Abstract
The paper provides a proof-theory (natural deduction and sequent calculus) for a negative presentation of classical logic based on a single primitive of exclusion (of variable arity), generalizing the known presentation via the binary ‘nand. The completeness is established via deductive equivalence to Gentzens NK/LK systems.
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References
Dekker, P.: Exclusively indexical deduction. Rev. Symb. Log. 9(3), 603–637 (2016). doi:10.1017/S1755020316000125
Dummett, M.: The Logical Basis of Metaphysics. Harvard University Press, Cambridge (1991)
Francez, N.: Proof-theoretic Semantics. College Publications, London (2015)
Pfenning, F., Davies, R.: A judgmental reconstruction of modal logic. Math. Struct. Comput. Sci. 11, 511–540 (2001)
Prior, A.N.: The runabout inference-ticket. Analysis 21, 38–39 (1960)
Read, S.: Sheffer’s stroke: a study in proof-theoretic harmony. Dan. Yearb. Philos. 34, 7–23 (1999)
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Francez, N., Kaminski, M. A Proof-Theoretic Semantics for Exclusion. Log. Univers. 11, 489–505 (2017). https://doi.org/10.1007/s11787-017-0179-y
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DOI: https://doi.org/10.1007/s11787-017-0179-y