Multivalued Coalgebraic Modal Logic for Multiagent Systems and Multiplayer Games
Nima Motamed
Abstract:
This thesis investigates coalgebraic generalizations of two multiagent modal logics from the literature, in which truth values are identified with sets of agents. In the first logic, which is due to Melvin Fitting, the truth value of a formula is identified as the set of agents for whom the formula is true, while in the second logic, which is due to Loes Olde Loohuis and Yde Venema, the truth value of a formula is identified as the set of players that have a winning strategy at a corresponding position in a multiplayer evaluation game. For the first logic, we identify a new base category of interest, from which the generalization comes forth naturally using the theory of coalgebraic modal logic, and give proofs of adequacy and expressivity. For the second logic, we define multiplayer evaluation games in which play proceeds nondeterministically, and use the well-known fact that predicate liftings induce transformations from coalgebras to neighbourhood frames. Finally, we prove that fragments of our generalizations are equiexpressive, and show how they can naturally describe situations with multiple agents.