Reverse Engineering Queries in Ontology-Enriched Systems The Case - - PowerPoint PPT Presentation

Reverse Engineering Queries in Ontology-Enriched Systems

The Case of Expressive Horn Description Logic Ontologies V´ ıctor Guti´ errez-Basulto Jean Christoph Jung Leif Sabellek International Joint Conference on Artificial Intelligence Stockholm, July 17th 2018

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Motivation

Knowledge base Ontology Database Non-expert user Unable to formulate conjunctive queries using the ontology What do Peter and Mary have in common? They are both born in Sweden.

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Query by example (QBE)

Input:

• a knowledge base (T , A)
• a set of positive examples S+ ⊆ dom(A)n
• a set of negative examples S− ⊆ dom(A)n

Question: Is there an n-ary query q that returns all the positive but none of the negative examples? We focus on conjunctive queries (CQ) q and Horn Description Logic Ontologies T . What do Peter and Mary have in common? They are both either Peter or Mary.

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The case without ontology

Idea: If there is a query that solves the problem, then the least general generalization lgg(x) is one. lgg(x) is constructed from the database and the positive examples. coNExpTime-Algorithm:

• Construct lgg(x).
• Verify that lgg(x) returns all positive examples.
• Verify that lgg(x) return none of the negative examples.

Theorem (ten Cate and Dalmau, 2015)

The problem QBE(CQ) (without ontology) is coNExpTime-complete.

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Adding ontologies

Construct the least general generalization lgg∞(x), using the universal model UT ,A and the positive examples. lgg∞(x) is usually infinite, but:

Theorem (Characterization)

There is a solution for the QBE problem, if and only if:

• T , A |

= lgg∞(a) for all a ∈ S+.

• T , A |

= lgg∞(b) for all b ∈ S−.

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Main results

L = Horn-ALCI Horn-ALC QBE(L, CQ) 2-ExpTime coNExpTime QBE(L, UCQ) ExpTime ExpTime QBEsig(L, CQ) 2-ExpTime coNExpTime QBEsig(L, UCQ) 2-ExpTime ExpTime Same results for the problem QDEF(L, (U)CQ), where the question is whether there is a query that returns precisely the positive examples.

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Sizes of witness queries

Theorem

If there exists a witness query, then there is one of size

• 2-exponential for QBE(Horn-ALC, CQ) and
• 4-exponential for QBE(Horn-ALCI, CQ).

Theorem

There is a family of instances for QBE(Horn-ALC, CQ), where the smallest witness queries are of 2-exponential size.

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Conclusion

Summary

• QBE with Horn-ALC ontologies is not harder than without
• ntology.
• Adding inverse roles makes the problem harder.
• UCQs are easier but less interesting.

Future work

• Close the gaps for exact sizes of witness queries.
• DL-Lite

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