Anchor: This sends a powerful message to potential new recruits that the position is important enough to the organization that it warrants senior executive attention.
Entailed: The position seems important to the organization if the senior executive needs to give it their attention. 
Contradiction: The position is unimportant if the executive gives it attention.
Contradiction: His family celebrated.
Contradiction: They are involved in reviews.
Contradiction: The Romanesque Collegiata is a real cathedral, although it is not referred to as the town's Duomo.
Contradiction: The sun is shining.