The increasing availability of knowledge bases (KBs) on the web has opened up the possibility of improved inference in automated query answering (QyA) systems. We have developed a rich inference framework (RIF) that responds to queries where no suitable answer is readily contained in any available data source, by applying functional inferences over heterogeneous data from the web. Our technique combines heuristics, logic and statistical methods to infer novel answers to queries. It also determines what facts are needed for inference, searches for them, and then integrates these diverse facts and their formalisms into a local query-specific inference tree. We explain the internal representation of RIF, the grammar and inference methods for expressing queries and the algorithm for inference. We also show how RIF estimates confidence in its answers, given the various forms of uncertainty faced by the framework.