Subframization and stabilization for superintuitionistic logics. (17th January 2019)

• Record Type: Journal Article
• Authors: Bezhanishvili, Guram; Bezhanishvili, Nick; Ilin, Julia
• Is Part Of: Journal of logic and computation. Volume 29:Number 1(2019)
• Page Start: 1
• Page End: 35
• Publication Date: 2019-01-17
• Subjects: Intuitionistic logic -- subframe logic -- intuitionistic modal logic -- lax logic -- multiple-conclusion consequence relation -- axiomatization; Logic programming -- Periodicals; Logic, Symbolic and mathematical -- Periodicals; Computational complexity -- Periodicals; 005.115
• DOI: 10.1093/logcom/exy035
• Languages: English
• ISSNs: 0955-792X

Abstract

Abstract: With each superintuitionistic logic (si-logic for short), we associate its downward and upward subframizations and characterize them by means of Zakharyaschev's canonical formulas, as well as by embedding si-logics into the extensions of the propositional lax logic $\textsf{PLL}$ . In an analogous fashion, with each si-logic, we associate its downward and upward stabilizations and characterize them by means of stable canonical formulas, as well as by embedding si-logics into extensions of the intuitionistic $\textsf{S4}$ .