Titlebook: Duration Calculus; A Formal Approach to Zhou Chaochen,Michael R. Hansen Book 2004 Springer-Verlag Berlin Heidelberg 2004 Duration Calculus.

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Relative Completeness,ng DC formulas in specifications, we want . to be the integral of a Boolean-valued function. Therefore, to show the completeness of DC, it must be shown that the axioms DCA1 — DCA6, together with the rules IR1 and IR2 and the axioms and rules of IL, are enough to ensure that temporal variables of the form . are definable by integrals.

有常识

Model Checking: Linear Duration Invariants,iscrete-time domains. In Chap. 6, decidable subclasses of DC formulas were identified. Some are decidable for both the continuous- and the discrete-time domains, while others are decidable for discrete time only.

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State Transitions and Events,he system enters a state, it will stay in that state throughout a period. An event of a system characterizes an . interaction of the system with its environment. This can drive both the system and its environment to change their behavior dramatically.

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GOAT

Virach Sornlertlamvanich,Canasai KruengkraiIn this chapter we give the syntax, semantics and proof system for interval logic (IL). This part is based mainly on [27, 28]. Furthermore, we develop theorems and rules of IL which are useful when constructing proofs.

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Mary Renck Jalongo,Olivia N. SarachoIn this chapter we consider a subset of formulas of DC for which the satisfiability of a formula is decidable. Since a formula . is valid if the formula ¬. is not satisfiable, we can decide whether a formula in the subset is valid as well. The decidability results presented here are based on [167].

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Induction

From Consumer to Producer of the LiteratureThe chop-based interval temporal logics, such as ITL [43], IL and DC, are useful for the specification and verification of safety properties of real-time systems. In these logics, one can easily express properties such as