On the algebra of order

Daniel J. Lehmann

On the algebra of order

Daniel J. Lehmann^*

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-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 language	English
Pages (from-to)	214-220
Number of pages	7
Journal	Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume	1978-October
State	Published - 1978
Externally published	Yes
Event	19th Annual Symposium on Foundations of Computer Science, SFCS 1978 - Ann Arbor, United States Duration: 16 Oct 1978 → 18 Oct 1978

Bibliographical note

Publisher Copyright:
© 1978 IEEE.

Cite this

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title = "On the algebra of order",

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.",

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AB - 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.

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AN - SCOPUS:85034741445

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VL - 1978-October

SP - 214

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JO - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

JF - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

T2 - 19th Annual Symposium on Foundations of Computer Science, SFCS 1978

Y2 - 16 October 1978 through 18 October 1978

ER -

On the algebra of order

Abstract

Bibliographical note

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