On the Model Checking of the Graded $$μ $$ -calculus on Trees - Bárcenas, Everardo; Benítez-Guerrero, Edgard; Lavalle, Jesús (Advances in Artificial Intelligence and Soft Computing, 2015)
The $$μ $$ -calculus is an expressive propositional modal logic augmented with least and greatest fixed-points, and encompasses many temporal, program, dynamic and description logics. The model checking problem for the $$μ $$ -calculus is known to be in NP $$\cap $$ Co-NP. In this paper, we study the model checking problem for the $$μ $$ -calculus extended with graded modalities. These constructors allow to express numerical constraints on the occurrence of accessible nodes (worlds) satisfying a certain formula. It is known that the model checking problem for the graded $$μ $$ -calculus with finite models is in EXPTIME. In the current work, we introduce a linear-time model checking algorithm for the graded $$μ $$ -calculus when models are finite unranked trees.