Cut-free sequent calculi are given for positive logic with weak negation, establishing Craig interpolation and PSPACE-completeness via termination proofs.
‘W eak negation in inquisitive semantics’, Journal of Logic, Language and Information , 24 (2015), 3, 323–355
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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.