Source: J. Symbolic Logic
Volume 70, Issue 4
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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