Intuitively, it's because lots of things we work with in CS don't have a good notion of inverse. In practice, this usually means you're building up a structure

Intuitively, it's because lots of things we work with in CS don't have a good notion of inverse. In practice, this usually means you're building up a structure out of smaller structures: you can always add more to the structure, but there's nothing you can add to undo what was added previously. Semirings are interesting for the same reason. "Fun with Semirings"[1] has some great examples, if you're curious. [1]: https://pdfs.semanticscholar.org/702d/348c32133997e992db362a19697d5607ab32.pdf https://pdfs.semanticscholar.org/702d/348c32133997e992db362a...