2000 character limit reached
Compositionality of the MSO+U Logic (2005.02384v1)
Published 5 May 2020 in cs.LO
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).