Reflection loops of spaces with congruence and hyperbolic incidence structure

In an absolute space (P,L,≡, α) with congruence there are line reflections and point reflections. With the help of point reflections one can define in a natural way an addition + of points which is only associative if the product of three point reflection is a point reflection again. In general, for example for the case that (P,L, α) is a linear space with hyperbolic incidence structure, the addition is not associative. (P,+) is a K-loop or a Bruck loop.