S5 knowledge without partitions

Synthese 172 (1):145 - 155 (2009)
  Copy   BIBTEX

Abstract

We study set algebras with an operator (SAO) that satisfy the axioms of S5 knowledge. A necessary and sufficient condition is given for such SAOs that the knowledge operator is defined by a partition of the state space. SAOs are constructed for which the condition fails to hold. We conclude that no logic singles out the partitional SAOs among all SAOs.

Categories

Keywords

Reprint years

2010

DOI

10.1007/s11229-009-9469-0

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 106,621

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

On a four-valued modal logic with deductive implication.Marcelo E. Coniglio & Martín Figallo - 2014 - Bulletin of the Section of Logic 43 (1/2):1-18.
Hyperboolean Algebras and Hyperboolean Modal Logic.Valentin Goranko & Dimiter Vakarelov - 1999 - Journal of Applied Non-Classical Logics 9 (2):345-368.
The Baire Closure and its Logic.G. Bezhanishvili & D. Fernández-Duque - 2024 - Journal of Symbolic Logic 89 (1):27-49.
Information Completeness in Nelson Algebras of Rough Sets Induced by Quasiorders.Jouni Järvinen, Piero Pagliani & Sándor Radeleczki - 2013 - Studia Logica 101 (5):1073-1092.
Epistemic Monadic Boolean Algebras.Juntong Guo & Minghui Ma - 2023 - In Natasha Alechina, Andreas Herzig & Fei Liang, Logic, Rationality, and Interaction: 9th International Workshop, LORI 2023, Jinan, China, October 26–29, 2023, Proceedings. Springer Nature Switzerland. pp. 135-148.
An Axiomatisation for the Multi-modal Logic of Knowledge and Linear Time LTK.Erica Calardo & Vladimir Rybakov - 2007 - Logic Journal of the IGPL 15 (3):239-254.
From Contact Relations to Modal Operators, and Back.Rafał Gruszczyński & Paula Menchón - 2023 - Studia Logica 111 (5):717-748.
Completeness and Doxastic Plurality for Topological Operators of Knowledge and Belief.Thomas Mormann - 2023 - Erkenntnis: 1 - 34, ONLINE.
Heyting Algebras with Operators.Yasusi Hasimoto - 2001 - Mathematical Logic Quarterly 47 (2):187-196.
Distributive Lattices with a Negation Operator.Sergio Arturo Celani - 1999 - Mathematical Logic Quarterly 45 (2):207-218.

Analytics

Added to PP
2009-02-21

Downloads
175 (#143,299)

6 months
12 (#294,666)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Knowledge and belief.Jaakko Hintikka - 1962 - Ithaca, N.Y.,: Cornell University Press.
Modal Logic: Graph. Darst.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - New York: Cambridge University Press. Edited by Maarten de Rijke & Yde Venema.
Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
Modal logic.Yde Venema - 2000 - Philosophical Review 109 (2):286-289.

View all 6 references / Add more references