Skip to main content
Springer Nature Link
Log in

A tractable temporal description logic for reasoning fuzzy spatiotemporal knowledge

  • Published:
World Wide Web Aims and scope Submit manuscript

Abstract

Fuzzy spatiotemporal reasoning is extensively used in various application fields such as Geographic Information Systems, Geospatial Artificial Intelligence, and Remote Sensing Systems. However, providing a tractable reasoning mechanism for fuzzy spatiotemporal knowledge is a challenging research problem. Description logics (DLs) are a type of logic-based tractable knowledge representation formalism that allow for describing knowledge structure of an application domain, but they are limited in their ability to express fuzzy spatiotemporal knowledge. To address this limitation, we propose a tractable temporal DL named f-\(\mathcal {ALC(S)}\)-LTL, which expands linear temporal logic (LTL) by utilizing fuzzy spatial DL f-\(\mathcal {ALC(S)}\). In this article, we first define the syntax and formal-semantic model of our logic and investigate a tableau rule-based reasoning procedure to verify satisfiability. We further show the correctness and computational complexity of the reasoning procedure and demonstrate a running example of its application. Finally, we implement a prototype reasoning tool that can determine the satisfiability problem. Our case studies show that our logic f-\(\mathcal {ALC(S)}\)-LTL is feasible and the prototype reasoning tool actually works. The logic f-\(\mathcal {ALC(S)}\)-LTL enables tractable reasoning about the dynamic evolution of fuzzy RCC relations over time.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Availability of data and material

Not applicable.

Notes

  1. https://github.com/haitaoneu/FSTsat

References

  1. Pfoser, D., Tryfona, N.: Capturing fuzziness and uncertainty of spatiotemporal objects. In: Proceedings of the 5th East-European Conference on Advances in Databases and Information Systems (ADBIS 2001), pp. 112–126 (2001)

  2. Klamma, R., Cao, Y., Spaniol, M., Leng, Y.: Spatiotemporal knowledge visualization and discovery in dynamic social networks. In: Proceedings of the 7th International Conference on Knowledge Management, Graz, Austria, Sept. 5-7, 2007, pp. 384–391 (2007)

  3. Cheng, H., Yan, L., Ma, Z., Ribarić, S.: Fuzzy spatio-temporal ontologies and formal construction based on fuzzy petri nets. Comput. Intell. 35(1), 204–239 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cheng, H.: Modeling and querying fuzzy spatiotemporal objects. J. Intell. Fuzzy Syst. 31(6), 2851–2858 (2016)

    Article  Google Scholar 

  5. Ribaric, S., Hrkac, T.: A model of fuzzy spatio-temporal knowledge representation and reasoning based on high-level petri nets. Inf. Syst. 37(3), 238–256 (2012)

    Article  Google Scholar 

  6. Cheng, H., Wang, R., Li, P., Xu, H.: Representing and reasoning fuzzy spatio-temporal knowledge with description logics: A survey. Intell. Data Anal. 23(S1), 113–132 (2019)

    Article  Google Scholar 

  7. Sioutis, M., Wolter, D.: Qualitative spatial and temporal reasoning: Current status and future challenges. In: Proceedings of the Thirtieth International Joint Conference on Artificial Intelligencez(IJCAI 2021), pp. 4594–4601. (2021)

  8. Nguyen, L.A., Ha, Q.-T., Nguyen, N.-T., Nguyen, T.H.K., Tran, T.-L.: Bisimulation and bisimilarity for fuzzy description logics under the gödel semantics. Fuzzy Sets Syst. 388, 146–178 (2020)

    Article  MATH  Google Scholar 

  9. Zhang, F., Cheng, J.: Verification of fuzzy UML models with fuzzy description logic. Appl. Soft Comput. 73, 134–152 (2018)

    Article  Google Scholar 

  10. Straccia, U.: Towards spatial reasoning in fuzzy description logics. In: Proceedings of IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2009), pp. 512–517. (2009)

