# 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.
* Theta grids
* jump [__ Ø]<agent>
* eat [__ (DP)]<agent, patient>
* see [__ (PP$_{for}$)]<experiencer, theme>
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. (Note: In computing, an event is an action detected by a program to be handled by an event handler. For example, when you click on a hyperlink, you trigger an onClick event.)
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:
* 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:
* 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
* To have an argument sans θ-role: *He jumps me
* To have two arguments with the same θ-role: *I gave it to John to David
* to have an argument with two θ-roles: *I bought a pen was blue.
This leads to the theta criterion, which is a principle. In Chomsky's words:
* Theta Criterion
* 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.