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A fuzzy spatial description logic for the semantic web

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Abstract

Spatial information is a critical feature in a large number of application domains. Spatial information, however, is often not crisp but with the nature of imprecision and fuzziness. As the increasing requirements of spatial applications, there emerges many challenges regarding to the representation and reasoning of spatial knowledge. Description logic (DL) is a logical basis for representing knowledge and realizing reasoning tasks in the Semantic Web. Therefore, how to extend DL to achieve the goal of representing and reasoning fuzzy spatial knowledge needs to be settled. In this work, we study a fuzzy spatial extension of the well known fuzzy \(\mathcal {ALC}\) DL to reason fuzzy spatial knowledge. First, we construct a fuzzy spatial concrete domain \(\mathcal {S}\) which is comprised of fuzzy spatial regions and fuzzy RCC relationships. More importantly, we give the admissibility proof of fuzzy spatial concrete domain \(\mathcal {S}\). Then we extend fuzzy \(\mathcal {ALC}\) with an admissible fuzzy spatial concrete domain \(\mathcal {S}\) and present a fuzzy spatial description logic f-\({\mathcal {ALC}}({\mathcal S})\). Finally, we address a decision procedure for f-\({\mathcal {ALC}}({\mathcal S})\) ABox consistency problem. Also, we show that the decision procedure is correct and the consistency problem for f-\({\mathcal {ALC}}({\mathcal S})\) is decidable in PSPACE-complete.

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References

  • Baader F, Hanschke P (1991) A scheme for integrating concrete domains into concept languages. In: Proceedings of the 12th international joint conference on artificial intelligence, pp 452–457

  • Belussi A, Migliorini S (2012) A framework for integrating multi-accuracy spatial data in geographical applications. Geoinformatica 16(3):523–561

    Article  Google Scholar 

  • Bobillo F, Straccia U (2009) Fuzzy description logics with general t-norms and datatypes. Fuzzy Sets Syst 160(23):3382–3402

    Article  MathSciNet  Google Scholar 

  • Bobillo F, Bou F, Straccia U (2011) On the failure of the finite model property in some fuzzy description logics. Fuzzy Sets Syst 172(1):1–12

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • Cheng H, Ma Z (2017) f-\(\cal{ALC(D)}\)-ltl: A fuzzy spatio-temporal description logic. In: Proceedings of the 10th international conference on knowledge science, engineering and management (KSEM 2017), pp 93–105

  • Cheng H, Ma Z (2019) Towards spatio-temporal reasoning in description logic f-\(\cal{ALC(D)}\)-ltl. In: Proceedings of the 32nd international workshop on description logics (DL 2019)

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Cristani M, Gabrielli N (2009) 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

  • Garg H, Arora R (2020) Maclaurin symmetric mean aggregation operators based on t-norm operations for the dual hesitant fuzzy soft set. J Ambient Intell Hum Comput 11(1):375–410

    Article  Google Scholar 

  • George JK, Bo Y (1995) Fuzzy sets and fuzzy logic: theory and applications. Prentice-Hall, Upper Saddle River

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Hájek P (2001) Metamathematics of fuzzy logic. Kluwer Academic Publishers, Dordrecht

    MATH  Google Scholar 

  • Hájek P (2005) Making fuzzy description logic more general. Fuzzy Sets Syst 154(1):1–15

    Article  MathSciNet  Google Scholar 

  • Hudelot C, Atif J, Bloch I (2010) Integrating bipolar fuzzy mathematical morphology in description logics for spatial reasoning. In: Proceedings of the19th European conference on artificial intelligence, pp 497–502

  • Hudelot C, Atif J, Bloch I (2014) 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

  • Kaplunova A, Haarslev V, Möller R (2002) Adding ternary complex roles to alcrp(d). In: Proceedings of the international workshop on description logics (DL 2002), pp 45–52

  • Karmarkar N (1984) A new polynomial-time algorithm for linear programming. Combinatorica 4(4):373–395

    Article  MathSciNet  Google Scholar 

  • Lu H, Li Y, Chen M, Kim H, Serikawa S (2018) Brain intelligence: go beyond artificial intelligence. Mob Netw Appl 23(2):368–375

    Article  Google Scholar 

  • Lu H, Wang D, Li Y, Li J, Li X, Kim H, Serikawa S, Humar I (2019) Conet: a cognitive ocean network. IEEE Wirel Commun 26(3):90–96

    Article  Google Scholar 

  • Lutz C (1999) Reasoning with concrete domains. In: Proceedings of the 16th international joint conference on artificial intelligence (IJCAI 1999), pp 90–95

  • Lutz C (2002a) The complexity of description logics with concrete domains. PhD thesis, Bibliothek der RWTH Aachen

  • Lutz C (2002b) Description logics with concrete domains-a survey. In: Proceedings of the 4th conference on advances in modal logic, pp 265–296

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

    Article  MathSciNet  Google Scholar 

  • Ma Z, Zhang F, Yan L, Cheng J (2014) Fuzzy knowledge management for the semantic web. Studies in fuzziness and soft computing. Springer, Berlin

