A Survey on Relation-Changing Modal Logics

Areces, C.. A Survey on Relation-Changing Modal Logics. In van Benthem, J. and Liu, F., editors, Graph Games and Logic Design, Trends in Logic, Springer Nature, Switzerland, 2026.

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Abstract

In this chapter, we present results on dynamic modal operators that can change the accessibility relation of a model during the evaluation of a formula. In particular, we extend the basic modal language with modalities that are able to delete, add or swap an edge between pairs of elements in the domain of a model. We define a generic framework to characterize this kind of operations. First, we investigate relation-changing modal logics as fragments of other, better investigated, logics, and in particular provide equivalence preserving translations into first order logic and hybrid logic. To investigate their expressive power, we define suitable notions of bisimulation for the logics introduced. We then turn to the complexity of different reasoning problems for these kind of logics. Finally, we discuss existing Hilbert-style axiomatizations, and the special techniques needed to establish completeness.

BibTeX

@incollection{areces:2026survey,
  author    = {Areces, C.},
  title     = {A Survey on Relation-Changing Modal Logics},
  booktitle = {Graph Games and Logic Design},
  editor    = {van Benthem, J. and Liu, F.},
  series    = {Trends in Logic},
  volume    = {66},
  publisher = {Springer Nature},
  year      = {2026},
  isbn      = {978-3-031-91360-0},
  address   = {Switzerland},
  abstract = "In this chapter, we present results on dynamic modal
                  operators that can change the accessibility relation
                  of a model during the evaluation of a formula. In
                  particular, we extend the basic modal language with
                  modalities that are able to delete, add or swap an
                  edge between pairs of elements in the domain of a
                  model. We define a generic framework to characterize
                  this kind of operations. First, we investigate
                  relation-changing modal logics as fragments of
                  other, better investigated, logics, and in
                  particular provide equivalence preserving
                  translations into first order logic and hybrid
                  logic. To investigate their expressive power, we
                  define suitable notions of bisimulation for the
                  logics introduced. We then turn to the complexity of
                  different reasoning problems for these kind of
                  logics. Finally, we discuss existing Hilbert-style
                  axiomatizations, and the special techniques needed
                  to establish completeness.",
}