Reestimation of Reified Rules in Semiring Parsing and Biparsing

We show that reifying the rules from hyperedge weights to first-class graph nodes automatically gives us rule expectations in any kind of grammar expressible as a deductive system, without any explicit algorithm for calculating rule expectations (such as the insideoutside algorithm). This gives us expectation maximization training for any grammar class with a parsing algorithm that can be stated as a deductive system, for free. Having such a framework in place accelerates turnover time for experimenting with new grammar classes and parsing algorithms—to implement a grammar learner, only the parse forest construction has to be implemented.