- New
-
Topics
- All Categories
- Metaphysics and Epistemology
- Value Theory
- Science, Logic, and Mathematics
- Science, Logic, and Mathematics
- Logic and Philosophy of Logic
- Philosophy of Biology
- Philosophy of Cognitive Science
- Philosophy of Computing and Information
- Philosophy of Mathematics
- Philosophy of Physical Science
- Philosophy of Social Science
- Philosophy of Probability
- General Philosophy of Science
- Philosophy of Science, Misc
- History of Western Philosophy
- Philosophical Traditions
- Philosophy, Misc
- Other Academic Areas
- Journals
- Submit material
- More
Stable Formulas in Intuitionistic Logic
Notre Dame Journal of Formal Logic 59 (3):307-324 (2018)
Abstract
In 1995 Visser, van Benthem, de Jongh, and Renardel de Lavalette introduced NNIL-formulas, showing that these are exactly the formulas preserved under taking submodels of Kripke models. In this article we show that NNIL-formulas are up to frame equivalence the formulas preserved under taking subframes of frames, that NNIL-formulas are subframe formulas, and that subframe logics can be axiomatized by NNIL-formulas. We also define a new syntactic class of ONNILLI-formulas. We show that these are the formulas preserved in monotonic images of frames and that ONNILLI-formulas are stable formulas as introduced by Bezhanishvili and Bezhanishvili in 2013. Thus, ONNILLI is a syntactically defined set of formulas axiomatizing all stable logics. This resolves a problem left open in 2013.Author Profiles
Links
PhilArchive
External links
(no proxy)
Setup an account with your affiliations in order to access resources via your University's proxy server
Through your library
- Sign in / register and customize your OpenURL resolver
- Configure custom resolver
My notes
Similar books and articles
Cofinal Stable Logics.Guram Bezhanishvili, Nick Bezhanishvili & Julia Ilin - 2016 - Studia Logica 104 (6):1287-1317.
Frame Based Formulas for Intermediate Logics.Nick Bezhanishvili - 2008 - Studia Logica 90 (2):139-159.
Canonical formulas for wk4.Guram Bezhanishvili & Nick Bezhanishvili - 2012 - Review of Symbolic Logic 5 (4):731-762.
Locally Finite Reducts of Heyting Algebras and Canonical Formulas.Guram Bezhanishvili & Nick Bezhanishvili - 2017 - Notre Dame Journal of Formal Logic 58 (1):21-45.
An application of the Rieger-Nishimura formulas to the intuitionistic modal logics.Dimiter Vakarelov - 1984 - Bulletin of the Section of Logic 13 (3):120-122.
Extendible Formulas in Two Variables in Intuitionistic Logic.Nick Bezhanishvili & Dick Jongh - 2012 - Studia Logica 100 (1-2):61-89.
Kripke completeness of some intermediate predicate logics with the axiom of constant domain and a variant of canonical formulas.Tatsuya Shimura - 1993 - Studia Logica 52 (1):23 - 40.
Unification and Passive Inference Rules for Modal Logics.V. V. Rybakov, M. Terziler & C. Gencer - 2000 - Journal of Applied Non-Classical Logics 10 (3-4):369-377.
Metalogic of Intuitionistic Propositional Calculus.Alex Citkin - 2010 - Notre Dame Journal of Formal Logic 51 (4):485-502.
On Some Semi-Intuitionistic Logics.Juan M. Cornejo & Ignacio D. Viglizzo - 2015 - Studia Logica 103 (2):303-344.
The elimination of de re formulas.Michael Kaminski - 1997 - Journal of Philosophical Logic 26 (4):411-422.
Hybridized Paracomplete and Paraconsistent Logics.Colin Caret - 2017 - Australasian Journal of Logic 14 (1):281-325.
Decidable Formulas Of Intuitionistic Primitive Recursive Arithmetic.Saeed Salehi - 2002 - Reports on Mathematical Logic 36 (1):55-61.
Moorean Phenomena in Epistemic Logic.Wesley H. Holliday & Thomas F. Icard - 2010 - In Lev Beklemishev, Valentin Goranko & Valentin Shehtman (eds.), Advances in Modal Logic 8. College Publications. pp. 178-199.
Analytics
Added to PP
2018-05-04
Downloads
29 (#550,776)
6 months
11 (#237,876)
2018-05-04
Downloads
29 (#550,776)
6 months
11 (#237,876)
Historical graph of downloads
Author Profiles
Citations of this work
Locally Finite Reducts of Heyting Algebras and Canonical Formulas.Guram Bezhanishvili & Nick Bezhanishvili - 2017 - Notre Dame Journal of Formal Logic 58 (1):21-45.
Hereditarily Structurally Complete Intermediate Logics: Citkin’s Theorem Via Duality.Nick Bezhanishvili & Tommaso Moraschini - 2023 - Studia Logica 111 (2):147-186.
Intermediate Logics Admitting a Structural Hypersequent Calculus.Frederik M. Lauridsen - 2019 - Studia Logica 107 (2):247-282.
Remarks on Stable Formulas in Intuitionistic Logic.Majid Alizadeh & Ali Bibak - forthcoming - Logic and Logical Philosophy:1.
References found in this work
Stable canonical rules.Guram Bezhanishvili, Nick Bezhanishvili & Rosalie Iemhoff - 2016 - Journal of Symbolic Logic 81 (1):284-315.
Canonical formulas for k4. part II: Cofinal subframe logics.Michael Zakharyaschev - 1996 - Journal of Symbolic Logic 61 (2):421-449.
An algebraic approach to subframe logics. Intuitionistic case.Guram Bezhanishvili & Silvio Ghilardi - 2007 - Annals of Pure and Applied Logic 147 (1):84-100.
Locally Finite Reducts of Heyting Algebras and Canonical Formulas.Guram Bezhanishvili & Nick Bezhanishvili - 2017 - Notre Dame Journal of Formal Logic 58 (1):21-45.
PhilPapers logo by Andrea Andrews and Meghan Driscoll.
This site uses cookies and Google Analytics (see our terms & conditions for details regarding the privacy implications). Use of this site is subject to terms & conditions.
All rights reserved by The PhilPapers Foundation
Server: philpapers-web-64dd777598-wg6s5 uwo