In generative grammar (in particular Government and binding theory and the Standard Theory of Transformational Grammar), a theta role or θ-role is the formal device for representing syntactic argument structure (the number and type of noun phrases) required syntactically by a particular verb. For example, the verb put requires three arguments (i.e., it is trivalent). The formal mechanism for implementing this requirement is based in theta roles. The verb put is said to "assign" three theta roles. This is coded in a theta grid associated with the lexical entry for the verb. The correspondence between the theta grid and the actual sentence is accomplished by means of a bijective filter on the grammar known as the Theta Criterion. Early conceptions of theta roles include (Fillmore 1968) (Fillmore called theta roles "cases") and (Gruber 1965).
Read more about Theta Role: Theta Roles and Thematic Relations, Theta Grids and The Theta Criterion, Thematic Hierarchies
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