Skip to main content
SpringerLink
Log in

Lightweight axiom pinpointing via replicated driver and customized SAT-solving

  • Research Article
  • Published:
Frontiers of Computer Science Aims and scope Submit manuscript

Abstract

In description logic, axiom pinpointing is used to explore defects in ontologies and identify hidden justifications for a logical consequence. In recent years, SAT-based axiom pinpointing techniques, which rely on the enumeration of minimal unsatisfiable subsets (MUSes) of pinpointing formulas, have gained increasing attention. Compared with traditional Tableau-based reasoning approaches, SAT-based techniques are more competitive when computing justifications for consequences in large-scale lightweight description logic ontologies. In this article, we propose a novel enumeration justification algorithm, working with a replicated driver. The replicated driver discovers new justifications from the explored justifications through cheap literals resolution, which avoids frequent calls of SAT solver. Moreover, when the use of SAT solver is inevitable, we adjust the strategies and heuristic parameters of the built-in SAT solver of axiom pinpointing algorithm. The adjusted SAT solver is able to improve the checking efficiency of unexplored sub-formulas. Our proposed method is implemented as a tool named RDMinA. The experimental results show that RDMinA outperforms the existing axiom pinpointing tools on practical biomedical ontologies such as Gene, Galen, NCI and Snomed-CT.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Baader F, Calvanese D, Mcguinness D L, et al. The Description Logic Handbook. Cambridge University Press, 2007

  2. Baader F, Peñaloza R, Suntisrivaraporn B. Pinpointing in the description logic \({\cal E}{{\cal L}^ + }\). In: Proceedings of the 30th Annual German Conference on Artificial Intelligence. 2007, 52–67

  3. Baader F, Suntisrivaraporn B. Debugging snomed CT using axiom pinpointing in the description logic \({\cal E}{{\cal L}^ + }\). In: Proceedings of the 3rd International Conference on Knowledge Representation in Medicine. 2008, 1

  4. Suntisrivaraporn B, Baader F, Schulz S, Spackman K. Replacing SEP-Triplets in SNOMED CT using tractable description logic operators. In: Proceedings of the 11th Conference on Artificial Intelligence in Medicine. 2007, 287–291

  5. Baader F, Brandt S, Lutz C. Pushing the \({\cal E}{\cal L}\) envelope. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence. 2005, 364–369

  6. Sebastiani R, Vescovi M. Axiom pinpointing in lightweight description logics via horn-sat encoding and conflict analysis. In: Proceedings of the 22nd International Conference on Automated Deduction. 2009, 84–99

  7. Arif M F, Mencía C, Marques-Silva J. Efficient axiom pinpointing with EL2MCS. In: Proceedings of the 38th Annual German Conference on Artificial Intelligence. 2015, 225–233

  8. Arif M F, Mencía C, Marques-Silva J. Efficient MUS enumeration of Horn formulae with applications to axiom pinpointing. In: Proceedings of the 18th International Conference on Theory and Applications of Satisfiability Testing. 2015, 324–342

  9. Manthey N, Peñaloza R, Rudolph S. Efficient axiom pinpointing in \({\cal E}{\cal L}\) using SAT technology. In: Proceedings of the 29th International Workshop on Description Logics. 2016

  10. Arif M F, Mencía C, Ignatiev A, Manthey N, Peñaloza R, Marques-Silva J. BEACON: an efficient SAT-based tool for debugging \({\cal E}{{\cal L}^ + }\) ontologies. In: Proceedings of the 19th International Conference on Theory and Applications of Satisfiability Testing. 2016, 521–530

  11. Ignatiev A, Marques-Silva J, Mencía C, Peñaloza R. Debugging \({\cal E}{{\cal L}^ + }\) ontologies through horn MUS enumeration. In: Proceedings of the 30th International Workshop on Description Logics. 2017, 1

  12. Kazakov Y, Skočovský P. Enumerating justifications using resolution. In: Proceedings of the 9th International Joint Conference on Automated Reasoning. 2018, 609–626

  13. Gao M, Ye Y, Ouyang D, Wang B. Finding justifications by approximating core for large-scale ontologies. In: Proceedings of the 28th International Joint Conference on Artificial Intelligence. 2019, 6432–6433

  14. Manthey N, Peñaloza R, Rudolph S. SATPIN: Axiom pinpointing for lightweight description logics through incremental SAT. KI-Künstliche Intelligenz, 2020, 34(3): 389–394

    Article  Google Scholar 

  15. Ye Y, Cui X, Ouyang D. Extracting a justification for OWL ontologies by critical axioms. Frontiers of Computer Science, 2020, 14(4): 144305

    Article  Google Scholar 

  16. Gao J, Ouyang D T, Ye Y. Exploring duality on ontology debugging. Applied Intelligence, 2020, 50(2): 620–633

    Article  Google Scholar 

  17. Sörensson N, Een N. MiniSat v1.13- A SAT solver with conflict-clause minimization. In: Proceedings of the 8th Conference on Theory and Applications of Satisfiability Testing. 2005, 502–518

  18. Minoux M. LTUR: a simplified linear-time unit resolution algorithm for Horn formulae and computer implementation. Information Processing Letters, 1988, 29(1): 1–12

    Article  MathSciNet  Google Scholar 

  19. Baader F, Lutz C, Suntisrivaraporn B. Efficient reasoning in \({\cal E}{{\cal L}^ + }\). In: Proceedings of the 2006 International Workshop on Description Logics. 2006, 15

  20. Bailey J, Stuckey P J. Discovery of minimal unsatisfiable subsets of constraints using hitting set dualization. In: Proceedings of the 7th International Symposium on Practical Aspects of Declarative Languages. 2005, 174–186

