Foundations of Software Science and Computation Structures

Volume 3921 of the series Lecture Notes in Computer Science pp 157-171

A Finite Model Construction for Coalgebraic Modal Logic

  • Lutz SchröderAffiliated withDepartment of Computer Science, University of Bremen


In recent years, a tight connection has emerged between modal logic on the one hand and coalgebras, understood as generic transition systems, on the other hand. Here, we prove that (finitary) coalgebraic modal logic has the finite model property. This fact not only reproves known completeness results for coalgebraic modal logic, which we push further by establishing that every coalgebraic modal logic admits a complete axiomatization of rank 1; it also enables us to establish a generic decidability result and a first complexity bound. Examples covered by these general results include, besides standard Hennessy-Milner logic, graded modal logic and probabilistic modal logic.