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International Symposium on Mathematical Foundations of Computer Science

MFCS 1993: Mathematical Foundations of Computer Science 1993 pp 442–452Cite as

Completeness results for linear logic on Petri nets

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 711))

Abstract

Completeness is shown for several versions of Girard's linear logic with respect to Petri nets as the class of models. The strongest logic considered is intuitionistic linear logic, with ⊗, ⊸, &, ⊕ and the exponential ! (“of course”), and forms of quantification. This logic is shown sound and complete with respect to atomic nets (these include nets in which every transition leads to a nonempty multiset of places). The logic is remarkably expressive, enabling descriptions of the kinds of properties one might wish to show of nets; in particular, negative properties, asserting the impossibility of an assertion, can also be expressed.

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References

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Authors and Affiliations

  1. Computer Science Department, Aarhus University, Ny Munkegade, DK-8000, Aarhus C, Denmark

    Uffe Engberg & Glynn Winskel

Authors
  1. Uffe Engberg
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  2. Glynn Winskel
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Andrzej M. Borzyszkowski Stefan Sokołowski

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© 1993 Springer-Verlag Berlin Heidelberg

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Engberg, U., Winskel, G. (1993). Completeness results for linear logic on Petri nets. In: Borzyszkowski, A.M., Sokołowski, S. (eds) Mathematical Foundations of Computer Science 1993. MFCS 1993. Lecture Notes in Computer Science, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57182-5_36

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  • DOI: https://doi.org/10.1007/3-540-57182-5_36

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57182-7

  • Online ISBN: 978-3-540-47927-7

  • eBook Packages: Springer Book Archive

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