A Matrix Characterization for Multiplicative Exponential Linear Logic

  • Authors:
  • Christoph Kreitz;Heiko Mantel

  • Affiliations:
  • Department of Computer Science, Cornell University, Ithaca, NY 14853-7501, U.S.A. e-mail: kreitz@cs.cornell.edu;Information Security, ETH Zürich, Haldeneggsteig 4, CH-8092-Zurich, Switzerland. e-mail: heiko.mantel@inf.ethz.ch

  • Venue:
  • Journal of Automated Reasoning
  • Year:
  • 2004

Quantified Score

Hi-index 0.00

Visualization

Abstract

We develop a matrix characterization of logical validity in MELL, the multiplicative fragment of propositional linear logic with exponentials and constants. To prove the correctness and completeness of our characterization, we use a purely proof-theoretical justification rather than semantical arguments. Our characterization is based on concepts similar to matrix characterizations proposed by Wallen for other nonclassical logics. It provides a foundation for developing proof search procedures for MELL by adopting techniques that are based on these concepts and also makes it possible to adopt algorithms that translate the machine-found proofs back into the usual sequent calculus for MELL.