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What is a theta role? Is it the same as a thematic role?
And what does it mean for a theta role to be undischarged/unsaturated? I came across these terms in a syntax paper. It seems like both undischarged/unsaturated were referring to the same effect. It might help to know what it means for a theta role to discharge/become saturated, and how it happens to discharge/become saturated.
There is a syntactic notion and a very closely related semantic notion of "thematic role" that are more or less meant to map onto one another. Essentially, a theta role is the label for how the referent of an NP acts in the event the sentence describes. So, in "John ate an apple", John is the eater, and the apple is the eatee. In linguistic theory we think we've come up with "general" theta roles that are what the syntax care about -- the eater in "John ate an apple", the kicker in "John kicked the ball" etc are "agents", the eaten thing and the kicked thing are the "patients". Mark Baker has proposed -- and it has been pretty standardly assumed to be true in Chomskyan syntax -- that these theta roles are tied to particular positions in the syntax (which is why "John loves Mary" and "Mary loves John" mean different things!). Theta theory says that each verb comes predetermined with a certain number of theta roles, and each theta role must be assigned to one and only one NP. That's why "John loves" doesn't mean the same thing as "John loves himself", and why "*John arrived Mary" isn't acceptable ("arrived" doesn't have an object theta role).
Theta role ≠ thematic role.
The term ‘thematic role’ is used fairly often in linguistic description to label the class of things like ‘agent’, ‘patient’, ‘goal’, ‘experiencer’, ‘instrument’, and so forth. These are semantic properties that most people take to be assigned by the verb or by adpositions to the various noun and adposition phrases occurring in the clause.
In English, the subject of an ordinary transitive verb usually receives the agent role, thus in ‘I hugged her’ the subject ‘I’ is the agent that does the hugging. But if the verb is passivized then the subject gets the patient role instead, thus in ‘she was hugged by me’ the subject ‘she’ is the patient. So thematic role (agent, patient, etc.) and verb argument (subject, object, etc.) are not identical.
The concept of theta role is basically limited to theories that descend from Government and Binding (GB). Other folks here have discussed it above so I’ll skip describing it. It arose from the concept of thematic roles, hence the use of the Greek letter θ. The idea of numbering them, as done in various flavours of GB, is due to Relational Grammar (RG) I believe. RG is also the source of the terms ‘unaccusative’ and ‘unergative’, describing the alignment of subjects of intransitive verbs with either agent or patient thematic roles and hence the syntactic consequences. (I think Geoff Pullum ranted about this in his Topic...Comment column under the heading “Citation etiquette beyond Thunderdome”.)
The idea of ‘saturating’ or ‘discharging’ a theta role is that on the one hand the verb has some theta roles to hand out to noun phrases, and that the noun phrases are sitting around waiting to get a theta role. If a verb ends up with extra theta roles, or if a noun phrase doesn’t get a theta role, then the sentence is ungrammatical (or its derivation ‘crashes’ in Minimalist terms). So noun phrases have theta roles that need to be saturated, and verbs have theta roles that need to be discharged. There are a couple of other terms such as ‘fulfilled’ and the like that are also used for the same phenomenon.
