Complexity of Axiom Pinpointing in the DL-Lite Family of Description Logics

We investigate the complexity of axiom pinpointing for different members of the DL-Lite family of Description Logics. More precisely, we consider the problem of enumerating all minimal subsets of a given DL-Lite knowledge base that have a given consequence. We show that for the DL-LiteH core, DL-LiteH krom and DLLiteHN horn fragments such minimal subsets are efficiently enumerable with polynomial delay, but for the DL-Litebool fragment they cannot be enumerated in output polynomial time unless P = NP. We also show that interestingly, for the DL-LiteHN horn fragment such minimal sets can be enumerated in reverse lexicographic order with polynomial delay, but it is not possible in the forward lexicographic order since computing the first one is already coNP-hard.

• Type: Journal
• Year: 2010
• Where: ECAI
• Authors: Rafael Peñaloza, Baris Sertkaya
• Keywords: Artificial Intelligence, ECAI 2010, Lexicographic Order, Minimal Subsets, Polynomial Delay