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Mirror, mirror in my hand: a duality between specifications and models of process behaviour†

Published online by Cambridge University Press:  04 March 2009

J. L. Fiadeiro  and
J. F. Costa
J. L. Fiadeiro
Affiliation:
Department of Informatics, Faculty of Sciences, University of Lisbon, Campo Grande, 1700 Lisboa, Portugal Email {llf.fgc}@di.fc.ul.pt
J. F. Costa
Affiliation:
Department of Informatics, Faculty of Sciences, University of Lisbon, Campo Grande, 1700 Lisboa, Portugal Email {llf.fgc}@di.fc.ul.pt
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Summary

Since Pnueli’s seminal paper in 1977, Temporal Logic has been used as a formalism for specifying and verifying the correctness of reactive systems. In this paper, we show that, besides its expressive power, Temporal Logic enjoys a very strong structural property: it is categorical on processes. That is, we show how temporal specifications (as theories) can be embedded in categories of process behaviour, and out of this adjunction we build an institution that is categorical in the sense of Meseguer. This characterisation means that temporal logic is, in a sense, ‘sound and complete’ with respect to process specification and interconnection techniques.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 6 , Issue 4 , August 1996 , pp. 353 - 373
Copyright
Copyright © Cambridge University Press 1996

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