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A Complete Fragment of HigherOrder Duration µCalculus
 LNCS 1974, SpringerVerlag
, 2000
"... The paper presents an extension HDC of Higherorder Duration Calculus (HDC,[ZGZ99]) by a polyadic least fixed point () operator and a class of nonlogical symbols with a finite variability restriction on their interpretations, which classifies these symbols as intermediate between rigid symbols and ..."
Abstract

Cited by 5 (3 self)
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The paper presents an extension HDC of Higherorder Duration Calculus (HDC,[ZGZ99]) by a polyadic least fixed point () operator and a class of nonlogical symbols with a finite variability restriction on their interpretations, which classifies these symbols as intermediate between rigid symbols and flexible symbols as known in DC. The operator and the new kind of symbols enable straightforward specification of recursion and data manipulation by HDC. The paper contains a completeness theorem about an extension of the proof system for HDC by axioms about and symbols of finite variability for a class of simple HDC formulas, which extends the original class of simple DC formulas introduced in [DW94]. The new class extends the original one by allowing subformulas of finite variability and existential quantification over both individual and program variables. The completeness theorem is proved by the method of local elimination of the extending operator , which was earlier used for a simil...
Formal Design of Hybrid Control Systems: Duration . . .
 February 2001 UNU/IIST, P.O. Box 3058, Macau References 54
, 2000
"... In this paper, we present an approach to the design of hybrid systems by combination of several comprehensive formalization techniques. We use Duration Calculus to specify the requirement and design of the system and to model controller at abstract level of system development. Then the high level de ..."
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Cited by 3 (1 self)
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In this paper, we present an approach to the design of hybrid systems by combination of several comprehensive formalization techniques. We use Duration Calculus to specify the requirement and design of the system and to model controller at abstract level of system development. Then the high level designs are further refined in control theory. A formal verification may be done either in DC if it is possible, or in predicate calculus using the semantics of DC or theorems from control theory. We show our techniques through a double water tank case study which is one of the bench mark problem for modern process control engineering.
Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems
 Logical Methods in Computer Science
"... Vol. 3 (3:3) 2007, pp. 1–43 ..."
Projection onto State in DC: . . .
, 2002
"... This report presents a relative completeness result for the operator of projection onto state in Duration Calculus (DC). This operator was introduced in 1999 and studied extensively in a revised form in 2002 in our earlier works. The completeness of a system of axioms and a proof rule for projection ..."
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This report presents a relative completeness result for the operator of projection onto state in Duration Calculus (DC). This operator was introduced in 1999 and studied extensively in a revised form in 2002 in our earlier works. The completeness of a system of axioms and a proof rule for projection onto state is established relative to the extension of DC by neighbourhood formulas, which express the neighbourhood values of boolean DC state expressions. (Neighbourhood formulas in DC themselves have a complete axiomatisation relative to DC.) The proof of relative completeness is constructive, relative to validity in DC without extending constructs.