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Order-Invariant First-Order Logic over Hollow Trees

Authors Julien Grange, Luc Segoufin



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Author Details

Julien Grange
  • ENS Paris & PSL & INRIA & CNRS, France
Luc Segoufin
  • INRIA & ENS Paris & PSL, France

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Julien Grange and Luc Segoufin. Order-Invariant First-Order Logic over Hollow Trees. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 23:1-23:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.CSL.2020.23

Abstract

We show that the expressive power of order-invariant first-order logic collapses to first-order logic over hollow trees. A hollow tree is an unranked ordered tree where every non leaf node has at most four adjacent nodes: two siblings (left and right) and its first and last children. In particular there is no predicate for the linear order among siblings nor for the descendant relation. Moreover only the first and last nodes of a siblinghood are linked to their parent node, and the parent-child relation cannot be completely reconstructed in first-order.

Subject Classification

ACM Subject Classification
  • Theory of computation → Finite Model Theory
Keywords
  • order-invariance
  • first-order logic

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References

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