2026-07-24T21:22:23Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:19655 2024-03-06T11:04:34Z ddc:004 open_access

Extending the WMSO+U Logic with Quantification over Tuples Badyl, Anita Parys, Paweł Boundedness logic decidability expressivity recursion schemes We study a new extension of the weak MSO logic, talking about boundedness. Instead of a previously considered quantifier 𝖴, expressing the fact that there exist arbitrarily large finite sets satisfying a given property, we consider a generalized quantifier 𝖴, expressing the fact that there exist tuples of arbitrarily large finite sets satisfying a given property. First, we prove that the new logic WMSO+𝖴_{tup} is strictly more expressive than WMSO+𝖴. In particular, WMSO+𝖴_{tup} is able to express the so-called simultaneous unboundedness property, for which we prove that it is not expressible in WMSO+𝖴. Second, we prove that it is decidable whether the tree generated by a given higher-order recursion scheme satisfies a given sentence of WMSO+𝖴_{tup}. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Anita Badyl and Paweł Parys 2024 Is Part Of LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2024.12 urn:nbn:de:0030-drops-196557 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.12 eng https://creativecommons.org/licenses/by/4.0/legalcode