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Extension Preservation in the Finite and Prefix Classes of First Order Logic

Authors Anuj Dawar , Abhisekh Sankaran

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Subject Classification

ACM Subject Classification
  • Theory of computation → Finite Model Theory
Keywords
  • finite model theory
  • preservation theorems
  • extension closed
  • composition
  • Datalog
  • Ehrenfeucht-Fraisse games

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Abstract

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.

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Anuj Dawar and Abhisekh Sankaran. Extension Preservation in the Finite and Prefix Classes of First Order Logic. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.CSL.2021.18

Author Details

Anuj Dawar
  • Department of Computer Science and Technology, University of Cambridge, UK
Abhisekh Sankaran
  • Department of Computer Science and Technology, University of Cambridge, UK

Funding

Research supported by the Leverhulme Trust through a Research Project Grant on "Logical Fractals"

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