Linear Logic and the Laws of Excluded Middle and Noncontradiction

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://t.co/hoHWUOhQE0

https://plato.stanford.edu/entries/contradiction/

https://ncatlab.org/nlab/show/paraconsistent+logic

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