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Communication Dans Un Congrès Année : 2020

Modal Logics with Composition on Finite Forests

Résumé

We study the expressivity and complexity of two modal logics interpreted on finite forests and equipped with standard modalities to reason on submodels. The logic ML(|) extends the modal logic K with the composition operator from ambient logic, whereas ML(*) features the separating conjunction * from separation logic. Both operators are second-order in nature. We show that ML(|) is as expressive as the graded modal logic GML (on trees) whereas ML(*) is strictly less expressive than GML. Moreover, we establish that the satisfiability problem is Tower-complete for ML(*), whereas it is (only) AExp_{Pol}-complete for ML(|), a result which is surprising given their relative expressivity. As by-products, we solve open problems related to sister logics such as static ambient logic and modal separation logic.
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Dates et versions

hal-03005865 , version 1 (14-11-2020)

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Bartosz Bednarczyk, Stéphane Demri, Raul Fervari, Alessio Mansutti. Modal Logics with Composition on Finite Forests. 35th Annual ACM/IEEE Symposium on Logic in Computer Science, Jul 2020, Saarbruecken, Germany. ⟨10.1145/3373718.3394787⟩. ⟨hal-03005865⟩
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