The formal mechanism for implementing a verb's argument structure is codified as theta roles.
The reason for this is simple: theta roles typically reference thematic relations.
Typically, although not always, this theta role maps to a noun phrase which bears an agent thematic relation.
One common way of thinking about theta roles is that they are bundles of thematic relations associated with a particular argument position (Carnie 2006).
The top row represents the names of the thematic relations contained in the theta role.
In some work (e.g., Carnie 2006), this box also contains information about the category associated with the theta role.
The bottom row gives a series of indexes which are associated with subscripted markers in the sentence itself which indicate that the NPs they are attached to have been assigned the theta role in question.
Drawing on observations based in typological cross-linguistic comparisons of languages (Fillmore 1968), linguists in the relational grammar (RG) tradition (e.g. Perlmutter & Postal 1984) observed that particular thematic relations and theta roles map on to particular positions in the sentence.
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.
Instead, the interpretive component of the grammar identifies the semantic role of an argument based on its position in the tree.
Lexical-functional grammar (LFG) (Falk 2001) and (Bresnan 2001) is perhaps the most similar to Chomskyan approaches in implementing theta-roles.
These mappings are further constrained by the following constraints: Function argument biuniqueness: Each a-structure role corresponds to a unique f-structure function, and each f-structure function corresponds to a unique a-structure role The Subject Condition: Every verb must have a SUBJF-structures are further constrained by the following two constraints which do much of the same labor as the θ-criterion: Coherence requires that every participant in the f-structure of a sentence must be mentioned in a-structure (or in a constituting equation) of a predicate in its clause.
Completeness: An f-structure for a sentence must contain values for all the grammatical functions mentioned in a-structure.