Rough sets use a partition of a base set induced by a given indiscernibility relation p. In practice such partitions can result from clustering the data. DLs with concept operators relying on a single p for upper and lower approximations of concepts have been investigated so far. The use of a hierarchy of such equivalence relations as it can result from hierarchical clustering methods is not explored yet in a DL setting. In this paper we extend the rough DL ℰℒpT with a hierarchy of indiscernibility relations as and develop a decision procedure for testing subsumption.
Penaloza, R., Turhan, A. (2024). Rough, Rougher, Roughest Extending ℰℒ with a Hierarchy of Indiscernibility Relations. In Proceedings of the 37th International Workshop on Description Logics (DL 2024) (pp.1-10). CEUR-WS.
Rough, Rougher, Roughest Extending ℰℒ with a Hierarchy of Indiscernibility Relations
Penaloza R.
;
2024
Abstract
Rough sets use a partition of a base set induced by a given indiscernibility relation p. In practice such partitions can result from clustering the data. DLs with concept operators relying on a single p for upper and lower approximations of concepts have been investigated so far. The use of a hierarchy of such equivalence relations as it can result from hierarchical clustering methods is not explored yet in a DL setting. In this paper we extend the rough DL ℰℒpT with a hierarchy of indiscernibility relations as and develop a decision procedure for testing subsumption.
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