PiL: A System to Learn Strategy in Problem-Solving(A Case Study in an Equation & Inequality of the First Degree)

Abstract

PiL (Paradigm-based inference Learner)is a learning system that can acquire strategy knowledge of problem solving. PiL has basic operators (primitive transformation rules) a priori, but can not solve a problem with only this knowledge. Because the conditions of basic operators are so general, if all possible operators are applied to a problem state, the search space gets too large to reach the goal state. So a teacher gives PiL solving examples and PiL generalizes the examples and specializes the basic operators by adding the generalized solving examples to the conditions as conjunction. PiL generalizes examples with the condition-propagation based generalization method that is a kind of explanation-based generalization. PiL generally consists of two modules, problem solving module, and knowledge maintenance module. The problem solving module solves the problem with production system, and details the given (or solved by itself) solving example. The knowledge maintenance module generalizes a solving example, extracts macro operators and absolute operators from generalized operator sequence, and arranges knowledge base. Further, PiL's knowledge base has hierarchical structure consisting of finish-condition rules, macro operators, absolute operators, heuristic operators and basic operators to control inference. When a problem is given, first PiL tries to solve it by itself, and if it can't, PiL requires a teacher to give a solving example. Next, PiL translates the given solving example to sequence of PiL's operators, and generalizes it with condition-propagation based generalization method. The condition-propagation based generalization is done by regressing the conditions of operators applied in the given solving example through operator sequence. Further more, from generalized operator sequence, PiL is able to extract absolute operators and macro operators that are powerful knowledge in problem solving. In this paper, We will report an application of PiL in an equation & inequality of the first degree.