A Finite Hilbert‐Style Axiomatization of the Implication‐Less Fragment of the Intuitionistic Propositional Calculus

&
Mathematical Logic Quarterly 40 (1):61-68 (1994)
  Copy   BIBTEX

Abstract

In this paper we obtain a finite Hilbert-style axiomatization of the implicationless fragment of the intuitionistic propositional calculus. As a consequence we obtain finite axiomatizations of all structural closure operators on the algebra of {–}-formulas containing this fragment

Categories

Keywords

Reprint years

DOI

10.1002/malq.19940400109

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 93,990

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

Characterizing Belnap's Logic via De Morgan's Laws.Alexej P. Pynko - 1995 - Mathematical Logic Quarterly 41 (4):442-454.
An alternative proof of the Hilbert-style axiomatization for the $$\{\wedge,\vee \}$$ { ∧, ∨ } -fragment of classical propositional logic.Luciano J. González - 2022 - Archive for Mathematical Logic 61 (5):859-865.
Axiomatizations of intuitionistic double negation.Milan Bozic & Kosta Došen - 1983 - Bulletin of the Section of Logic 12 (2):99-102.
On Quasivariety Semantics Of Fragments Of Intuitionistic Propositional Logic Without Exchange And Contraction Rules.C. Van Alten & J. Raftery - 1997 - Reports on Mathematical Logic:3-55.
Propositional Quantification in the Monadic Fragment of Intuitionistic Logic.Tomasz Połacik - 1998 - Journal of Symbolic Logic 63 (1):269-300.
On the computational content of intuitionistic propositional proofs.Samuel R. Buss & Pavel Pudlák - 2001 - Annals of Pure and Applied Logic 109 (1-2):49-64.
Finite structural axiomatization of every finite-valued propositional calculus.Zdzislaw Dywan - 1979 - Bulletin of the Section of Logic 8 (2):61-65.
Finite axiomatizability of logics of distributive lattices with negation.Sérgio Marcelino & Umberto Rivieccio - forthcoming - Logic Journal of the IGPL.
The finite model property for the implicational fragment of IPC without exchange and contraction.C. van Alten & J. Raftery - 1999 - Studia Logica 63 (2):213-222.
Intuitionistic Sahlqvist Theory for Deductive Systems.Damiano Fornasiere & Tommaso Moraschini - forthcoming - Journal of Symbolic Logic:1-59.

Analytics

Added to PP
2013-12-01

Downloads
28 (#558,165)

6 months
9 (#436,380)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Proof Systems for Exact Entailment.Johannes Korbmacher - 2023 - Review of Symbolic Logic 16 (4):1260-1295.

Add more citations

References found in this work

Elements of Intuitionism.Michael Dummett - 1977 - New York: Oxford University Press. Edited by Roberto Minio.
Elements of Intuitionism.Nicolas D. Goodman - 1979 - Journal of Symbolic Logic 44 (2):276-277.
Distributive Lattices.Raymond Balbes & Philip Dwinger - 1977 - Journal of Symbolic Logic 42 (4):587-588.
Axiomatizing logics closely related to varieties.W. Rautenberg - 1991 - Studia Logica 50 (3-4):607 - 622.

Add more references