In the present paper, we endow semi De Morgan logic and a family of its axiomatic extensions with proper multi-type display calculi which are sound, complete, conservative, and enjoy cut elimination and subformula property. Our proposal builds on an algebraic analysis of the variety of semi De Morgan algebras, and applies the guidelines of the multi-type methodology in the design of display calculi.
Greco, G., Liang, F., Moshier, M.A. et al. Semi De Morgan Logic Properly Displayed. Stud Logica (2020). https://doi.org/10.1007/s11225-020-09898-y