We introduce a stochastic model of language change in a population of speakers who are divided into social or geographical groups. We assume that sequences of language changes are driven by the inference of grammatical rules from memorised linguistic patterns. These paths of inference are controlled by an inferability matrix which can be structured to model a wide range of linguistic change processes. The extent to which speakers are able to determine the dominant linguistic patterns in their speech community is captured by a temperature-like parameter. This can induce symmetry breaking phase transitions, where communities select one of two or more possible branches in the evolutionary tree of language. We use the model to investigate a grammatical change (the rise of the phrasal possessive) which took place in English and Continental North Germanic languages during the Middle Ages. Competing hypotheses regarding the sequences of precursor changes which allowed this to occur each generate a different structure of inference matrix. We show that the inference matrix of a "Norway Hypothesis" is consistent with Norwegian historical data, and because of the close relationships between these languages, we suggest that this hypothesis might explain similar changes in all of them.