clause the V head is occupied by the verb know, which takes two arguments: an experiencer in the specifier of the vP, which moves to the specifier of the IP for Case, and a propositional, which is a CP and occupies the specifier position of the VP. The verb adjoins to the light verb. The CP is again in a Case position, and moves to the right adjoining to the VP. Inside the CP, the V is occupied by the verb give. Give takes three arguments: an agent in the specifier of the vP, a theme in the specifier of the VP and a goal PP in the complement position of the verb. The DP Mary moves to the specifier of the IP, while the DP his book receives Case in its base position from the v head. The DP Jane is assigned Case in its base position by the preposition to. Besides all this the thematic verbs undergo the usual movements to the tense v and then to I, which appears in a simplified form in the tree to avoid a really disturbing abundance of traces (notice, however, that e.g. knows is made up of two morphemes, know and -s, so there should be two traces in tense v).
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