The geometry of non-distributive logics

Greg Restall*, Francesco Paoli

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1108-1126
Number of pages19
JournalJournal of Symbolic Logic
Issue number4
Publication statusPublished - Dec 2005


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