theta roles. Only arguments of the verb bear theta roles; optional adjunct modifiers—even if they are prepositional phrases (PPs) such as on Friday or noun phrases (NPs) like yesterday—don't take theta roles. But almost all NPs (except expletives) express thematic relations. An argument can bear only one theta role, but can take multiple thematic relations. For example, in Susan gave Bill the paper, Susan bears both Agent and Source thematic relations, but it only bears one theta role (the external "agent" role). Thematic relations are properties of nouns and noun phrases. Theta roles can be assigned to any argument including noun phrases, prepositional phrases and embedded clauses. Thematic relations are not assigned to embedded clauses, and prepositions typically mark the thematic relation on an NP. One common way of thinking about theta roles is that they are bundles of thematic relations associated with a particular argument position . Theta grids and the theta criterion Theta roles are stored in a verb's theta grid. Grids typically come in two forms. The simplest and easiest to type is written as an ordered list between angle brackets. The argument associated with the external argument position (which typically ends up being the subject in active sentences) is written first and underlined. The theta roles are named by the most prominent thematic relation that they contain. In this notation, the theta grid for a verb such as give is <agent, theme, goal>. The other notation (see for example the textbook examples in and ) separates the theta roles into boxes, in which each column represents a theta role. The top row represents the names of the thematic relations contained in the theta role. In some work (e.g., ), this box also contains information about the category associated with the theta role. This mingles theta-theory with the notion of subcategorization. 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. When applied to the sentence [S[NP Susan]i gave [NP the food]j [PPto Biff]k] the indices mark that Susan is assigned the external theta role of agent/source, the food is assigned the theme role, and to Biff is assigned the goal role. The theta criterion (or θ-criterion) is the formal device in Government and Binding Theory for enforcing the one to one