Semi-supervised clustering with logic programming (Prolog)
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For instance, if a system is putting tags on RSS articles or photos, those tags can be put on with a truth value of "indeterminate". Tags attached by users are "true". For subjective decision making systems, however, it's not sufficient for the absence of the tag to be "false", as the auto-tagged could possibly put back wrong tags, so if a tag is "removed" by the user it really is put in the "false" state which is a definite statement that the tag does not apply to the content.
1. There is either a tag or there is not.
2. If there is a tag, it is either a is_x tag or a is_not_x tag.
3. If there is a tag, it is either validated or it isn't.
Three valued logic has different semantics.