We invent referential translation machines (RTMs), a computational model for identifying the translation acts between any two data sets with respect to a reference corpus selected in the same domain, which can be used for judging the semantic similarity between text. RTMs make quality and semantic similarity judgments possible by using retrieved relevant training data as interpretants for reaching shared semantics. An MTPP (machine translation performance predictor) model derives features measuring the closeness of the test sentences to the training data, the difficulty of translating them, and the presence of acts of translation involved. We view semantic similarity as paraphrasing between any two given texts. Each view is modeled by an RTM model, giving us a new perspective on the binary relationship between the two. Our prediction model is the $15$th on some tasks and $30$th overall out of $89$ submissions in total according to the official results of the Semantic Textual Similarity (STS 2013) challenge.