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):

θ-criterion: Each argument bears one and only one θ-role, and each θ-role is assigned to one and only one argument.

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. (Carnie 2007, p. 224). In other words, theta-criterion sorts sentences into grammatical and ungrammatical bins based on c-selection and s-selection.

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.

...
Wikipedia