Case study: Additive linear logic and lattices

  • Jean-Yves Marion
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1234)


We investigate sequent calculus where contexts, called additive contexts, are governed by the operations of a non-distributive lattice. We present a sequent calculus ALL m with multiple antecedents and succedents. ALL m is complete for non-distributive lattices and is equivalent to the additive fragment of linear logic. Weakenings and contractions are postulated for ALL m and cut is redundant. We extend this construction in order to get a sequent calculus for propositional linear logic with both additive and multiplicative contexts.

Then we show that a bottom-up decision procedure based on the cut-free sequent calculi runs in exponential time. We provide a decision algorithm that exploits analytic cuts and whose runtime is polynomial.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Jean-Yves Marion
    • 1
  1. 1.Projet CalligrammeUniversité Nancy 2, CRIN - CNRS & INRIA LorraineVand∄uvre-lès-Nancy CedexFrance

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