https://aclanthology.org/C08-5001.pdf

Also good was section 4 of

https://par.nsf.gov/servlets/purl/10237543

Both work with semirings, which are a structure with two monoids.

I found these papers fairly readable on a quick skim, but I have a background in closely related stuff. They might not be so readable if you're not used to the style of presentation.