An Algebraic Semantics for Duration Calculus

Abstract. We present an algebraic semantics for Duration Calculus based on semirings and quantales. Duration Calculus was originally introduced in 1991 as a powerful logic for specifying the safety of real-time systems. We embed the Duration Calculus into the theory of Boolean semirings and extend them to Kleene algebras and ω-algebras, respectively, to express finite and infinite iteration. This allows us to calculate easily with the safety requirements and to see special results of the Duration Calculus in a more general context. When formulating an algebraic semantics we also generalise parts of von Karger’s work about reactive systems, especially, the engineer’s induction.