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Multi-focused cut elimination

  • TAUS BROCK-NANNESTAD (a1) and NICOLAS GUENOT (a2)
Abstract

We investigate cut elimination in multi-focused sequent calculi and the impact on the cut elimination proof of design choices in such calculi. The particular design we advocate is illustrated by a multi-focused calculus for full linear logic using an explicitly polarised syntax and incremental focus handling, for which we provide a syntactic cut elimination procedure. We discuss the effect of cut elimination on the structure of proofs, leading to a conceptually simple proof exploiting the strong structure of multi-focused proofs.

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D. Baelde (2012). Least and greatest fixed points in linear logic. ACM Transactions on Computational Logic 13 (1) 2.

K. Chaudhuri (2008). Focusing strategies in the sequent calculus of synthetic connectives. In: I. Cervesato , H. Veith and A. Voronkov (eds.) Logic for Programming, Artificial Intelligence and Reasoning, Lecture Notes in Computer Science, vol. 5330, 467481. Available at http://link.springer.com/book/10.1007%2F978-3-540-89439-1.

K. Chaudhuri , F. Pfenning and G. Price (2008v). A logical characterization of forward and backward chaining in the inverse method. Journal of Automated Reasoning 40 (2–3) 133177.

G. Gentzen (1934). Untersuchungen über das logische Schließen, I. Mathematische Zeitschrift 39 176210. Available at http://link.springer.com/article/10.1007%2FBF01201353.

S. Guerrini , S. Martini and A. Masini (2001). Proof nets, garbage, and computations. Theoretical Computer Science 253 (2) 185237.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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