  We study the logic of comparative concept similarity $\CSL$ introduced by
Sheremet, Tishkovsky, Wolter and Zakharyaschev to capture a form of qualitative
similarity comparison. In this logic we can formulate assertions of the form "
objects A are more similar to B than to C". The semantics of this logic is
defined by structures equipped by distance functions evaluating the similarity
degree of objects. We consider here the particular case of the semantics
induced by \emph{minspaces}, the latter being distance spaces where the minimum
of a set of distances always exists. It turns out that the semantics over
arbitrary minspaces can be equivalently specified in terms of preferential
structures, typical of conditional logics. We first give a direct
axiomatisation of this logic over Minspaces. We next define a decision
procedure in the form of a tableaux calculus. Both the calculus and the
axiomatisation take advantage of the reformulation of the semantics in terms of
preferential structures.
