A framework for modeling query semantics as graph properties is presented. In this framework, a single definition of a query automatically gives rise to several semantics for evaluating that query under varying degrees of incomplete information. For example, defining natural joins automatically gives rise to full disjunctions. Two of the proposed semantics have incremental-polynomial-time query-evaluation algorithms for all types of queries that can be defined in this framework. Thus, the proposed framework generalizes previous definitions of semantics for incomplete information and improves previous complexity results for query evaluation. %%% Local Variables: %%% mode: latex %%% TeX-master: "main" %%% End: