Partial metric monoids and semivaluation spaces

Stable partial metric spaces form a fundamental concept in Quantitative Domain Theory. Indeed, all domains have been shown to be quantifiable via a stable partial metric. Monoid operations arise naturally in a quantitative context and hence play a crucial role in several applications. Here, we show that the structure of a stable partial metric monoid provides a suitable framework for a unified approach to some interesting examples of monoids that appear in Theoretical Computer Science. We also introduce the notion of a semivaluation monoid and show that there is a bijection between stable partial metric monoids and semivaluation monoids.