Tensors Over Semirings For Latent-Variable Weighted Logic Programs

Semiring parsing (Goodman, 1999) is an elegant framework for describing parsers by using semiring weighted logic programs. In this paper we present a generalization of this concept: latent-variable semiring parsing. With our framework, any semiring weighted logic program can be latentified by transforming weights from scalar values of a semiring to rank-n arrays, or tensors, of semiring values, allowing the modeling of latent variables within the semiring parsing framework. Semiring is too strong a notion when dealing with tensors, and we have to resort to a weaker structure: a partial semiring.(1) We prove that this generalization preserves all the desired properties of the original semiring framework while strictly increasing its expressiveness.