On the Complexity of Graded Modal Logics with Converse.

Bartosz BednarczykBartosz Bednarczyk, Emanuel KierońskiEmanuel Kieroński, Piotr WitkowskiPiotr Witkowski

Bartosz Bednarczyk, Emanuel Kieroński, Piotr Witkowski
On the Complexity of Graded Modal Logics with Converse.
JELIA 2019, to appear

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KurzfassungAbstract
A complete classification of the complexity of the local and global satisfiability problems for graded modal language over traditional classes of frames has already been established. By 'traditional' classes of frames we mean those characterized by any positive combination of reflexivity, seriality, symmetry, transitivity, and the Euclidean property. In this paper we fill the gaps remaining in an analogous classification of the graded modal language with graded converse modalities. In particular we show its NExpTime-completeness over the class of Euclidean frames, demonstrating this way that over this class the considered language is harder than the language without graded modalities or without converse modalities. We also consider its variation disallowing graded converse modalities, but still admitting basic converse modalities. Our most important result for this variation is confirming an earlier conjecture that it is decidable over transitive frames. This contrasts with the undecidability of the language with graded converse modalities.
Weitere Informationen unter:Further Information: Link
Forschungsgruppe:Research Group: Computational LogicComputational Logic

@inproceedings{BKW2019,
  author    = {Bartosz Bednarczyk and Emanuel Kiero{\'{n}}ski and Piotr
               Witkowski},
  title     = {On the Complexity of Graded Modal Logics with Converse.},
  booktitle = {JELIA 2019},
  year      = {2019},
  month     = {May}
}