(first introduced by Sheremet, Tishkovsky, Wolter and Zakharyaschev in 2005) allows one to reason about distance comparison and similarity comparison within a modal language. The logic can express assertions of the kind ”A is closer/more similar to B than to C” and has a natural application to spatial reasoning, as well as to reasoning about concept similarity in ontologies. The semantics of
is defined in terms of models based on different classes of distance spaces and it generalizes the logic S4
of topological spaces. In this paper we consider
defined over arbitrary distance spaces. The logic comprises a binary modality to represent comparative similarity and a unary modality to express the existence of the minimum of a set of distances. We first show that the semantics of
can be equivalently defined in terms of preferential models. As a consequence we obtain the finite model property of the logic with respect to its preferential semantic, a property that does not hold with respect to the original distance-space semantics. Next we present an analytic tableau calculus based on its preferential semantics. The calculus provides a decision procedure for the logic, its termination is obtained by imposing suitable blocking restrictions.