Case" and "grammatical function" are central to syntactic theories, but rigorous treatments of these notions in surface-oriented grammars like Dynamic Syntax (DS) are pending. Within DS, it is simply held that a case particle resolves structural uncertainty (i.e., unfixed node) in the course of incremental tree update. We model the relation between "case" and "grammatical function" with special reference to Japanese. In this language, the nominative case particle ga normally marks a "subject" NP, but it may mark an "object" NP. Moreover, ga may occur more than once within a single clause. We will address these issues by proposing the "maximal exclusion" approach to structural uncertainty.