Logica Universalis

, Volume 11, Issue 4, pp 489–505 | Cite as

A Proof-Theoretic Semantics for Exclusion

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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.

Keywords

Exclusion nand classical logic proof-theoretic semantics 

Mathematics Subject Classification

Primary 03F03 Secondary 03B22 03A02 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Computer Science deptTechnion-IITHaifaIsrael

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