 Yet the advocate of relative identity cannot simply reject any form of LL. There are true and indispensable instances of LL: If \(x\) and \(y\) are the same dog, then, surely, if \(x\) is a Dalmatian, so is \(y\). The problem is that of formulating and motivating restricted forms of LL that are nonetheless strong enough to bear the burden of identity claims. There has been little systematic work done in this direction, crucial though it is to the relative identity project. (See Deutsch 1997 for discussion of this issue.) There are, however, equivalence relations that do satisfy restricted forms of LL. These are sometimes called ‘congruence relations’ and they turn up frequently in mathematics. For example, say that integers \(n\) and \(m\) are congruent if their difference \(n - m\) is a multiple of 3. This relation preserves multiplication and addition, but not every property. The numbers 2 and 11 are thus congruent but 2 is even and 11 is not. There are also non-mathematical congruencies. For example, the relation x and y are traveling at the same speed preserves certain properties and not others. If objects \(x\) and \(y\) are traveling at the same speed and \(x\) is traveling faster than \(z\), the same is true of \(y\). Such similarity relations satisfy restricted forms of LL. In fact, any equivalence relation satisfies a certain minimal form of LL (see below).