This paper demonstrates a new kind of thematic theory (Alberti 1993, 1994, 1997) and its descriptive and explanatory power in the selection of binder from coreferring arguments (an area where the application of (hierarchical) thematic theories is often argued for). The novelty of this thematic theory lies in the fact that roles are regarded as no semantic primitives, which have proved to be inevitably vague and unreliable, but positions in an abstract internal structure of argument frames, which expresses both some argument hierarchy (Jackendoff 1972, Wilkins 1988, Grimshaw 1990) and polarities of arguments (Dowty 1991) simultaneously. The abstract roles have similar semantic interpretations to those of traditional thematic roles but they are justified by calculations on the basis of morphosyntactic data.