  21. Bendík J, Benes N, Cerná I, Barnat J. Tunable online MUS/MSS enumeration. In: Proceedings of the 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. 2016, 50: 1–50: 13

  22. Narodytska N, Bjørner N, Marinescu M C, Sagiv M. Core-guided minimal correction set and core enumeration. In: Proceedings of the 27th International Joint Conference on Artificial Intelligence. 2018, 1353–1361

  23. Bendík J, Černá I, Beneš N. Recursive online enumeration of all minimal unsatisfiable subsets. In: Proceedings of the 16th International Symposium on Automated Technology for Verification and Analysis. 2018, 143–159

  24. Bendík J, Černá I. Replication-guided enumeration of minimal unsatisfiable subsets. In: Proceedings of the 26th International Conference on Principles and Practice of Constraint Programming. 2020, 37–54

  25. Bendík J, Černá I. MUST: Minimal unsatisfiable subsets enumeration tool. In: Proceedings of the 26th International Conferences on Tools and Algorithms for the Construction and Analysis of Systems. 2020, 135–152

  26. Peñaloza R, Sertkaya B. On the complexity of axiom pinpointing in the EL family of description logics. In: Proceedings of the 12th International Conference on Principles of Knowledge Representation and Reasoning. 2010, 280–289

  27. Marques-Silva J, Ignatiev A, Mencía C, Peñaloza R. Efficient reasoning for inconsistent horn formulae. In: Proceedings of the 15th European Conference on Logics in Artificial Intelligence. 2016, 336–352

  28. Belov A, Marques-Silva J. MUSer2: an efficient MUS extractor. Journal on Satisfiability, Boolean Modeling and Computation, 2012, 8(3–4): 123–128

    Article  Google Scholar 

  29. Bacchus F, Katsirelos G. Using minimal correction sets to more efficiently compute minimal unsatisfiable sets. In: Proceedings of the 27th International Conference on Computer Aided Verification. 2015, 70–86

  30. Kilby P, Slaney J, Thiébaux S, Walsh T. Backbones and backdoors in satisfiability. In: Proceedings of the 20th National Conference on Artificial Intelligence. 2005, 1368–1373

  31. Audemard G, Simon L. Predicting learnt clauses quality in modern SAT solvers. In: Proceedings of the 21st International Joint Conference on Artificial Intelligence. 2009, 399–404

  32. Moskewicz M W, Madigan C F, Zhao Y, Zhang L, Malik S. Chaff: engineering an efficient SAT solver. In: Proceedings of the 38th Annual Design Automation Conference. 2001, 530–535

  33. Liang J H, Ganesh V, Zulkoski E, Zaman A, Czarnecki K. Understanding VSIDS branching heuristics in conflict-driven clause-learning SAT solvers. In: Proceedings of the 11th International Haifa Verification Conference on Hardware and Software: Verification and Testing. 2015, 225–241

  34. Oh C. Between SAT and UNSAT: the fundamental difference in CDCL SAT. In: Proceedings of the 18th International Conference on Theory and Applications of Satisfiability Testing. 2015, 307–323

  35. Morgado A, Liffiton M, Marques-Silva J. MaxSAT-based MCS enumeration. In: Proceedings of the 8th International Haifa Verification Conference on Hardware and Software: Verification and Testing. 2012, 86–101

  36. Liffiton M H, Sakallah K A. Algorithms for computing minimal unsatisfiable subsets of constraints. Journal of Automated Reasoning, 2008, 40(1): 1–33

    Article  MathSciNet  Google Scholar 

  37. Liffiton M H, Previti A, Malik A, Marques-Silva J. Fast, flexible MUS enumeration. Constraints, 2016, 21(2): 223–250

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. 42050103, 62076108, and U19A2061).

Author information

Authors and Affiliations

  1. College of Computer Science and Technology, Jilin University, Changchun, 130012, China

    Dantong Ouyang, Mengting Liao & Yuxin Ye

  2. Key Laboratory of Symbolic Computation and Knowledge Engineering (Jilin University), Ministry of Education, Changchun, 130012, China

    Dantong Ouyang & Yuxin Ye

Authors
  1. Dantong Ouyang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mengting Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuxin Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuxin Ye.

Additional information

Dantong Ouyang received her PhD degree in computer software and theory from Jilin University, China in 1998. She is currently a professor and PhD supervisor in the College of Computer Science and Technology, Jilin University, China. She is a senior member of China Computer Federation (CCF). She also serves on some academic organizations, such as CCF TCAIPR, CCF TTCS, CAAI KE&DS, and so on. Her main research interests include artificial intelligence, automatic reasoning, model based diagnosis, constraint problem, and so on.

Mengting Liao received her BS degree in computer science and technology from Jilin University, China in 2019. She is currently working toward the MS degree in computer software and theory in the Key Laboratory of Symbolic Computation and Knowledge Engineering (Jilin University), Ministry of Education, China. Her main research interests include semantic Web and ontology engineering.

Yuxin Ye received his PhD degree in computer software and theory from Jilin University, China in 2010. He is currently a professor and PhD supervisor in the College of Computer Science and Technology, Jilin University, China. He also serves on Key Laboratory of Symbolic Computation and Knowledge Engineering (Jilin University), Ministry of Education, China. He has more than 10 years of experience in ontology engineering and semantic Web research and has more than 40 publications in these areas. He is a Member of China Computer Federation (CCF) and Chinese Association of Artificial Intelligence (CAAI). His main research interests include semantic Web, ontology engineering, and knowledge graph.

Electronic Supplementary Material

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ouyang, D., Liao, M. & Ye, Y. Lightweight axiom pinpointing via replicated driver and customized SAT-solving. Front. Comput. Sci. 17, 172315 (2023). https://doi.org/10.1007/s11704-022-1360-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11704-022-1360-x

Keywords

Search

Navigation