Theta criterion

The theta-criterion (also named θ-criterion) is a constraint on x-bar theory that was first proposed by Noam Chomsky (1981) as a rule within the system of principles of the government and binding theory, called theta-theory (θ-theory). As theta-theory is concerned with the distribution and assignment of theta-roles (a.k.a. thematic roles), the theta-criterion describes the specific match between arguments and theta-roles (θ-roles) in logical form (LF):

Being a constraint on x-bar theory, the criterion aims to filter out ill-formed sentences. Thus, if the number or categories of arguments in a sentence do not meet the theta-role assigner's requirement in any given sentence, that sentence will be deemed ungrammatical. (Carnie 2007, p. 224). In other words, theta-criterion sorts sentences into grammatical and ungrammatical bins based on c-selection and s-selection.

Applied

Theta grid A theta-role is a status of thematic relation (Chomsky 1981, p. 35). In other words, a theta-role describes the connection of meaning between a predicate or a verb and a constituent selected by this predicate. The number, types and positions of theta-roles that a lexicon assigns is encoded in its lexical entry (Chomsky 1981, p. 38) and must be satisfied in syntactic structure following Projection Principle. The selection of a constituent by a head based on meaning is called s-selection (semantic-selection) and those based on grammatical categories are called c-selection. (Sportiche, Koopman & Stabler 2014, p. 141) Such information can be expressed with a theta grid. In the example below the verb 'love' has two theta-roles to assign: agent (the entity who loves) and theme (the entity being loved). In accordance with the theta-criterion, each theta-role must have its argument counterpart.

In Example 1a, Megan and Kevin are the arguments that the verb assigns the agent and theme theta-roles to, respectively. Because there is a one-to-one mapping of argument to theta-role, the theta-criterion is satisfied and the sentence is deemed grammatical (Carnie 2007, p. 225). Below are two examples where the theta-criterion has not been fulfilled and are thus ungrammatical.

Example 1b is ungrammatical (marked with *) because there are more theta-roles available than there are arguments. The theta-role theme does not have an argument matched to it. On the other hand, in example (1c), there are more arguments than theta-roles. Both theta-roles are matched to arguments (Megan with Agent and Jason with theme), but there is an argument left without a corresponding theta-role (Kevin has no theta-role) (Carnie 2007). Thus for reasons of inequality in number between theta-roles and arguments, with either having more than the other, the result will be ungrammatical.

Consequence on movement Since trace transmits theta-role, movements resulting in non-local relations between theta-role assigners and receivers in surface structure don't violate theta-criterion. This allows us to generate sentences with DP-raising, head movement, wh-movement, etc. However, if a phrase occupies a theta-position (complement or selected subject) in D-structure, it can no longer move to another theta-position or it will receive two theta-roles (Chomsky 1981, p. 46).

Special cases

Transitivity Verbs that can be either transitive or intransitive at the first glance could present a problem for the theta-criterion. For a transitive verb, such as "hit," we assign the theta-roles agent and theme to the arguments, as shown in (2b), (2c), and (2d):

The action of hitting here requires an animate subject, an agent, carry out the action. The theme is then someone or something that undergoes the action. For an intransitive verb, such as "arrive," we assign the theta-role theme to the sole argument, since "Mary" is the one that undergoes the action:

The theta-criterion assigns the theta-role in the underlying structure, as shown by (3c). The past-tense morpheme then requires a subject at the spec-TP position and forces the movement of "Mary," as shown by (3d). A verb like "eat" can choose to take an object, as shown in (4):

For this type of verb, the potential object is usually semantically limited and therefore can be inferred from the verb at a default value (Rice 1988, pp. 203–4). For instance, for (4a), the listener/reader automatically assumes that John ate "something." What necessitates the object in (4c) is the distinction from the default meaning achieved by specifying what John ate (Rice 1988, p. 208). As a result, this type of verb can be treated the same as transitive verbs. The theta-roles of "agent" and "theme" can be assigned:

In summary, by assigning the correct theta-roles, theta-criterion is able to tell the real intransitive verbs, such as "arrive" apart from verbs that can appear intransitive, such as "eat."

PRO and pro

PRO PRO (pronounced 'big pro') is a null pronoun phrase that occurs in a position where it does not get case (or gets null case) but takes the theta-role assigned by the non-finite verb to its subject. PRO's meaning is determined by the precedent DP that controls it (Carnie 2012, p. 429). As theta criterion states that each argument is assigned a theta-role, and those theta-roles must consist of a syntactic category that the verb selects even when there is no overt subject. This is where PRO comes in to help satisfy theta-criterion by appearing as the null subject attaining the appropriate theta role (Camacho 2013). Below is an example containing PRO in a sentence:

(5) a. Jeani is likely [ti to leave]. b. Jean is reluctant [PRO to leave]. (Carnie 2012, p. 430 (1))

Example (5a) is a raising sentence, and in contrast, (5b) is a control sentence, meaning it does not involve any DP movement. The PRO, which is a "null DP" is in the subject position of the embedded clause.

(6) a. Jean wants Briani [ti to leave]. b. Jean persuaded Brian [PRO to leave]. (Carnie 2012, p. 430 (4)

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