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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Dicher, Bogdan 2016. A Proof-Theoretic Defence of Meaning-Invariant Logical Pluralism. Mind, Vol. 125, Issue. 499, p. 727.

    MARES, EDWIN 2014. BELIEF REVISION, PROBABILISM, AND LOGIC CHOICE. The Review of Symbolic Logic, Vol. 7, Issue. 04, p. 647.

    Sernadas, A. Sernadas, C. Rasga, J. and Coniglio, M. 2009. A Graph-theoretic Account of Logics. Journal of Logic and Computation, Vol. 19, Issue. 6, p. 1281.


The geometry of non-distributive logics

  • Greg Restall (a1) and Francesco Paoli (a2)
  • DOI:
  • Published online: 01 March 2014

In this paper we introduce a new natural deduction system for the logic of lattices, and a number of extensions of lattice logic with different negation connectives. We provide the class of natural deduction proofs with both a standard inductive definition and a global graph-theoretical criterion for correctness, and we show how normalisation in this system corresponds to cut elimination in the sequent calculus for lattice logic. This natural deduction system is inspired both by Shoesmith and Smiley's multiple conclusion systems for classical logic and Girard's proofnets for linear logic.

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[15]D. J. D. Hughes and R. J. van Glabbeek , Proof nets for unit-free multiplicative-additive linear logic, Proceedings of the 18th Annual IEEE Symposium on Logic and Computer Science (Ottawa), 062003, extended abstract, pp. 110.

[17]A. G. Oliveira and R. J. G. B. de Queiroz , Geometry of deduction via graphs of proof Logic for concurrency and synchronization (R. J. G. B. de Queiroz , editor), Kluwer, 2003, pp. 388.

[19]J. Schülte Monting , Cut elimination and word problem for varieties of lattices, Algebra Universalis, vol. 12 (1981), pp. 290321.

[20]L. Tortora de Falco , The additive multiboxes, Annals of Pure and Applied Logic, vol. 120 (2003), pp. 65102.

[21]L. Tortora de Falco , Additives of linear logic and normalization. Part I: A (restricted) Church-Rosser property, Theoretical Computer Science, vol. 294 (2003), pp. 489524.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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