On Dynamic Topological Logic of the Real Line
| العنوان: | On Dynamic Topological Logic of the Real Line |
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| المؤلفون: | Aleksey Nogin, Maria Nogin |
| المصدر: | Journal of Logic and Computation. 18:1029-1045 |
| بيانات النشر: | Oxford University Press (OUP), 2008. |
| سنة النشر: | 2008 |
| مصطلحات موضوعية: | Arts and Humanities (miscellaneous), Continuous function, Topological algebra, Logic, Hardware and Architecture, Modal language, Focus (optics), Topology, Real line, Software, Topological quantum number, Theoretical Computer Science, Mathematics |
| الوصف: | This article explores the topological interpretations of the modal language with two modalities—□, which is interpreted as the interior operation and ◯ (‘next’) which is interpreted as the pre-image operation for a continuous function. It is known that the □◯ logic S4C is complete with respect to topological interpretations in ℝn for n≥2, yet it is incomplete with respect to topological interpretations in ℝ. We focus on the logic L□◯(ℝ) of all the □◯ formulas that are sound with respect to topological interpretations in ℝ. In this article we present two formulas in L□◯(ℝ)–S4C, and prove that they are sound in ℝ and independent. We also establish that the previously known examples of formulas in L□◯(ℝ)–S4C are instances of a particular consequence of one of the two formulas presented. |
| تدمد: | 1465-363X 0955-792X |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::073f62c616660b73522801493895cae5 https://doi.org/10.1093/logcom/exn034 |
| رقم الأكسشن: | edsair.doi...........073f62c616660b73522801493895cae5 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 1465363X 0955792X |
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