Forgetting Concepts in DL-Lite

To support the reuse and combination of ontologies in Semantic Web applications, it is often necessary to obtain smaller ontologies from existing larger ontologies. In particular, applications may require the omission of many terms, e.g., concept names and role names, from an ontology. However, the task of omitting terms from an ontology is challenging because the omission of some terms may affect the relationships between the remaining terms in complex ways. We present the first solution to this problem by adapting the technique of forgetting, previously used in other domains. Specifically, we present a semantic definition of forgetting for description logics in general, which generalizes the standard definition for classical logic. We then introduce algorithms that implement forgetting in both DL-Lite TBoxes and ABoxes, and in DL-Lite knowledge bases. We prove that the algorithms are correct with respect to the semantic definition of forgetting, and that they run in polynomial time.

[1]  Hans Tompits,et al.  Forgetting in Managing Rules and Ontologies , 2006, 2006 IEEE/WIC/ACM International Conference on Web Intelligence (WI 2006 Main Conference Proceedings)(WI'06).

[2]  Kewen Wang,et al.  Forgetting and Conflict Resolving in Disjunctive Logic Programming , 2006, AAAI.

[3]  Flemming Nielson,et al.  Principles of Program Analysis , 1999, Springer Berlin Heidelberg.

[4]  Ian Horrocks,et al.  A Logical Framework for Modular Integration of Ontologies , 2006 .

[5]  Diego Calvanese,et al.  DL-Lite: Tractable Description Logics for Ontologies , 2005, AAAI.

[6]  Abdul Sattar,et al.  A Theory of Forgetting in Logic Programming , 2005, AAAI.

[7]  Diego Calvanese,et al.  Tractable Reasoning and Efficient Query Answering in Description Logics: The DL-Lite Family , 2007, Journal of Automated Reasoning.

[8]  Diego Calvanese,et al.  Data Complexity of Query Answering in Description Logics , 2006, Description Logics.

[9]  R. Reiter,et al.  Forget It ! , 1994 .

[10]  Carsten Lutz,et al.  Did I Damage My Ontology? A Case for Conservative Extensions in Description Logics , 2006, KR.

[11]  Diego Calvanese,et al.  The Description Logic Handbook , 2007 .

[12]  Maurizio Lenzerini,et al.  On the Update of Description Logic Ontologies at the Instance Level , 2006, AAAI.

[13]  Maurizio Lenzerini,et al.  On the Approximation of Instance Level Update and Erasure in Description Logics , 2007, AAAI.

[14]  C. A. R. Hoare,et al.  An axiomatic basis for computer programming , 1969, CACM.

[15]  Ian Horrocks,et al.  A Logical Framework for Modularity of Ontologies , 2007, IJCAI.

[16]  Frank S. de Boer,et al.  Verification of Sequential and Concurrent Programs , 1997, Texts and Monographs in Computer Science.

[17]  Ian Horrocks,et al.  Just the right amount: extracting modules from ontologies , 2007, WWW '07.