Tableau calculi for CSL over minspaces

The logic of comparative concept similarity CSL has been introduced in 2005 by Shemeret, Tishkovsky, Zakharyashev and Wolter in order to express a kind of qualitative similarity reasoning about concepts in ontologies. The semantics of the logic is defined in terms of distance spaces; however it can be equivalently reformulated in terms of preferential structures, similar to those ones of conditional logics. In this paper we consider CSL interpreted over symmetric and non-symmetric distance models satisfying the limit assumption, the so-called minspace distance models. We contribute to automated deduction for CSL in two ways. First we prove by the finite filtration method that the logic has the effective finite model property with respect to its preferential semantics. Then we present a decision procedure in the form of a labelled tableau calculus for both cases of CSL interpreted over symmetric and non-symmetric minspace distance models. The termination of the calculus is obtained by imposing suitable blocking conditions.