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Axiomatic semantics of projection temporal logic programs†

Published online by Cambridge University Press:  27 October 2010

XIAOXIAO YANG ,
ZHENHUA DUAN  and
QIAN MA
XIAOXIAO YANG
Affiliation:
Institute of Computing Theory and Technology, and ISN Laboratory, Xidian University, Xi'an, 710071China and Laboratory for Computer Science, Institute of Software, Chinese Academy of Sciences, P.O. Box 8718, Beijing 100080China Email: xxyang@ios.ac.cn
ZHENHUA DUAN
Affiliation:
Institute of Computing Theory and Technology, and ISN Laboratory, Xidian University, Xi'an, 710071China Email: zhhduan@mail.xidian.edu.cn
QIAN MA
Affiliation:
Institute of Computing Theory and Technology, and ISN Laboratory, Xidian University, Xi'an, 710071China Email: qma@mail.xidian.edu.cn
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Abstract

In this paper, we investigate the axiomatic semantics of the projection temporal logic programming language MSVL. To this end, we employ Propositional Projection Temporal Logic (PPTL) as an assertion language to specify the desired properties. We give a set of state axioms and state inference rules. In order to deduce a program over an interval, we also formalise a set of rules in terms of a Hoare logic-like triple. These rules enable us to deduce a program into its normal form and from the current state to the next one. They also enable us to verify properties over intervals. In this way, an axiom system for proving the correctness of MSVL programs is established. The axiom system is proved to be sound and relatively complete with respect to an operational model of MSVL, and give an example showing how the axiom system works. Finally, we employ a recently developed prototype verifier based on PVS as an example of semi-automatic verification using MSVL.

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