The theta-criterion (also named θ-criterion) is a constraint on x-bar theory that was first proposed by 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.
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.