Tableau calculus for preference-based conditional logics: PCL and its extensions
ACM Transactions on Computational Logic (TOCL)
Weak AGM postulates and strong Ramsey Test: A logical formalization
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
Tableau calculi for CSL over minspaces
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Tableau calculus for the logic of comparative similarity over arbitrary distance spaces
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Comparative similarity, tree automata, and diophantine equations
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Interpolative reasoning with default rules
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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The logic of Comparative Similarity CSL (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.