Proof Theory for Positive Logic with Weak Negation

0505107 - ÚI 2021 RIV NL eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR GA17-04630S
Institucionální podpora: RVO:67985807
Klíčová slova: Minimal propositional logic * Weak negation * Intuitionistic propositional logic * Sequent calculus * Terminating sequent calculus * Decidability * Complexity
Obor OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impakt faktor: 0.585, rok: 2020
Způsob publikování: Omezený přístup
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.
Trvalý link: http://hdl.handle.net/11104/0296624