In this paper I have proposed that an independent projection is needed in the LFG architecture to represent discourse-function information: i-structure. The argument structure of predicates, as represented in the f-structure, is inappropriate for the i-structure in that it leads to incorrect scoping of the discourse functions. Instead, the core value of the predicate must be used. The internal organisation of i-structure is left for further research; here it is represented as a simple attribute-value matrix.
This paper gives rise to two major questions which remain unanswered: First, should any discourse function information be in the f-structure? Topic, and to a much lesser extent focus, have been syntacticized in a number of languages to the extent that they show agreement like f-structure grammatical functions. In such cases it might be argued that there is a syntactic (=f-structure) topic and focus, as presented in Bresnan and Mchombo 1987 and Alsagoff 1992, as well as the i-structure representation. That is, all f-structure grammaticalized discourse functions will have the corresponding i-structure role, but most i-structure roles will not be grammaticalized into the f-structure. Second, what is in i-structure and how is it organized? It is widely assumed that all ``substantial'' lexical items have a discourse function; this can be represented in LFG by all items with a PRED having an i-structure function; this is ensured via the s-structure. However, how these functions are organised and what divisions are needed remains to be investigated as a largely i-structure internal phenomenon despite the substantial literature on this topic.