Relational Semantics for Modal Logics

Bernd{Holger Schlinglo Institut f ur Informatik, Technische Universitat M unchen, e-mail: [email protected] Wolfgang Heinle Institut f ur angewandte Mathematik, Universitat Bern, e-mail: [email protected] Abstract In this work we survey the connections between modal logic and relation algebra. We compare various modal and relational languages for the speci cation of reactive systems by giving new translation algorithms between these languages. We then characterize the expressiveness of the languages algebraically with p-morphisms (or bisimulations). Furthermore, we show how completeness and incompleteness proofs of modal logic can be transferred to relation algebra, and give a relation algebraic treatment of modal correspondence theory. We show how our methods can be applied to stronger languages like those containing derivation rules or xpoint operators.