Connections Between Cylindric Algebras and Relation Algebras View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2001

AUTHORS

Robin Hirsch , Ian Hodkinson

ABSTRACT

We investigate the class SRaCA n for 4 ≤ n ω and survey some recent results. We see that RA n — the subalgebras of relation algebras with relational bases — is too weak, and that the class of relation algebras whose canonical extension has an n-dimensional cylindric basis is too strong to define the class. We introduce the notion of an n-dimensional hyperbasis and show that for any relation algebra A the canonical extension A + has such a hyperbasis if and only if A ∈ SRaCA n . We introduce techniques that can be used to show that the hierarchies RA4 ⊃ RA5 ⊃... and SRaCA4 ⊃ SRaCA5 ⊃... are strict and each step is not finitely axiomatisable. We outline a relativized semantics that characterises RA n and another one for the class of subalgebras of relation algebras with n-dimensional cylindric bases. More... »

PAGES

239-246

Book

TITLE

Relational Methods for Computer Science Applications

ISBN

978-3-662-00362-6
978-3-7908-1828-4

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-7908-1828-4_14

DOI

http://dx.doi.org/10.1007/978-3-7908-1828-4_14

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1004513669


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