The Method of Axiomatic Rejection for the Intuitionistic Propositional Logic

Studia Logica 48 (4):449-459 (1989)
  Copy   BIBTEX

Abstract

We prove that the intuitionistic sentential calculus is Ł-decidable, i.e. the sets of these of Int and of rejected formulas are disjoint and their union is equal to all formulas. A formula is rejected iff it is a sentential variable or is obtained from other formulas by means of three rejection rules. One of the rules is original, the remaining two are Łukasiewicz's rejection rules: by detachement and by substitution. We extensively use the method of Beth's semantic tableaux.

Categories

Keywords

Reprint years

DOI

10.1007/bf00370199

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 101,505

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Metalogic of Intuitionistic Propositional Calculus.Alex Citkin - 2010 - Notre Dame Journal of Formal Logic 51 (4):485-502.
Extendible Formulas in Two Variables in Intuitionistic Logic.Nick Bezhanishvili & Dick Jongh - 2012 - Studia Logica 100 (1-2):61-89.
Extendible Formulas in Two Variables in Intuitionistic Logic.Nick Bezhanishvili & Dick de Jongh - 2012 - Studia Logica 100 (1):61-89.
An intuitionistic formula hierarchy based on high‐school identities.Taus Brock-Nannestad & Danko Ilik - 2019 - Mathematical Logic Quarterly 65 (1):57-79.
On normal forms in Łukasiewicz logic.A. Di Nola & A. Lettieri - 2004 - Archive for Mathematical Logic 43 (6):795-823.
Undecidability of the Problem of Recognizing Axiomatizations of Superintuitionistic Propositional Calculi.Evgeny Zolin - 2014 - Studia Logica 102 (5):1021-1039.
Unification and admissible rules for paraconsistent minimal Johanssonsʼ logic J and positive intuitionistic logic IPC.Sergei Odintsov & Vladimir Rybakov - 2013 - Annals of Pure and Applied Logic 164 (7-8):771-784.
On Some Semi-Intuitionistic Logics.Juan M. Cornejo & Ignacio D. Viglizzo - 2015 - Studia Logica 103 (2):303-344.
Refutation Systems for a System of Nonsense-Logic.Robert Sochacki - 2011 - Logic and Logical Philosophy 20 (3):233-239.
Intuitionistic sequent calculi for finitely many-valued logics.E. Reznik & P. Curmin - 2001 - Logic Journal of the IGPL 9 (6):793-812.

Analytics

Added to PP
2009-01-28

Downloads
60 (#356,604)

6 months
8 (#591,777)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Shifting Priorities: Simple Representations for Twenty-seven Iterated Theory Change Operators.Hans Rott - 2009 - In Jacek Malinowski David Makinson & Wansing Heinrich (eds.), Towards Mathematical Philosophy. Springer. pp. 269–296.
Refutation systems in modal logic.Valentin Goranko - 1994 - Studia Logica 53 (2):299 - 324.
Rejection in Łukasiewicz's and Słupecki's Sense.Urszula Wybraniec-Skardowska - 2018 - In Urszula Wybraniec-Skardowska & Ángel Garrido (eds.), The Lvov-Warsaw School. Past and Present. Cham, Switzerland: Springer- Birkhauser,. pp. 575-597.
Proving unprovability in some normal modal logics.Valentin Goranko - 1991 - Bulletin of the Section of Logic 20 (1):23-29.

View all 12 citations / Add more citations

References found in this work

On proofs of rejection.Walenty Staszek - 1971 - Studia Logica 29 (1):17 - 25.
Pewna interpretacja teorii zdań odrzuconych.W. Staszek - 1972 - Studia Logica 30 (1):151-151.

Add more references