TABLEAUX '07 Proceedings of the 16th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Comparative Concept Similarity over Minspaces: Axiomatisation and Tableaux Calculus
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
CSL-lean: A Theorem-prover for the Logic of Comparative Concept Similarity
Electronic Notes in Theoretical Computer Science (ENTCS)
Tableau calculi for CSL over minspaces
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Comparative similarity, tree automata, and diophantine equations
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Preferential semantics for the logic of comparative similarity over triangular and metric models
JELIA'12 Proceedings of the 13th European conference on Logics in Artificial Intelligence
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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 and it generalizes the logic S4u of topological spaces. In this paper we consider CSL 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 CSL 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.