Two variant axiom systems for presence/absence based dissimilarity coefficients

The axiomatic treatment of presence/absence based dissimilarity coefficients presented by Baulieu (1989) is extended. Independence of the axiom sets is established. Global order equivalence is examined as well as its relation to the axiom sets for two variations of the model. It is shown that if paired absences are to be ignored in the calculation of dissimilarity values, then one variant model admits only a single dissimilarity coefficient (up to global order equivalence): (a + b)/(a + b + c).