    Book  Google Scholar 

  • Merz D, Penaloza R, Turhan AY (2014) Reasoning in alc with fuzzy concrete domains. In: Proceedings of the 37th annual german conference on artificial intelligence (KI 2014), pp 171–182

  • Mousavi SM, Harwood A, Karunasekera S, Maghrebi M (2018) Enhancing the quality of geometries of interest (gois) extracted from gps trajectory data using spatio-temporal data aggregation and outlier detection. J Ambient Intell Hum Comput 9(1):173–186

    Article  Google Scholar 

  • Na KS, Kong H, Cho M, Kim P, Baik DK (2006) Multimedia information retrieval based on spatiotemporal relationships using description logics for the semantic web. Int J Intell Syst 21(7):679–692

    Article  Google Scholar 

  • Randell DA, Cui Z, Cohn AG (1992) 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

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

    Article  Google Scholar 

  • Rigaux P, Scholl M, Voisard A (2001) Spatial databases with application to GIS. Morgan Kaufmann, Burlington

    Google Scholar 

  • Schmidt-Schau M, Smolka G (1991) Attributive concept descriptions with complements. Artif Intell 48(1):1–26

    Article  MathSciNet  Google Scholar 

  • Schneider M (1999) Uncertainty management for spatial data in databases: fuzzy spatial data types. In: The Sixth international symposium on advances in spatial databases, pp 330–351

  • Schockaert S, De Cock M, Kerre EE (2008a) Fuzzy region connection calculus: an interpretation based on closeness. Int J Approx Reason 48:332–347

    Article  MathSciNet  Google Scholar 

  • Schockaert S, De Cock M, Kerre EE (2008b) Fuzzy region connection calculus: representing vague topological information. Int J Approx Reason 48:314–331

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Schockaert S, Cock MD, Kerre E (2010) Reasoning about fuzzy temporal and spatial information from the web. World Scientific Publishing, Singapore

    Book  Google Scholar 

  • Singh M, Soni SK (2019) Fuzzy based novel clustering technique by exploiting spatial correlation in wireless sensor network. J Ambient Intell Hum Comput 10(4):1361–1378

    Article  Google Scholar 

  • Straccia U (2001) Reasoning within fuzzy description logics. J Artif Intell Res 14:137–166

    Article  MathSciNet  Google Scholar 

  • Straccia U (2005) Description logics with fuzzy concrete domains. In: Proceedings of the 21st conference on uncertainty in artificial intelligence (UAI2005), pp 559–567

  • Straccia U (2006) A fuzzy description logic for the semantic web. Fuzzy logic and the semantic web. Elsevier, Capturing Intelligence, Amsterdam, pp 73–90

    Book  Google Scholar 

  • Straccia U (2009) Towards spatial reasoning in fuzzy description logics. In: IEEE international conference on fuzzy systems (FUZZ-IEEE 2009), pp 512–517

  • Straccia U (2015) All about fuzzy description logics and applications. In: Faber W, Paschke A (eds) Reasoning Web 2015. Springer, Heidelberg, pp 1–31

    Google Scholar 

  • Tobies S (2001) Complexity results and practical algorithms for logics in knowledge representation. PhD thesis, Rheinisch-Westfalischen Technischen Hochschule Aachen

  • Torres-Ruiz M, Loza E, Al-Halabi WS, Moreno M (2016) Qualitative spatial reasoning methodology to determine the particular domain of a set of geographic objects. Comput Hum Behav 59:115–133

    Article  Google Scholar 

  • Wang Ss, Liu Dy (2008) 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

  • Wessel M (2002) On spatial reasoning with description logics—position paper. In: Proceedings of the 2002 international workshop on description logics (DL 2002), pp 156–163

  • Xu X, He L, Lu H, Gao L, Ji Y (2019) Deep adversarial metric learning for cross-modal retrieval. World Wide Web 22(2):657–672

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  Google Scholar 

  • Zhang Y, Gravina R, Lu H, Villari M, Fortino G (2018) Pea: parallel electrocardiogram-based authentication for smart healthcare systems. J Netw Comput Appl 117:10–16

    Article  Google Scholar 

Download references

Acknowledgements

The work is supported by National Key R&D Program of China (No. 2018YFB1003201), National Natural Science Foundation of China (Nos. 61672296, 61602261), Major Natural Science Research Projects in Colleges and Universities of Jiangsu Province (No. 18KJA520008), and NUPTSF (No. NY219053, NY217133).

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Authors and Affiliations

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

    Haitao Cheng & Peng Li

  2. Jiangsu High Technology Research Key Laboratory for Wireless Sensor Networks, Nanjing, 210023, China

    Haitao Cheng & Peng Li

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

    Zongmin Ma

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  1. Haitao Cheng
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  2. Zongmin Ma
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  3. Peng Li
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Correspondence to Haitao Cheng.

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Cheng, H., Ma, Z. & Li, P. A fuzzy spatial description logic for the semantic web. J Ambient Intell Human Comput 13, 4991–5009 (2022). https://doi.org/10.1007/s12652-020-01864-9

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