License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2023.76
URN: urn:nbn:de:0030-drops-186101
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18610/
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Ratschan, Stefan

Deciding Predicate Logical Theories Of Real-Valued Functions

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LIPIcs-MFCS-2023-76.pdf (0.7 MB)

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.

BibTeX - Entry

@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/opus/volltexte/2023/18610},
  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}
}

Keywords: decision procedures, first-order predicate logical theories, real numbers, real-valued functions
Collection: 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)
Issue Date: 2023
Date of publication: 21.08.2023

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