Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 55, Number 1 (2014), 41-61.
Nested Sequents for Intuitionistic Logics
Relatively recently nested sequent systems for modal logics have come to be seen as an attractive deep-reasoning extension of familiar sequent calculi. In an earlier paper I showed that there was a strong connection between modal nested sequents and modal prefixed tableaux. In this paper I show that the connection continues to intuitionistic logic, both standard and constant domain, relating nested intuitionistic sequent calculi to intuitionistic prefixed tableaux. Modal nested sequent machinery generalizes one-sided sequent calculi—intuitionistic nested sequents similarly generalize two-sided sequents. It is noteworthy that the resulting system for constant domain intuitionistic logic is particularly simple. It amounts to a combination of intuitionistic propositional rules and classical quantifier rules, a combination that is known to be inadequate when conventional intuitionistic sequent systems are used.
Notre Dame J. Formal Logic, Volume 55, Number 1 (2014), 41-61.
First available in Project Euclid: 20 January 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03B20: Subsystems of classical logic (including intuitionistic logic)
Secondary: 03B44: Temporal logic 03B60: Other nonclassical logic 68T15: Theorem proving (deduction, resolution, etc.) [See also 03B35]
Fitting, Melvin. Nested Sequents for Intuitionistic Logics. Notre Dame J. Formal Logic 55 (2014), no. 1, 41--61. doi:10.1215/00294527-2377869. https://projecteuclid.org/euclid.ndjfl/1390246437