Standard

Interval Extensions of Orders and Temporal Approximation Spaces. / Stukachev, A. I.

In: Siberian Mathematical Journal, Vol. 62, No. 4, 07.2021, p. 730-741.

Research output: Contribution to journal › Article › peer-review

Harvard

Stukachev, AI 2021, 'Interval Extensions of Orders and Temporal Approximation Spaces', Siberian Mathematical Journal, vol. 62, no. 4, pp. 730-741. https://doi.org/10.1134/S0037446621040157

APA

Stukachev, A. I. (2021). Interval Extensions of Orders and Temporal Approximation Spaces. Siberian Mathematical Journal, 62(4), 730-741. https://doi.org/10.1134/S0037446621040157

Vancouver

Stukachev AI. Interval Extensions of Orders and Temporal Approximation Spaces. Siberian Mathematical Journal. 2021 Jul;62(4):730-741. doi: 10.1134/S0037446621040157

Author

Stukachev, A. I. / Interval Extensions of Orders and Temporal Approximation Spaces. In: Siberian Mathematical Journal. 2021 ; Vol. 62, No. 4. pp. 730-741.

BibTeX

@article{1c4aad2376c2450ebbd74ea8cab09060,
title = "Interval Extensions of Orders and Temporal Approximation Spaces",
abstract = "Studying the algorithmic properties ofinterval extensions of dense linear orders,in particular,the complexity degrees(namely,the $ s\Sigma $-degree)of the extensions,we show thatcontinuity is a necessary and sufficient conditionfor the equality between the complexity degreesof an order and its interval extension.We treat temporal approximation spaces over interval extensionsas mathematical models of verb semantics in natural languages.We show thatthe continuity of order impliesthe effectiveness of checking the validity of$ \Delta_{0}^{DL} $-formulasin spaces over$ sc $-simple enrichments.As a corollary,we obtain an effective description of the intervalscorresponding to various verb tenses in English.",
keywords = "510.5, approximation space, effective model theory, interval extension, linear order, mathematical linguistics",
author = "Stukachev, {A. I.}",
note = "Funding Information: The author was supported by the Mathematical Center in Akademgorodok under Agreement No. 075–15–2019–1613 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",
year = "2021",
month = jul,
doi = "10.1134/S0037446621040157",
language = "English",
volume = "62",
pages = "730--741",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",
number = "4",

}

RIS

TY - JOUR

T1 - Interval Extensions of Orders and Temporal Approximation Spaces

AU - Stukachev, A. I.

N1 - Funding Information: The author was supported by the Mathematical Center in Akademgorodok under Agreement No. 075–15–2019–1613 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: © 2021, Pleiades Publishing, Ltd.

PY - 2021/7

Y1 - 2021/7

N2 - Studying the algorithmic properties ofinterval extensions of dense linear orders,in particular,the complexity degrees(namely,the $ s\Sigma $-degree)of the extensions,we show thatcontinuity is a necessary and sufficient conditionfor the equality between the complexity degreesof an order and its interval extension.We treat temporal approximation spaces over interval extensionsas mathematical models of verb semantics in natural languages.We show thatthe continuity of order impliesthe effectiveness of checking the validity of$ \Delta_{0}^{DL} $-formulasin spaces over$ sc $-simple enrichments.As a corollary,we obtain an effective description of the intervalscorresponding to various verb tenses in English.

AB - Studying the algorithmic properties ofinterval extensions of dense linear orders,in particular,the complexity degrees(namely,the $ s\Sigma $-degree)of the extensions,we show thatcontinuity is a necessary and sufficient conditionfor the equality between the complexity degreesof an order and its interval extension.We treat temporal approximation spaces over interval extensionsas mathematical models of verb semantics in natural languages.We show thatthe continuity of order impliesthe effectiveness of checking the validity of$ \Delta_{0}^{DL} $-formulasin spaces over$ sc $-simple enrichments.As a corollary,we obtain an effective description of the intervalscorresponding to various verb tenses in English.

KW - 510.5

KW - approximation space

KW - effective model theory

KW - interval extension

KW - linear order

KW - mathematical linguistics

UR - http://www.scopus.com/inward/record.url?scp=85112631605&partnerID=8YFLogxK

U2 - 10.1134/S0037446621040157

DO - 10.1134/S0037446621040157

M3 - Article

AN - SCOPUS:85112631605

VL - 62

SP - 730

EP - 741

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 4

ER -

ID: 33990593