This chapter proposes a framework for specifying, constructing, and managing aparticular class of approximate knowledge structures for use with intelligent artifacts rangingfrom simpler devices such as personal digital assistants (PDAs) to more complex ones suchas unmanned aerial vehicles (UAVs). This chapter introduces the notion of an approximationtransducer, which takes approximate relations as input and generates a (possibly moreabstract) approximate relation as output by combining the approximate input relations witha crisp local logical theory representing dependencies between input and output relations.Approximation transducers can be combined to produce approximation trees, which representcomplex approximate knowledge structures characterized by the properties of elaborationtolerance, groundedness in the application domain, modularity, and context dependency.Approximation trees are grounded through the use of primitive concepts generated with supervisedlearning techniques. Changes in definitions of primitive concepts or in the locallogical theories used by transducers result in changes in the knowledge stored in approximationtrees by increasing or decreasing precision in the knowledge qualitatively. Intuitionsand techniques from rough set theory are used to define approximate relations where eachhas an upper and a lower approximation. The constituent components in a rough set havecorrespondences in a logical language used to relate crisp and approximate knowledge. Theinference mechanism associated with the use of approximation trees is based on a generalizationof deductive databases that we call rough relational databases. Approximation trees andqueries to them are characterized in terms of rough relational databases and queries to them.By placing certain syntactic restrictions on the local theories used in transducers, the computationalprocesses used in the query/answering and generation mechanism for approximationtrees remain in PTIME.