A Non-commutative Extension of MELL

  • Alessio Guglielmi
  • Lutz Straßburger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2514)

Abstract

We extend multiplicative exponential linear logic(M EL)L by a non-commutative, self-dual logical operator. The extended system, called NEL is defined in the formalism of the calculus of structures, which is a generalisation of the sequent calculus and provides a more refined analysis of proofs. We should then be able to extend the range of applications of M E L,L by modelling a broad notion of sequentiality and providing new properties of proofs. We show some proof theoretical results: decomposition and cut elimination. The new operator represents a significant challenge: to get our results we use here for the first time some novel techniques, which constitute a uniform and modular approach to cut elimination, contrary to what is possible in the sequent calculus.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Alessio Guglielmi
    • 1
  • Lutz Straßburger
    • 1
  1. 1.Fakultaät InformatikTechnische Universität DresdenDresdenGermany

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