A proof-search procedure for intuitionistic propositional logic (Q377482)

The author presents a sequent-root proof-search procedure for intuitionistic propositional logic, essentially based on Glivenko's theorem (see [\textit{V. Glivenko}, Bull. Cl. Sci., V. Sér., Acad. R. Belg. 15, 183--188 (1929; JFM 55.0030.05)]). It is shown that, in the context of modified intuitionistic multi-succedent and classical sequent calculi, both belonging to the family of the contraction-free Kleene's G3-style calculi (see [\textit{S. C. Kleene}, Introduction to metamathematics. Amsterdam: North-Holland Publishing Co (1952; Zbl 0047.00703)]), a sequent is provable iff the corresponding prefixed-sequent is derivable in the procedure.