  11. Cheng, H., Ma, Z., Peng, L.: A fuzzy spatial description logic for the Semantic Web. J. Ambient. Intell. Humaniz. Comput. 13(11), 4991–5009 (2022)

    Article  Google Scholar 

  12. Hudelot, C., Atif, J., Bloch, I.: ALC(F): A new description logic for spatial reasoning in images. In: Proceedings of The13th European Conference on Computer Vision (ECCV Workshop 2014), pp. 370–384. (2014)

  13. Artale, A., Franconi, E.: A survey of temporal extensions of description logics. Ann. Math. Artif. Intell. 30(1), 171–210 (2001)

    MathSciNet  MATH  Google Scholar 

  14. Lutz, C., Wolter, F., Zakharyaschev, M.: Temporal description logics: A survey. In: Proceedings of the 15th International Symposium on Temporal Representation and Reasoning (TIME 2008), pp. 3–14. (2008)

  15. Babenyshev, S., Rybakov, V.: Linear temporal logic LTL: basis for admissible rules. J. Log. Comput. 21(2), 157–177 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Cristani, M., Gabrielli, N.: Practical issues of description logics for spatial reasoning. In: Proceedings of the 2009 AAAI Spring Symposium: Benchmarking of Qualitative Spatial and Temporal Reasoning Systems, pp. 5–10. (2009)

  17. Kaplunova, A., Haarslev, V., Moller, R.: Adding ternary complex roles to ALCRP(D). In: Proceedings of the International Workshop on Description Logics (DL 2002), pp. 112–126. (2002)

  18. Lutz, C., Milicic, M.: A tableau algorithm for description logics with concrete domains and general tboxes. J. Autom. Reason. 38(1), 227–259 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  19. Haarslev, V., Lutz, C., Moller, R.: A description logic with concrete domains and a role-forming predicate operator. J. Log. Comput. 9(3), 351–384 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  20. Wang, S., Liu, D.: Spatial description logic and its application in geospatial Semantic Web. In: Proceedings of the 2008 International Multi-symposiums on Computer and Computational Sciences, pp. 214–221. (2008)

  21. Hudelot, C., Atif, J., Bloch, I.: Integrating bipolar fuzzy mathematical morphology in description logics for spatial reasoning. In: ECAI, pp. 497–502. (2010)

  22. Bobillo, F., Straccia, U.: The fuzzy ontology reasoner fuzzydl. Knowl.-Based Syst. 95, 12–34 (2016)

    Article  Google Scholar 

  23. Huitzil, I., Straccia, U., Bobed, C., Mena, E., Bobillo, F.: The serializable and incremental semantic reasoner fuzzydl. In: 2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 1–8. (2020)

  24. Wolter, F., Zakharyaschev, M.: Temporalizing description logics. Frontiers of Combining Systems 2, 379–402 (1999)

    MATH  Google Scholar 

  25. Baader, F., Ghilardi, S., Lutz, C.: LTL over description logic axioms. ACM Trans. Comput. Log. 13(3), 21 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  26. Artale, A., Franconi, E.: A temporal description logic for reasoning about actions and plans. J. Artif. Intell. Res. 9, 463–506 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  27. Chang, L., Shi, Z., Gu, T., Zhao, L.: A family of dynamic description logics for representing and reasoning about actions. J. Autom. Reason. 49(1), 1–52 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  28. Lutz, C., Baader, F.: The complexity of description logics with concrete domains. Technical report, Fakultät für Mathematik, Informatik und Naturwissenschaften (2002)

  29. Sturm, H., Wolter, F.: A tableau calculus for temporal description logic: the expanding domain case. J. Log. Comput. 12(5), 809–838 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  30. Manna, Z., Pnueli, A.: The temporal logic of reactive and concurrent systems (1992)

  31. Flaminio, T., Tiezzi, E.B.: On metric temporal łukasiewicz logic. Electron. Notes Theor. Comput. Sci. 246, 71–85 (2009)

