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On conditions for semirings to induce compact information algebras

Published online by Cambridge University Press:  15 May 2015

XUECHONG GUAN ,
YONGMING LI  and
JUERG KOHLAS
XUECHONG GUAN
Affiliation:
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China Email: [email protected]
YONGMING LI
Affiliation:
College of Computer Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, China
JUERG KOHLAS
Affiliation:
Department of Informatics, University of Fribourg, Fribourg, Switzerland
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Abstract

In this paper, we study the relationship between ordering structures on semirings and semiring-induced valuation algebras. We show that a semiring-induced valuation algebra is a complete (resp. continuous) lattice if and only if the semiring is complete (resp. continuous) lattice with respect to the reverse order relation on semirings. Furthermore, a semiring-induced information algebra is compact, if the dual of the semiring is an algebraic lattice.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 27 , Special Issue 4: Symposium on Domain Theory (ISDT 2013) , May 2017 , pp. 460 - 469
Copyright
Copyright © Cambridge University Press 2015 

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