Compositionality of the MSO+U Logic

Paweł Parys

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arXiv · 2005.02384

Compositionality of the MSO+U Logic

Paweł Parys

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Abstract

We prove that the MSO+U logic is compositional in the following sense: whether an MSO+U formula holds in a tree T depends only on MSO+U-definable properties of the root of T and of subtrees of T starting directly below the root. Another kind of compositionality follows: every MSO+U formula whose all free variables range only over finite sets of nodes (in particular, whose all free variables are first-order) can be rewritten into an MSO formula having access to properties of subtrees definable by MSO+U sentences (without free variables).

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Paweł Parys. 2020-05-05. Compositionality of the MSO+U Logic. https://arxiv.org/abs/2005.02384

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