  Semiring parsing 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 modelling 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. We prove that this
generalization preserves all the desired properties of the original semiring
framework while strictly increasing its expressiveness.
