Proof Theory for Positive Logic with Weak Negation

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

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Double Negation as Minimal Negation.Satoru Niki - 2023 - Journal of Logic, Language and Information 32 (5):861-886.

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References found in this work

Inquisitive Semantics.Ivano Ciardelli, Jeroen Groenendijk & Floris Roelofsen - 2018 - Oxford, England: Oxford University Press. Edited by J. A. G. Groenendijk & Floris Roelofsen.
The Connectives.Lloyd Humberstone - 2011 - MIT Press. Edited by Lloyd Humberstone.
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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