match between arguments and theta roles. This acts as a filter on the D-structure of the sentence. If an argument fails to have the correct match between the number of arguments (typically NPs, PPs, or embedded clauses) and the number of theta roles, the sentence will be ungrammatical or unparseable. Chomsky's formulation is: The theta criterion Each argument bears one and only one θ-role, and each θ-role is assigned to one and only one argument. Although it is often not explicitly stated, adjuncts are excluded from the theta criterion. Thematic hierarchies Drawing on observations based in typological cross-linguistic comparisons of languages , linguists in the relational grammar (RG) tradition (e.g. ) observed that particular thematic relations and theta roles map on to particular positions in the sentence. For example, in unmarked situations agents map to subject positions, themes onto object position, and goals onto indirect objects. In RG, this is encoded in the Universal Alignment Hypothesis (or UAH), where the thematic relations are mapped directly into argument position based on the following hierarchy: Agent < Theme < Experiencer < Others. Mark Baker adopted this idea into GB theory in the form of the Uniformity of Theta Assignment Hypothesis (or UTAH) . UTAH explains how identical thematic relationships between items are shown by identical structural relationships. A different approach to the correspondence is given in and , where there are no such things as underlying theta roles or even thematic relations. Instead, the interpretive component of the grammar identifies the semantic role of an argument based on its position in the tree. Argument structure in other formal approaches Lexical-functional grammar (LFG) Lexical-functional grammar (LFG) and is perhaps the most similar to Chomskyan approaches in implementing theta-roles. However, LFG uses three distinct layers of structure for representing the relations or functions of arguments: θ-structure, a-structure (argument structure) and f-structure (functional structure) which expresses grammatical relations. These three layers are linked together using a set of intricate linking principles. Thematic relations in the θ-structure are mapped onto a set of positions in the a-structure which are tied to features [+o] (roughly "object") and [±r] (roughly "restricted" meaning it is marked explicitly by a preposition or a case marking). Themes map to [-r], second themes map to [+o] and non-themes map to [-o]. These features then determine how the arguments are mapped to specific grammatical functions in the sentence. The first [-o] argument is