Metric Right Propositional Neighborhood Logic with an Equivalence Relation

In [13] Montanari et al. proved that the satisfiability problem for the fragments A and AA of Halpern and Shoham’s modal logic of intervals extended with an equivalence relation ∼ over points, namely the logics A∼ and AA∼ respectively, is decidable and retains the same complexity (i.e., NEXPTIME-complete) of the same fragments deprived of the equivalence relation. In the same work the authors proved that the satisfiability problem for the logic AA∼ extended with metric constraints, namely MPNL∼, may be reduced to the reachability problem for Vector Addition Systems with States (VASS) [11] whose complexity upper bound is still unknown. In this paper we make a step forward in completing the picture by proving that the satisfiability problem for the missing fragment A∼ extended with metric constraints, namely MRPNL∼, is in 3EXPSPACE and it is EXPSPACE-hard.

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