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Relational Semantics for Modal Logics

By Bernd--holger Schlingloff and Wolfgang Heinle


In this work we survey the connections between modal logic and relation algebra. We compare various modal and relational languages for the specification 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 fixpoint operators.

Year: 1995
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