In this paper we introduce the data structures and process structure of an incremental parser which reflects the underspecified nature of the information encoded in the NL string. We show how this parser can deal with so called crossover phenomena in a way other systems cannot. The the parser is formulated within the LDS framework and constructs parse trees with the help of a modal logic for finite trees. Wh-expressions are interpreted as constituents with underspecified tree location. The dynamics of the parser is formulated in terms of transition system in which the transitions between the parser states are effected by deduction rules.Article