Cut-free sequent calculi are given for positive logic with weak negation, establishing Craig interpolation and PSPACE-completeness via termination proofs.
‘Der Minimalkalk¨ ul, ein reduzierter intuitionistische r Formalismus’, Compositio mathematica , 4 (1937), 119–136
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Proof Theory for Positive Logic with Weak Negation
Cut-free sequent calculi are given for positive logic with weak negation, establishing Craig interpolation and PSPACE-completeness via termination proofs.