Specifying Various Time Models with Temporal Propositional Variables in Duration Calculus

Many extensions of Duration Calculus (DC) have been proposed for handling different aspects of real-time systems. For each extension several different semantics are defined for different time structures which are suitable for different applications and achieve low complexity for the decidability of some properties. Hence, different proof systems have to be developed for reasoning in different calculi. We demonstrate that with temporal propositional letters, many useful time structures and operators can be completely described in the original DC with continuous time. Hence, we can use the proof system for original DC and the specification of the specific time structure to reason in that time structure without the need of introducing a new calculus. Dang Van Hung is a research fellow for the research project “Theories and Design Methods for Real-time Systems” since October 1995 being on leave of absence from Institute of Information Technology, Nghia Do, Cau Giay, Hanoi, Vietnam. He has a PhD (equivalent) degree in Computer Science (concurrent systems) in 1988, Computer and Automation Research Institute (SZTAKI), Hungarian Academy of Sciences, Budapest, Hungary, and a BSc degree in Mathematics (numerical methods) in 1977, Hanoi University, Hanoi, Vietnam. His research interests include Formal Techniques of Programming, Concurrent and Distributed Computing, Design Techniques for Real-Time systems. e-mail: [email protected] Copyright c © 2007 by UNU-IIST