Proof Theory for Positive Logic with Weak Negation

0505107 - ÚI 2021 RIV NL eng J - Journal Article
Bílková, Marta - Colacito, A.
Proof Theory for Positive Logic with Weak Negation.
Studia Logica. Roč. 108, č. 4 (2020), s. 649-686. ISSN 0039-3215. E-ISSN 1572-8730
R&D Projects: GA ČR GA17-04630S
Institutional support: RVO:67985807
Keywords : Minimal propositional logic * Weak negation * Intuitionistic propositional logic * Sequent calculus * Terminating sequent calculus * Decidability * Complexity
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impact factor: 0.585, year: 2020
Method of publishing: Limited access
http://dx.doi.org/10.1007/s11225-019-09869-y

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.
Permanent Link: http://hdl.handle.net/11104/0296624