The correspondence between partial metrics and semivaluations

The relationship between partial metrics and semivaluations was analyzed. A new defination of semivaluation as a natural generalization of a valuation to the context of semilattices was presented. A bijection between invariant partial metric semilattices and semivaluation spaces was obtained. It was found that the results allowed for a simplified representation of well known partial metric spaces, where the semivaluation involved is simply the partial metric self-distance function.