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DOI: 10.4230/LIPIcs.MFCS.2023.76

Deciding Predicate Logical Theories Of Real-Valued Functions

Authors: Stefan Ratschan

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract

The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that reason about real-valued functions. This paper defines a first-order predicate language for reasoning about multi-dimensional smooth real-valued functions and their derivatives, and demonstrates that - despite the obvious undecidability barriers - certain positive decidability results for such a language are indeed possible.

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Stefan Ratschan. Deciding Predicate Logical Theories Of Real-Valued Functions. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 76:1-76:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ratschan:LIPIcs.MFCS.2023.76,
  author =	{Ratschan, Stefan},
  title =	{{Deciding Predicate Logical Theories Of Real-Valued Functions}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{76:1--76:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.76},
  URN =		{urn:nbn:de:0030-drops-186101},
  doi =		{10.4230/LIPIcs.MFCS.2023.76},
  annote =	{Keywords: decision procedures, first-order predicate logical theories, real numbers, real-valued functions}
}

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Deciding Predicate Logical Theories Of Real-Valued Functions

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