Preferential Semantics for the Logic of Comparative Similarity over Triangular and Metric Models

The logic CSL (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 CSL is defined in terms of models based on different classes of distance spaces. In this work we consider the cases where the distance satisfies the triangular inequality and the one where it is a metric. We show that in both cases the semantics can be equivalently specified in terms of preferential structures. Finally, we consider the relation of CSL with conditional logics and we provide semantics and axiomatizations of conditional logics over distance models with these properties. ∗A full paper containing all the proofs can be found in http://www.lsis.org/alendar/techreports.