The article “Preferences in an Open World” published in the Proceedings of ADT 2009 contains some errors in writing which do not put the overall argumentation into question, but which may cause confusion when reading. This erratum provides corrections and marks them in red.
ERRATUM FOR “PREFERENCES IN AN OPEN WORLD”
Corrections for the article Preferences in an Open World published in the Proceedings of the 1st International Conference on Algorithmic Decision Theory, Lecture Notes in Computer Science Volume 5783, 2009, pp 215-224, Springer:
Page 3: definition 2 introduces the concept of a viewpoint extension, which is central for the paper. As preference relations contain pairs of outcomes, they do not agree on selected outcomes, but on selected pairs of outcomes:
Page 5: a typographical error in the definition of preferential independence:
Page 7: the published article defined a strong transitive reduction of a binary relation as “ a greatest subset of this relation that is anti-transitive ”. However, there may be several greatest anti-transitive subsets of a relation. Hence, those subsets do not have the property stipulated by equation 2, which says that the strong transitive reduction of a binary relation can be computed by removing all transitive links from this relation. If a relation has a transitive link, then a transitive reduction of the relation minus the link is also a transitive reduction of that relation. For each transitive link, there thus exists a transitive reduction that does not contain this link. As a consequence, the intersection of all transitive reductions of a relation does not contain any of the transitive links. Moreover, if a link is not a transitive link, then the relation minus this link does not have the same transitive closure as the original link. Hence, those links belong to all transitive reductions of a relation. The intersection of all transitive reductions therefore fulfills equation 2, thus permitting a modification of the definition of a strong transitive reduction. It should be noted that the remainder of the published article is only based on equation 2 and not on the definition of strong transitive reductions:
Page 9: the explanatory text that precedes proposition 4 says that the relation ∆ 1 is added to the strong transitive reduction and the relation ∆ 2 is removed from it, whereas proposition 4 said the inverse. It will be more convenient if proposition 4 uses these symbols in the same way as the explanatory text. Moreover, the proposition is only valid if the added preferences are unrelated to each other under the original preference order:
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