Modeling Students’ Reasoning About Qualitative Physics: Heuristics for Abductive Proof Search

We describe a theorem prover that is used in the Why2-Atlas tutoring system for the purposes of evaluating the correctness of a student’s essay and for guiding feedback to the student. The weighted abduction framework of the prover is augmented with various heuristics to assist in searching for a proof that maximizes measures of utility and plausibility. We focus on two new heuristics we added to the theorem prover: (a) a specificity-based cost for assuming an atom, and (b) a rule choice preference that is based on the similarity between the graph of cross-references between the propositions in a candidate rule and the graph of cross-references between the set of goals. The two heuristics are relevant to any abduction framework and knowledge representation that allow for a metric of specificity for a proposition and cross-referencing of propositions via shared variables.