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Approximation Spaces of Temporal Processes and Effectiveness of Interval Semantics

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Distributed Computing and Artificial Intelligence, Special Sessions, 17th International Conference (DCAI 2020)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1242))

Abstract

A series of positive results related to the generalized problem of Yu.L. Ershov on the structure of \(\varSigma \)-degrees of dense linear orders is obtained. In particular, we prove that interval models of temporal logic, as well as finite fragments of approximation spaces generated by interval Boolean algebras, are \(\varSigma \)-definable (effectively interpretable) in hereditarily finite superstructures over dense linear orders. These results are used in the analysis of semantics of verbs in natural languages within the approach in formal semantics proposed by R. Montague.

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Acknowledgement

This work was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. 0314-2019-0003), and partially supported by the RFBR grant no. 18-01-00624-a.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Alexey Stukachev

  2. Novosibirsk State University, Novosibirsk, Russia

    Alexey Stukachev

Authors
  1. Alexey Stukachev
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Correspondence to Alexey Stukachev .

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Editors and Affiliations

  1. IoT European Digital Innovation Hub, Bioinformatics Intelligent Systems and Educational Technology Research Group, Department of Computer Science, Faculty of Science, University of Salamanca, Salamanca, Spain

    Sara Rodríguez González

  2. GRASIA Research Group, Facultad de Informática, Universidad Complutense de Madrid, Madrid, Spain

    Alfonso González-Briones

  3. Faculty of Mechanical Engineering, Department of Production Computerisation and Robotisation, Lublin University of Technology, Lublin, Poland

    Arkadiusz Gola

  4. Cerca Trova Ltd, Sofia, Bulgaria

    George Katranas

  5. Department of Biology, Ecology and Earth Science, University of Calabria, Arcavacata di Rende, Cosenza, Italy

    Michela Ricca

  6. Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, Sofia, Bulgaria

    Roussanka Loukanova

  7. Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, Salamanca, Spain

    Javier Prieto

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Stukachev, A. (2021). Approximation Spaces of Temporal Processes and Effectiveness of Interval Semantics. In: Rodríguez González, S., et al. Distributed Computing and Artificial Intelligence, Special Sessions, 17th International Conference. DCAI 2020. Advances in Intelligent Systems and Computing, vol 1242. Springer, Cham. https://doi.org/10.1007/978-3-030-53829-3_5

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