Complete representation by partial functions for composition, intersection and anti-domain
- Author
- Brett McLean (UGent)
- Organization
- Abstract
- For representation by partial functions in the signature with intersection, composition and anti-domain, we show that a representation is meet complete if and only if it is join complete. We show that a representation is complete if and only if it is atomic, but that not all atomic representable algebras are completely representable. We show that the class of completely representable algebras is not axiomatizable by any existential-universal-existential first-order theory. By giving an explicit representation, we show that the completely representable algebras form a basic elementary class, axiomatizable by a universal-existential-universal sentence.
- Keywords
- Complete representation, partial functions, intersection, anti-domain, axiomatizable
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01GK70H6NFRPC39FNCN6Y2SFGH
- MLA
- McLean, Brett. “Complete Representation by Partial Functions for Composition, Intersection and Anti-Domain.” JOURNAL OF LOGIC AND COMPUTATION, vol. 27, no. 4, OXFORD UNIV PRESS, 2017, pp. 1143–56, doi:10.1093/logcom/exu081.
- APA
- McLean, B. (2017). Complete representation by partial functions for composition, intersection and anti-domain. JOURNAL OF LOGIC AND COMPUTATION, 27(4), 1143–1156. https://doi.org/10.1093/logcom/exu081
- Chicago author-date
- McLean, Brett. 2017. “Complete Representation by Partial Functions for Composition, Intersection and Anti-Domain.” JOURNAL OF LOGIC AND COMPUTATION 27 (4): 1143–56. https://doi.org/10.1093/logcom/exu081.
- Chicago author-date (all authors)
- McLean, Brett. 2017. “Complete Representation by Partial Functions for Composition, Intersection and Anti-Domain.” JOURNAL OF LOGIC AND COMPUTATION 27 (4): 1143–1156. doi:10.1093/logcom/exu081.
- Vancouver
- 1.McLean B. Complete representation by partial functions for composition, intersection and anti-domain. JOURNAL OF LOGIC AND COMPUTATION. 2017;27(4):1143–56.
- IEEE
- [1]B. McLean, “Complete representation by partial functions for composition, intersection and anti-domain,” JOURNAL OF LOGIC AND COMPUTATION, vol. 27, no. 4, pp. 1143–1156, 2017.
@article{01GK70H6NFRPC39FNCN6Y2SFGH,
abstract = {{For representation by partial functions in the signature with intersection, composition and anti-domain, we show that a representation is meet complete if and only if it is join complete. We show that a representation is complete if and only if it is atomic, but that not all atomic representable algebras are completely representable. We show that the class of completely representable algebras is not axiomatizable by any existential-universal-existential first-order theory. By giving an explicit representation, we show that the completely representable algebras form a basic elementary class, axiomatizable by a universal-existential-universal sentence.}},
author = {{McLean, Brett}},
issn = {{0955-792X}},
journal = {{JOURNAL OF LOGIC AND COMPUTATION}},
keywords = {{Complete representation,partial functions,intersection,anti-domain,axiomatizable}},
language = {{eng}},
number = {{4}},
pages = {{1143--1156}},
publisher = {{OXFORD UNIV PRESS}},
title = {{Complete representation by partial functions for composition, intersection and anti-domain}},
url = {{http://doi.org/10.1093/logcom/exu081}},
volume = {{27}},
year = {{2017}},
}
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