On the algebra of order

Daniel J. Lehmann*

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

3 Scopus citations

Abstract

Algebras whose carriers are partially ordered sets and operations are monotone and algebras whose carriers are complete partial orders and operations are continuous are studied. A quotient construction is provided for both types of algebras. The notion of a variety of algebras is defined and it is shown that the analogue of Birkhoff variety theorem holds for ordered algebras but not for continuous algebras. The results presented are a good first step towards a theory of ordered data types and a study of families of interpretations of schemas.

Original languageEnglish
Pages (from-to)214-220
Number of pages7
JournalProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume1978-October
StatePublished - 1978
Externally publishedYes
Event19th Annual Symposium on Foundations of Computer Science, SFCS 1978 - Ann Arbor, United States
Duration: 16 Oct 197818 Oct 1978

Bibliographical note

Publisher Copyright:
© 1978 IEEE.

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