  We argue in this paper that many common adverbial phrases generally taken to
signal a discourse relation between syntactically connected units within
discourse structure, instead work anaphorically to contribute relational
meaning, with only indirect dependence on discourse structure. This allows a
simpler discourse structure to provide scaffolding for compositional semantics,
and reveals multiple ways in which the relational meaning conveyed by adverbial
connectives can interact with that associated with discourse structure. We
conclude by sketching out a lexicalised grammar for discourse that facilitates
discourse interpretation as a product of compositional rules, anaphor
resolution and inference.
