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 parse out ill-formed sentences. Thus, if the number or categories of arguments in a sentence does not meet the theta-role assigner's requirement in any given sentence, that sentence will be deemed ungrammatical. . 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 . 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 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. 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 . 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) . 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 .
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 . 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 . 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 . 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 .
Below is an example containing PRO in a sentence:
 (5) a. "Jeani is likely [ti to leave]".
 b. "Jean is reluctant [PRO to leave]".
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]".
Similarly, example (6a) is a raising-to-object sentence; "Brian" raises to the object position of the verb "want." In contrast, (6b) is an object control sentence. The verb "persuade" has three theta-roles to assign: "agent" to "Jean", "theme" to "Brian", and "proposition" to the clause ["PRO to leave"]. There is no raising, but there is a PRO in the subject position of the embedded clause that takes the verb leave's only theta-role, "agent". Since Brian does not receive theta-role from "leave", it only bears one theta-role, nor does PRO receive a second theta-role from "persuade". Every argument only receives one theta-role, and every theta-role of the two predicates is assigned to only one argument. The sentence is thus grammatical.
pro.
pro, also known as little pro, is an empty category that occurs in a subject or object position of a finite clause (finite clauses must contain a verb which shows tense) in languages like Italian, Spanish, Portuguese, Chinese, and some Arabic dialects (; ). pro differs from PRO in that it contains case. The meaning of pro is determined not by its antecedent but by verb agreement in the sentence. The DP is 'dropped' from a sentence if its reference can be recovered from the context. For example:
The verb "restituire" 'give back' assigns three theta-roles, but there are only two overt arguments in the sentence. It ultimately satisfies theta-criterion because the role, theme, is taken by a pro, whose existence can be proved by the properly bound reflexive pronoun "se stessi". Compare (7a) with (7b) below:
 (7b) *"Un bravo psicanalista può dare aiuto a se stessi".
 A good psychoanalyst can give help to oneself.
 'A good psychoanalyst can give help to themselves'.
 (Adapted from )
When the reflexive pronoun "se stessi" 'themselves' doesn't have a proper antecedent to co-refer to, the sentence can't be grammatical. This indicates that in (7a) "se stessi" must have a proper antecedent in the sentence—the pro that takes the theme role.
Cognate object.
Cognate objects are nominal complements of their cognate verbs that are normally intransitive. For example,
 (8) "John died a gruesome death."
Such a structure posed a problem for theta-criterion because normally the verb assigns only one theta-role, theme, which is already taken by the DP, "John." The sentence should be thus predicted ill-formed. To explain the phenomenon, one way is to re-categorize such a verb as "die" so as to change the way it assigns theta-roles. For that purpose, (8) can be interpreted as follows:
 (9) "John met a gruesome death."
Or John "underwent" a gruesome death. If the verb "die" is essentially similar to the operation-verb "meet," the cognate objects should be assigned a theta-role—one restricted to the nominal form of the verb head . In other words, "die" is now classified as a potentially transitive verb, assigning two theta-roles, agent to "John" and theme to "a gruesome death." Such a possibility is falsified, however, because cognate object constructions cannot be passivized .
 (10) a. "A gruesome death was met by John."
 b. "*A gruesome death was died by John."
As we can no longer consider verbs that take cognate objects the same as potentially transitive verbs, argues, based on the framework of , that cognate objects are adjuncts rather than arguments, having the same meaning and structure as the manner adverbs in (12b).
Such an analysis restores cognate objects to the group of arguments satisfying the theta-criterion, as adjuncts, by definition, are not counted as arguments and therefore need not be restricted by theta criterion. The tree form (11c) shows the adjunct DP in its relative position.
Deverbal nouns.
Deverbal nouns are derived from verbs and thus assign theta-roles as their verb stems do. For example,
 (12) (i) "the barbarians' destruction of Rome"
 (ii) "Rome's destruction (by the barbarians)"
 (iii) "the destruction of Rome (by the barbarians)"
 (iv) "*the barbarian's destruction"
According to , the constructions in (12) are analogous to "the barbarians destroyed Rome" and "destruction" needs to assign theta-roles in line with theta-criterion. It assigns "agent" to "the barbarians" and "theme" to "Rome" so (i) is fine. The verb "destroy" alone doesn't obligatorily assign theta-role to its subject so (ii) and (iii) is well-formed, too. However, "destroy" must assign a "theme", so (iv) is ruled out.
Alternative approaches.
Theta-criterion experienced its golden age in the 1980s when people discussed its application to various languages and structures and developed many other theories from it. However, after the minimalist program challenged some cornerstones of government and binding theory, people started to question the validity of this criterion, especially the number of theta-roles allowed to be taken by an argument. Hornstein and Boeckx, for example, proposed that there is no upper limit on the number of theta-roles an argument can receive during derivation. In their theory, the function of selecting correct number of arguments is shouldered by case theory, and theta-roles are just features on verbs that needs to be checked .