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A tractable temporal description logic for reasoning fuzzy spatiotemporal knowledge

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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.

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

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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).

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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

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  1. Haitao Cheng
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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.

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Correspondence to Haitao Cheng.

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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

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