Equivalence of multiplicative fragments of cyclic linear logic and noncommutative linear logic

  • Mati Pentus
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1234)


In this paper we consider two associative noncommutative analogs of Girard's linear logic. These are Abrusci's noncommutative linear logic and Yetter's cyclic linear logic.

We give a linear-length translation from the multiplicative fragment of Abrusci's noncommutative linear logic into the multiplicative fragment of Yetter's cyclic linear logic and vice versa. As a corollary we obtain that the decidability problems for derivability in these two calculi are in polynomial time reducible to each other.


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  1. 1.
    Abrusci, V. M.: Phase semantics and sequent calculus for pure noncommutative classical linear propositional calculus. Journal of Symbolic Logic, 56 (1991) 1403–1451Google Scholar
  2. 2.
    Girard, J.-Y.: Linear logic. Theoretical Computer Science, 50 (1987) 1–102Google Scholar
  3. 3.
    Yetter, D. N.: Quantales and noncommutative linear logic. Journal of Symbolic Logic, 55 (1990) 41–64Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Mati Pentus
    • 1
  1. 1.Department of Mathematical Logic, Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia

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