Remarks on Stable Formulas in Intuitionistic Logic
Keywordsintuitionistic logic, intermediate logic, subframe logics, monotonic maps, stable logics, uniform interpolation property
ONNILLI-formulas were introduced in  and were shown to be the set of formulas that are preserved under monotonic images of descriptive or Kripke frames. As a result, ONNILLI is a syntactically defined set of formulas that axiomatize all stable logics. In this paper, among other things, by proving the uniform interpolation property for ONNILLI we show that ONNILLI is exactly the set of formulas that are preserved in monotonic bijections of descriptive or (finite) Kripke models. This resolves an open problem in .
Bezhanishvili, G., and N. Bezhanishvili, “Locally finite reducts of Heyting algebras and canonical formulas”, Notre Dame J. Formal Logic 58, 1 (2017): 21–25. DOI: http://dx.doi.org/10.1215/00294527-3691563
Bezhanishvili, N., and D. de Jongh, “Stable formulas in intuitionistic logic”, Notre Dame J. Formal Logic 59, 3 (2018): 307–324. DOI: http://dx.doi.org/10.1215/00294527-2017-0030
Chagrov, A., and M. Zakharyaschev, Modal Logic, vol. 35 of Oxford Logic Guides, The Clarendon Press, New York, 1995.
Fine, K., “Logics containing K4. Part II”, Journal of Symbolic Logic 50, 3 (1985): 619–651. DOI: http://dx.doi.org/10.2307/2274318
Visser, A., D. de Jongh, J. van Benthem, and G. Renardel de Lavalette, “NNIL, a study in intuitionistic logic”, pages 289–326 in Modal Logics and Process Algebra: A Bisimulation Perspective, 1995.
Zakharyaschev, M., “Syntax and semantics of superintutionistic logics”, Algebra and Logic 28, 4 (1989): 262–282.
Zakharyaschev, M., “Canonical formulas for K4. Part II: Cofinal subframe logics”, Journal of Symbolic Logic 61, 2 (1996): 421–449. DOI: http://dx.doi.org/10.2307/2275669
How to Cite
Number of views and downloads: 377
Number of citations: 0