# Theory-Based Inductive Learning: An Integration of Symbolic and Quantitative Methods

The objective of this paper is to propose a method that will generate a causal explanation of observed events in an uncertain world and then make decisions based on that explanation. Feedback can cause the explanation and decisions to be modified. I call the method Theory-Based Inductive Learning (T-BIL). T-BIL integrates deductive learning, based on a technique called Explanation-Based Generalization (EBG) from the field of machine learning, with inductive learning methods from Bayesian decision theory. T-BIL takes as inputs (1) a decision problem involving a sequence of related decisions over time, (2) a training example of a solution to the decision problem in one period, and (3) the domain theory relevant to the decision problem. T-BIL uses these inputs to construct a probabilistic explanation of why the training example is an instance of a solution to one stage of the sequential decision problem. This explanation is then generalized to cover a more general class of instances and is used as the basis for making the next-stage decisions. As the outcomes of each decision are observed, the explanation is revised, which in turn affects the subsequent decisions. A detailed example is presented that uses T-BIL to solve a very general stochastic adaptive control problem for an autonomous mobile robot.

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