Multi-valued model checking games

This work extends the game-based framework of μ-calculus model checking to the multi-valued setting. In multi-valued model checking a formula is interpreted over a Kripke structure defined over a lattice. The value of the formula is also an element of the lattice. We define a new game for this problem and derive from it a direct model checking algorithm that handles the multi-valued structure without any reduction. We investigate the properties of the new game, both independently, and in comparison to the automata-based approach. We show that the usual resemblance between the two approaches does not hold in the multi-valued setting and show how it can be regained by changing the nature of the game.