Studia Logica 108 (4):649-686 (2020)

Abstract
Proof-theoretic methods are developed for subsystems of Johansson’s logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems. In particular, cut-free complete sequent calculi are introduced and used to provide a proof of the fact that the systems satisfy the Craig interpolation property. Alternative versions of the calculi are later obtained by means of an appropriate loop-checking history mechanism. Termination of the new calculi is proved, and used to conclude that the considered logical systems are PSPACE-complete.
Keywords minimal propositional logic  weak negation  intuitionistic propositional logic  sequent calculus  terminating sequent calculus  decidability  complexity
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DOI 10.1007/s11225-019-09869-y
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References found in this work BETA

Inquisitive Semantics.Ivano Ciardelli, Jeroen A. G. Groenendijk & Floris Roelofsen - 2018 - Oxford, England: Oxford University Press.
Weak Negation in Inquisitive Semantics.Vít Punčochář - 2015 - Journal of Logic, Language and Information 24 (3):323-355.
Lattice Theory.Garrett Birkhoff - 1940 - Journal of Symbolic Logic 5 (4):155-157.

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