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Information 2014, 5(2), 219-254; doi:10.3390/info5020219

An Algebraic Theory of Information: An Introduction and Survey

1,*  and 2
1 Department of Informatics, University of Fribourg, Bvd. de Perolles 90, CH-1700 Fribourg, Switzerland 2 Mathematical Institute, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
* Author to whom correspondence should be addressed.
Received: 22 November 2013 / Revised: 8 April 2014 / Accepted: 8 April 2014 / Published: 10 April 2014
(This article belongs to the Section Information Theory and Methodology)
Download PDF [315 KB, 24 June 2014; original version 10 April 2014]


This review examines some particular, but important and basic aspects of information: Information is related to questions and should provide at least partial answers. Information comes in pieces, and it should be possible to aggregate these pieces. Finally, it should be possible to extract that part of a piece of information which relates to a given question. Modeling these concepts leads to an algebraic theory of information. This theory centers around two different but closely related types of information algebras, each containing operations for aggregation or combination of information and for extracting information relevant to a given question. Generic constructions of instances of such algebras are presented. In particular, the close connection of information algebras to logic and domain theory will be exhibited.
Keywords: information; information theory; universal logic; domain theory; order theory information; information theory; universal logic; domain theory; order theory
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Kohlas, J.; Schmid, J. An Algebraic Theory of Information: An Introduction and Survey. Information 2014, 5, 219-254.

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