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Order-Invariant First-Order Logic over Hollow Trees

Julien Grange
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Luc Segoufin
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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.
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Dates and versions

hal-02310749 , version 1 (10-10-2019)
hal-02310749 , version 2 (07-04-2020)



Julien Grange, Luc Segoufin. Order-Invariant First-Order Logic over Hollow Trees. CSL 2020 - 28th annual conference of the European Association for Computer Science Logic, Jan 2020, Barcelona, Spain. pp.1-23, ⟨10.4230/LIPIcs.CSL.2020.23⟩. ⟨hal-02310749v2⟩
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