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A Non-commutative Extension of MELL

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,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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Authors and Affiliations

  1. Fakultaät Informatik, Technische Universität Dresden, 01062, Dresden, Germany

    Alessio Guglielmi & Lutz Straßburger

Authors
  1. Alessio Guglielmi
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  2. Lutz Straßburger
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Editor information

Editors and Affiliations

  1. Abteilung für Theoretische Informatik, Institut für Algebra und Diskrete Mathematik, Wiedner Hauptstr. 8-10, 1040, Wien, Austria

    Matthias Baaz

  2. Department of Computer Science, University of Manchester, Kilburn Building, Oxford Road, Manchester, M13, 9PL, UK

    Andrei Voronkov

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Guglielmi, A., Straßburger, L. (2002). A Non-commutative Extension of MELL. In: Baaz, M., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2002. Lecture Notes in Computer Science(), vol 2514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36078-6_16

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  • DOI: https://doi.org/10.1007/3-540-36078-6_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00010-5

  • Online ISBN: 978-3-540-36078-0

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