Weak representations of relation algebras and relational bases

, &
Journal of Symbolic Logic 76 (3):870 - 882 (2011)
  Copy   BIBTEX

Abstract

It is known that for all finite n ≥ 5, there are relation algebras with n-dimensional relational bases but no weak representations. We prove that conversely, there are finite weakly representable relation algebras with no n-dimensional relational bases. In symbols: neither of the classes RA n and wRRA contains the other

Categories

Keywords

Reprint years

DOI

10.2178/jsl/1309952524

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,323

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

Step by step – Building representations in algebraic logic.Robin Hirsch & Ian Hodkinson - 1997 - Journal of Symbolic Logic 62 (1):225-279.
Nonfinite axiomatizability results for cylindric and relation algebras.Roger D. Maddux - 1989 - Journal of Symbolic Logic 54 (3):951-974.
Frontal Operators in Weak Heyting Algebras.Sergio A. Celani & Hern?N. J. San Mart?N. - 2012 - Studia Logica 100 (1-2):91-114.
Frontal Operators in Weak Heyting Algebras.Sergio A. Celani & Hernán J. San Martín - 2012 - Studia Logica 100 (1-2):91-114.
Relation algebra reducts of cylindric algebras and an application to proof theory.Robin Hirsch, Ian Hodkinson & Roger D. Maddux - 2002 - Journal of Symbolic Logic 67 (1):197-213.
Finite algebras of relations are representable on finite sets.H. Andréka, I. Hodkinson & I. Németi - 1999 - Journal of Symbolic Logic 64 (1):243-267.
An equational axiomatization of dynamic negation and relational composition.Marco Hollenberg - 1997 - Journal of Logic, Language and Information 6 (4):381-401.
Weakly associative relation algebras with polyadic composition operations.Vera Stebletsova - 2000 - Studia Logica 66 (2):297-323.
Complete representations in algebraic logic.Robin Hirsch & Ian Hodkinson - 1997 - Journal of Symbolic Logic 62 (3):816-847.
On canonicity and completions of weakly representable relation algebras.Ian Hodkinson & Szabolcs Mikulás - 2012 - Journal of Symbolic Logic 77 (1):245-262.
Inequivalent representations of geometric relation algebras.Steven Givant - 2003 - Journal of Symbolic Logic 68 (1):267-310.
The origin of relation algebras in the development and axiomatization of the calculus of relations.Roger D. Maddux - 1991 - Studia Logica 50 (3-4):421 - 455.

Analytics

Added to PP
2013-09-30

Downloads
68 (#241,208)

6 months
9 (#317,373)

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

A sequent calculus for relation algebras.Roger Maddux - 1983 - Annals of Pure and Applied Logic 25 (1):73-101.
Relation algebras of every dimension.Roger D. Maddux - 1992 - Journal of Symbolic Logic 57 (4):1213-1229.

Add more references