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A modal logic for message passing processes. (English) Zbl 0827.68102
Summary: A first-order modal logic is given for describing properties of processes which may send and receive values or messages along communication ports. We give two methods for proving that a process enjoys such a property. The first is the construction, for each process $$P$$ and formula $$F$$, of a characteristic formula $$P \text{ sat } F$$ such that $$P$$ enjoys the property $$F$$ if and only if the formula $$P \text{ sat }F$$ is logically equivalent to $$\mathbf t\mathbf t$$. The second is a sound and complete proof system whose judgements take the form $$B \vdash P : F$$, meaning: under the assumption $$B$$ the process $$P$$ enjoys the property $$F$$. The notion of symbolic operational semantics plays a crucial role in the design of both the characteristic formulae and the proof system.

##### MSC:
 68T27 Logic in artificial intelligence 03B45 Modal logic (including the logic of norms)
LOTOS
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##### References:
 [1] R. Cleaveland, J. Parrow, B. Steffen: The concurrency workbench. University of Edinburgh, Scotland, 1988 [2] J.C. Godskesen, K.G. Larsen, M. Zeeberg: Tav – tools for automatic verification – users manual. Technical Report R 89-19, Department of Matheamtics and Computer Science, Aalborg University, 1989. Presented at workshop on Automatic Methods for Finite State, Systems, Grenoble, France, Juni 1989 [3] S. Graf, J. Sifakis: A logic for the description of non-deterministic programs and their properties. Information and Control, 68 (1–3), 1986 [4] M. Hennessy: A proof system for communicating processes with value-passing.Formal Aspects of Computer Science, 3:346–366, 1991 · Zbl 0736.68057 · doi:10.1007/BF01642508 [5] M. Hennessy, H. Lin: Symbolic bisimulation. Technical Report Technical Report 1/92, School of Congnitive and Computing Sciences, University of Sussex, 1992 [6] M. Hennessy, X. Liu: A modal logic for message passing processes. Technical Report Technical Report 3/93, School of Congnitive and Computing Sciences, University of Sussex 1993 [7] A. Ingolfsdottir, B. Thomsen: Semantic models for ccs with values. Technical Report 63, Programming Methodology Group, Chalmers University of Technology, 1992. In Proceedings of the Workshop on Concurrency [8] K.G. Larsen: Proof systems for Hennessy-Milner logic with recursion.Lecture Notes In Computer Science, Springer Verlag, 299, 1988. in Proceedings of 13th Colloquium on Trees in Algebra and Programming 1988 · Zbl 0647.68012 [9] H. Lin: A verification tool for value-passing processes. Technical report, School of Congnitive and Computing Sciences, University of Sussex, 1993. To appear [10] R. Milner:Communication and Concurrency. Prentice-Hall, 1989 · Zbl 0683.68008 [11] R. Milner, J. Parrow, D. Walker: Modal logics for mobile processes.Theoretical Computer Science, 1992. To appear · Zbl 0778.68033 [12] B. Steffen, A. Ingolfsdottir: Characteristic formulae for processes with divergence. Technical Report Technical Report 1/91, School of Congnitive and Computing Sciences, University of Sussex, 1991 [13] C. Stirling: Modal logics for communicating systems.Theoretical Computer Science, (311–347), 1987 · Zbl 0624.68019
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