2026-07-22T23:45:55Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18610 2024-03-06T11:02:15Z ddc:004 open_access

Deciding Predicate Logical Theories Of Real-Valued Functions Ratschan, Stefan decision procedures first-order predicate logical theories real numbers real-valued functions 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Stefan Ratschan 2023 Is Part Of LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2023.76 urn:nbn:de:0030-drops-186101 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.76 eng https://creativecommons.org/licenses/by/4.0/legalcode