    Article  MATH  Google Scholar 

  32. Frigeri, A., Pasquale, L., Spoletini, P.: Fuzzy time in linear temporal logic. ACM Transactions on Computational Logic (TOCL) 15(4), 1–22 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  33. Moon, S.-I., Lee, K.H., Lee, D.: Fuzzy branching temporal logic. IEEE Trans. Syst. Man Cybern. B Cybern. 34(2), 1045–1055 (2004)

    Article  Google Scholar 

  34. Ghazouani, F., Farah, I.R., Solaiman, B.: Qualitative semantic spatio-temporal reasoning based on description logics for modeling dynamics of spatio-temporal objects in satellite images. In: 2018 4th International Conference on Advanced Technologies for Signal and Image Processing (ATSIP), pp. 1–6 (2018)

  35. George J, K., Bo, Y.: Fuzzy sets and fuzzy logic: theory and applications. (2008)

  36. Zadeh, L.A.: Fuzzy sets. Information. Control 8(3), 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  37. Hájek, P.: Metamathematics of Fuzzy Logic (1998)

  38. Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connection. In: Proceedings of the 3rd International Conference on Knowledge Representation and Reasoning (KR-92), pp. 165–176 (1992)

  39. Schockaert, S., De Cock, M., Cornelis, C., Kerre, E.E.: Fuzzy region connection calculus: An interpretation based on closeness. Int. J. Approximate Reasoning 48(1), 332–347 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  40. Schockaert, S., Cock, M.D., Cornelis, C., Kerre, E.E.: Fuzzy region connection calculus: An interpretation based on closeness. Int. J. Approximate Reasoning 48(1), 332–347 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  41. Schockaert, S., De Cock, M., Kerre, E.E.: Spatial reasoning in a fuzzy region connection calculus. Artif. Intell. 173(2), 258–298 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  42. Straccia, U.: All about fuzzy description logics and applications. In: Reasoning Web 2015, pp. 1–31 (2015)

  43. Seylan, I., Jamroga, W.: Coalition description logic with individuals. Electron. Notes Theor. Comput. Sci. 262, 231–248 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  44. Bienvenu, M.: Consequence finding in modal logic. PhD thesis, Ph. D. thesis, Université de Toulouse (2009)

  45. Wolper, P.: The tableau method for temporal logic: an overview. Logique et Anal. (N.S.) 110, 119–136 (1985)

    MathSciNet  MATH  Google Scholar 

  46. Goranko, V., Shkatov, D.: Tableau-based decision procedures for logics of strategic ability in multiagent systems. ACM Trans. Comput. Log. 11(1), 1–51 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  47. Gaintzarain, J., Hermo, M., Lucio, P., Navarro, M.: Systematic semantic tableaux for PLTL. Electron. Notes Theor. Comput. Sci. 206, 59–73 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  48. BenAri, M.: Mathematical Logic for Computer Science (2012)

  49. Kurucz, A., Wolter, F., Zakharyaschev, M., Gabbay, D.M.: Many-Dimensional Modal Logics: Theory and Applications (2003)

Download references

Funding

This work is supported by National Natural Science Foundation of China (No.62102194, No.62176121) and Natural Science Foundation of the Higher Education Institutions of Jiangsu Province(No. 20KJB520001).

Author information

Authors and Affiliations

  1. School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China

    Haitao Cheng

  2. College of Computer Science & Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

    Zongmin Ma

Authors
  1. Haitao Cheng
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Zongmin Ma
    View author publications

    You can also search for this author inPubMed Google Scholar

Contributions

Haitao Cheng wrote the main manuscript text, prepared all figures and tables and provided the conceptualization and methodology. Zongmin Ma provided formal analysis, writing-review, and editing. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Haitao Cheng.

Ethics declarations

Ethics approval

Not applicable.

Competing interests

The authors declare that they have no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheng, H., Ma, Z. A tractable temporal description logic for reasoning fuzzy spatiotemporal knowledge. World Wide Web 26, 3155–3182 (2023). https://doi.org/10.1007/s11280-023-01180-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11280-023-01180-0

Keywords