The geometry of non-distributive logics
2005 ◽
Vol 70
(4)
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pp. 1108-1126
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Keyword(s):
AbstractIn 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.
2007 ◽
Vol 17
(5)
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pp. 957-1027
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2018 ◽
Vol 29
(8)
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pp. 1177-1216
2018 ◽
Vol 13
(3)
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pp. 509-540
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2017 ◽
Vol 23
(1)
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pp. 83-104
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Keyword(s):
2021 ◽
Vol 43
(2)
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pp. 1-55