The Theory of Correlation Formulas and Their Application to Discourse Coherence
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The Winograd Schema Challenge (WSC) was proposed as a measure of machine intelligence. It boils down to anaphora resolution, a task familiar from computational linguistics. Research in linguistics and AI has coalesced around discourse coherence as the critical factor in solving this task, and the process of establishing discourse coherence relies fundamentally on world and commonsense knowledge. In this thesis, we build on an approach to establishing coherence on the basis of it correlation. The utility of this approach lies in its conceptual clarity and ability to flexibly represent commonsense knowledge. We work to fill some conceptual holes with the Correlation Calculus approach. First, understanding the calculus in a vacuum is not straightfoward unless it has a precise semantics. Second, existing demonstrations of the Correlation Calculus on Winograd Schema Challenge problems have not been linguistically credible. We hope to ameliorate some---but by no means all---of the outstanding issues with the Correlation Calculus. We do so first by providing a precise semantics of the calculus, which relates our intuitive understanding of correlation with a precise notion involving probabilities. Second, we formulate the establishment of discourse coherence by correlation formulas within the framework of Discourse Representation Theory. This provides a more complete and linguistically credible account of the relationship between the Correlation Calculus, discourse coherence, and Winograd Schema Challenge problems.