Abstract
Euclidean geometry and Newtonian time with floating point numbers are common computational models of the physical world. However, to achieve the kind of cyber-physical collaboration that arises in the IoT, such a literal representation of space and time may not be the best choice. In this chapter we survey location models from robotics, the internet, cyber-physical systems, and philosophy. The diversity in these models is justified by differing application demands and conceptualizations of space (spatial ontologies). To facilitate interoperability of spatial knowledge across representations, we propose a logical framework wherein a spatial ontology is defined as a model-theoretic structure. The logic language induced from a collection of such structures may be used to formally describe location in the IoT via semantic localization. Space-aware IoT services gain advantages for privacy and interoperability when they are designed for the most abstract spatial-ontologies as possible. We finish the chapter with definitions for open ontologies and logical inference.
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Notes
- 1.
Imagine overlaying two circles to form a venn-diagram, but with polygons instead of circles.
- 2.
A friendlier introduction can be found at https://plato.stanford.edu/entries/modeltheory-fo/
- 3.
Of course we don’t actually know the contents of A∗ because it contains the information we currently don’t know in A. But it is nevertheless useful to define A∗ as a model so we may make explicit our assumptions about the missing information.
- 4.
We do not always explicitly augment the domain of an open ontology to include ⊥, but this may be assumed.
- 5.
Essentially a semantic repository is a database for relational data.
- 6.
We refer to models of things moving through space as “Lagrangian Models” and models of space with things moving within as “Eulerian Models”. The terminology comes from the analysis of fluid flows.
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Acknowledgements
The work in this chapter was supported in part by the National Science Foundation (NSF), award #CNS-1836601 (Reconciling Safety with the Internet) and the iCyPhy Research Center (Industrial Cyber-Physical Systems), supported by Camozzi Industries, Denso, Siemens, and Toyota.
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Weber, M., Lee, E.A. (2021). Semantic Localization for IoT. In: Pandey, R., Paprzycki, M., Srivastava, N., Bhalla, S., Wasielewska-Michniewska, K. (eds) Semantic IoT: Theory and Applications. Studies in Computational Intelligence, vol 941. Springer, Cham. https://doi.org/10.1007/978-3-030-64619-6_16
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