Cut-free sequent calculi are given for positive logic with weak negation, establishing Craig interpolation and PSPACE-completeness via termination proofs.
Minimal and Subminimal Logic of Negation , Master’s thesis, ILLC Master of Logic Series MoL-2016-14, Universiteit van Amsterdam
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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.