Approximation Transducers and Trees: A Technique for Combining Rough and Crisp Knowledge

Summary

This chapter proposes a framework for specifying, constructing, and managing a particular class of approximate knowledge structures for use with intelligent artifacts ranging from simpler devices such as personal digital assistants (PDAs) to more complex ones such as unmanned aerial vehicles (UAVs). This chapter introduces the notion of an approximation transducer, which takes approximate relations as input and generates a (possibly more abstract) approximate relation as output by combining the approximate input relations with a crisp local logical theory representing dependencies between input and output relations. Approximation transducers can be combined to produce approximation trees, which represent complex approximate knowledge structures characterized by the properties of elaboration tolerance, groundedness in the application domain, modularity, and context dependency. Approximation trees are grounded through the use of primitive concepts generated with supervised learning techniques. Changes in definitions of primitive concepts or in the local logical theories used by transducers result in changes in the knowledge stored in approximation trees by increasing or decreasing precision in the knowledge qualitatively. Intuitions and techniques from rough set theory are used to define approximate relations where each has an upper and a lower approximation. The constituent components in a rough set have correspondences in a logical language used to relate crisp and approximate knowledge. The inference mechanism associated with the use of approximation trees is based on a generalization of deductive databases that we call rough relational databases. Approximation trees and queries 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 computational processes used in the query/answering and generation mechanism for approximation trees remain in PTIME.