Relation-Changing Logics as Fragments of Hybrid Logics

TL;DR

This paper explores relation-changing modal logics, providing translations to hybrid logic, identifying decidable fragments, and comparing their expressive power, thereby advancing understanding of dynamic model modifications in modal logic.

Contribution

It introduces translations from relation-changing modal logics to hybrid logic, implements these translations, and identifies decidable fragments, enhancing the analysis of dynamic modal systems.

Findings

Translations enable analysis of relation-changing logics within hybrid logic.

Decidable fragments are identified through these translations.

Relation-changing logics have comparable expressive power to hybrid logics.

Abstract

Relation-changing modal logics are extensions of the basic modal logic that allow changes to the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to delete, add, and swap edges in the model, both locally and globally. We provide translations from these logics to hybrid logic along with an implementation. In general, these logics are undecidable, but we use our translations to identify decidable fragments. We also compare the expressive power of relation-changing modal logics with hybrid logics.