Sequent Calculi for Semi-De Morgan and De Morgan Algebras [article]

Minghui Ma, Fei Liang
2016 arXiv   pre-print
A contraction-free and cut-free sequent calculus G3SDM for semi-De Morgan algebras, and a structural-rule-free and single-succedent sequent calculus G3DM for De Morgan algebras are developed. The cut rule is admissible in both sequent calculi. Both calculi enjoy the decidability and Craig interpolation. The sequent calculi are applied to prove some embedding theorems: G3DM is embedded into G3SDM via Gödel-Gentzen translation. G3DM is embedded into a sequent calculus for classical propositional
more » ... ogic. G3SDM is embedded into the sequent calculus G3ip for intuitionistic propositional logic.
arXiv:1611.05231v1 fatcat:5ekitrl6njhm7mkx4adjsakpze