Remarks on Stable Formulas in Intuitionistic Logic

Majid Alizadeh, Ali Bibak



ONNILLI-formulas were introduced in [2] 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 [2].


intuitionistic logic; intermediate logic; subframe logics; monotonic maps; stable logics; uniform interpolation property

Full Text:



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:

Bezhanishvili, N., and D. de Jongh, “Stable formulas in intuitionistic logic”, Notre Dame J. Formal Logic 59, 3 (2018): 307–324. DOI:

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:

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:

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism