Symmetric Minkowski planes ordered by separation

In Karzel et al. (J. Geom. 99: 116–127, 2009) we introduced for a symmetric Minkowski plane an order concept by the notion of an orthogonal valuation for the circles of Λ and showed that there is a one to one correspondence between the valuations and the halforderings of the accompanying commutative field. Here we consider an order concept which is based on the notion of separation for quadruples of concyclic points and establish the connections between these two notions. Our main result (cf. Theorem 3.3) states that these concepts are equivalent.