In our ICCS95 paper, An Implementation Model for Contexts and Negation in Conceptual Graphs, we made some important advances relative to storing conceptual graphs in a generalization hierarchy. These included a simplified definition of both Formation and Inference Rules, a mechanism for storing nested, negative contexts, an extension to Method III for updating the database and truth values, a further extension to propagate some inferences, and a mechanism for representing and sometimes detecting contradictions. In this paper we show how to use properties of lattices and a context sensitive superresolution inference rule to propagate truth values in a database of nested, possibly negated, conceptual graphs and, as this is done, detect any consequent contradictions.