Modal Logics with Composition on Finite Forests: Expressivity and Complexity

Bartosz BednarczykBartosz Bednarczyk, Stéphane DemriStéphane Demri, Raul FervariRaul Fervari, Alessio MansuttiAlessio Mansutti

Bartosz Bednarczyk, Stéphane Demri, Raul Fervari, Alessio Mansutti
Modal Logics with Composition on Finite Forests: Expressivity and Complexity
Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2020), June 2020

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KurzfassungAbstract
We investigate the expressivity and computational complexity of two modal logics on finite forests equipped with operators to reason on submodels. The logic ML(|) extends the basic modal logic ML with the composition operator | from static ambient logic, whereas ML(∗) contains the separating conjunction ∗ from separation logic. Though both operators are second-order in nature, we show that ML(|) is as expressive as the graded modal logic GML (on finite trees) whereas ML(∗) lies strictly between ML and GML. Moreover, we establish that the satisfiability problem for ML(∗) is Tower-complete, whereas for ML(|) is (only) AExpPol-complete.As a by-product, we solve several open problems related to sister logics, such as static ambient logic, modal separation logic, and second-order modal logic on finite trees.
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Forschungsgruppe:Research Group: Computational LogicComputational Logic

@inproceedings{BDFM2020,
  author    = {Bartosz Bednarczyk and St{\'{e}}phane Demri and Raul Fervari and
               Alessio Mansutti},
  title     = {Modal Logics with Composition on Finite Forests: Expressivity and
               Complexity},
  booktitle = {Proceedings of the 35th Annual {ACM/IEEE} Symposium on Logic in
               Computer Science (LICS 2020)},
  year      = {2020},
  month     = {June},
  doi       = {10.1145/3373718.3394787}
}