Guarded Fragments Meet Dynamic Logic: The Story of Regular Guards (Extended Version)
Abstract
We study the Guarded Fragment with Regular Guards (RGF), which combines the expressive power of the Guarded Fragment (GF) with Propositional Dynamic Logic with Intersection and Converse (ICPDL). Our logic generalizes, in a uniform way, many previously-studied extensions of GF, including (conjunctions of) transitive or equivalence guards, transitive or equivalence closure and more. We prove 2EXPTIME-completeness of the satisfiability problem for RGF, showing that RGF is not harder than ICPDL or GF. Shifting to the query entailment problem, we provide undecidability results that significantly strengthen and solidify earlier results along those lines. We conclude by identifying, in a natural sense, the maximal EXPSPACE-complete fragment of RGF.
Keywords
Cite
@article{arxiv.2509.09218,
title = {Guarded Fragments Meet Dynamic Logic: The Story of Regular Guards (Extended Version)},
author = {Bartosz Bednarczyk and Emanuel Kieroński},
journal= {arXiv preprint arXiv:2509.09218},
year = {2025}
}
Comments
This is an extended version of our paper that will appear at KR 2025. The current appendix has not yet been revised; an updated version will be released in the near future