Dimensions and Values for Reasoning with Legal Cases

In this paper we build on two recent attempts to formalise reasoning with dimensions. Both of these approaches effectively map dimensions into factors, which enables propositional reasoning, but we show that sometimes a balance between dimensions needs to be struck. To permit trade offs we need to keep the magnitudes and reason more geometrically. We also revisit the link between dimensions and values, showing that values play a number of distinct roles, not only explaining preferences between factors, but also ensuring that all the purposes of the underlying law are considered.