Combining Bayesian Networks and Formal Reasoning for Semantic Classification of Student Utterances

We describe a combination of a statistical and symbolic approaches for automated scoring of student utterances according to their semantic content. The proposed semantic classifier overcomes the limitations of bag-of-wordsmethods by mapping natural language sentences into predicate representations and matching them against the automatically generated deductive closure of the domain givens, buggy assumptions and domain rules. With the goal to account for uncertainties in both symbolic representations of natural language sentences and logical relations between domain statements, this work extends the deterministic symbolic approach by augmenting the deductive closure graph structure with conditional probabilities, thus creating a Bayesian network. By deriving the structure of the network formally, instead of estimating it from data, we alleviate the problem of sparseness of training data. We compare the performance of the Bayesian network classifier with the deterministic graph matching-based classifiers and baselines.