Government and Binding Theory/Theta Theory

In our previous chapters, we have tracked down X-bar structures down to the minutest detail. Yet if we look back, there's something fundamental that our grammar is thus far yet to explain. When we utter this sentence:
(1a) I do my homework.
We know that the speaker does his homework. Yet when we utter this:
(1b) My homework does me.
We will not interpret "my homework" as the agent and "me" as the patient, even though (1b) makes no sense at all. This implies that there is something else going on, known as theta theory.
θ-grids and θ-roles.
We can see that when we use different verbs, the subject and object will take up different semantic roles. For example:
(2a) I saw him.
(2b) I helped him.
In (2a), "I" is the experiencer and "him" is the theme; in (2b), "I" is the agent and "him" is the patient. Note that in this book, we are more precise with our terminology: Patients actually receive the action, while themes don't receive anything.
As you have probably guessed, semantic roles are determined in the lexicon, next to verb entries. To differentiate between GB roles and the roles we've learnt in basic semantics, we will call semantic roles theta-roles (θ-roles) and the part of the lexicon dealing with theta roles is called the theta grid.
jump [__ Ø]&lt;agent&gt;
eat [__ (DP)]&lt;agent, patient&gt;
see [__ (PPfor)]&lt;experiencer, theme&gt;
Back to our (2a), "saw" is known as the predicate because it expresses the state or process in which the arguments, i.e. the sentence elements with thematic roles, are concerned. (This isn't a book on semantics, so we don't need the technical definitions.)
Assigning θ-roles.
When a predicate is introduced to our sentence, it assigns θ-roles to arguments. For example, in (2a), "saw" assigned the θ-role of experiencer to "I" and the θ-role of theme to "him". There's a small problem with this: Sometimes, more than one θ-role can apply to a subject, and the argument itself also plays a role in θ-role determination:
(3a) The mouse triggered an event.
(3b) The user triggered an event.
(4a) John tripped.
(4b) John tripped David.
In (3a), "the mouse" is an instrument while in (3b), "the user" is an agent. "An event" remains the patient. Likewise, in (4a), "John" is the patient and in (4b), "John" is the agent. Thus the object is known as the internal argument and its θ-role is assigned by the verb; the subject is the external argument, its θ-role affected by other factors like the object in (4).
As we have seen in (4), "David" played a role in determining the θ-role of "John", but so did "tripped". This suggests that it is V′ that assigns the θ-role to "John".
Yet there is another question to be asked. The subject is the specifier of the IP, which is a long way from V′. How does assignment occur over such a long distance? See, for example, how "see" assigns the role of experiencer in "I saw him":
Linguists have thus suggested the VP-Internal Subject Hypothesis:
The subject is the specifier of the VP.
This is what our VP looks like now:
Movement occurs to move the subject from the VP to the IP when we go from D-structure to S-structure:
With the VP-Internal Subject Hypothesis, we notice that theta roles are only assigned to sisters, i.e. nodes under the same mother. This leads to the Sisterhood Condition:
An element can only assign θ-roles to its sisters.
Also note that, as you can see in this stage, theta role assignment, like X-bar projection, occurs at D-structure. This is a very important concept, as we will soon see in the analysis of Chinese VPs.
Theta Criterion.
Apart from what we have seen above, we must note that it is impossible
This leads to the theta criterion, which is a principle. In Chomsky's words:
Each argument bears one and only one θ-role, and each θ-role is assigned to one and only one argument.
Now that we've learnt θ-theory, we can look at movement.