Proof theory for positive logic with weak negation

Bílková, Marta; Colacito, Almudena (2020). Proof theory for positive logic with weak negation. Studia logica, 108(4), pp. 649-686. Springer Science + Business Media 10.1007/s11225-019-09869-y

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Proof-theoreticmethods 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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Colacito, Almudena

Subjects:

500 Science > 510 Mathematics

ISSN:

0039-3215

Publisher:

Springer Science + Business Media

Language:

English

Submitter:

Sebastiano Don

Date Deposited:

10 Feb 2021 17:06

Last Modified:

10 Feb 2021 17:06

Publisher DOI:

10.1007/s11225-019-09869-y

ArXiv ID:

1907.05411

Uncontrolled Keywords:

Minimal propositional logic, Weak negation, Intuitionistic propositional logic, Sequent calculus, Terminating sequent calculus, Decidability, Complexity

BORIS DOI:

10.48350/151262

URI:

https://boris.unibe.ch/id/eprint/151262

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