2026-07-23T01:24:23Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:13452 2024-03-06T10:52:07Z ddc:004 open_access

Extension Preservation in the Finite and Prefix Classes of First Order Logic Dawar, Anuj Sankaran, Abhisekh finite model theory preservation theorems extension closed composition Datalog Ehrenfeucht-Fraisse games It is well known that the classic Łoś-Tarski preservation theorem fails in the finite: there are first-order definable classes of finite structures closed under extensions which are not definable (in the finite) in the existential fragment of first-order logic. We strengthen this by constructing for every n, first-order definable classes of finite structures closed under extensions which are not definable with n quantifier alternations. The classes we construct are definable in the extension of Datalog with negation and indeed in the existential fragment of transitive-closure logic. This answers negatively an open question posed by Rosen and Weinstein. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Anuj Dawar and Abhisekh Sankaran 2021 Is Part Of LIPIcs, Volume 183, 29th EACSL Annual Conference on Computer Science Logic (CSL 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2021.18 urn:nbn:de:0030-drops-134520 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2021.18 eng https://creativecommons.org/licenses/by/3.0/legalcode