If LEM is the Law of Excluded Middle and LNC is the Law of Non-contradiction then
- Classical Logic preserves both LEM and LNC
- Intuitionistic Logic preserves LNC, but rejects LEM
- Co-Intuitionistic Logic preserves LEM, but rejects LNC
- Linear Logic broadly preserves neither, but narrowly preserves and rejects them with its pairs of conjunctive and disjunctive logical operators
Above is shown the four operators of Linear Logic and the statements for their preservation and rejection of LEM and LNC.
Further Reading:
https://en.wikipedia.org/wiki/Law_of_excluded_middle
https://en.wikipedia.org/wiki/Law_of_noncontradiction
https://plato.stanford.edu/entries/logic-classical/
https://plato.stanford.edu/entries/logic-intuitionistic/
https://plato.stanford.edu/entries/logic-linear/
Pete Wolfendale / Essay on Transcendental Realism
(at PhilPapers)
https://plato.stanford.edu/entries/contradiction/
https://ncatlab.org/nlab/show/paraconsistent+logic
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