Parys, Paweł - Recursion Schemes, the MSO Logic, and the U quantifier

lmcs:4885 - Logical Methods in Computer Science, February 18, 2020, Volume 16, Issue 1 - https://doi.org/10.23638/LMCS-16(1:20)2020
Recursion Schemes, the MSO Logic, and the U quantifier

Authors: Parys, Paweł

We study the model-checking problem for recursion schemes: does the tree generated by a given higher-order recursion scheme satisfy a given logical sentence. The problem is known to be decidable for sentences of the MSO logic. We prove decidability for an extension of MSO in which we additionally have an unbounding quantifier U, saying that a subformula is true for arbitrarily large finite sets. This quantifier can be used only for subformulae in which all free variables represent finite sets (while an unrestricted use of the quantifier leads to undecidability). We also show that the logic has the properties of reflection and effective selection for trees generated by recursion schemes.


Volume: Volume 16, Issue 1
Published on: February 18, 2020
Submitted on: October 12, 2018
Keywords: Computer Science - Logic in Computer Science


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