Spoon yogurt onto several layers of heavy-duty paper towels, and spread to 1/2-inch thickness. Cover yogurt with additional paper towels, and let stand 5 minutes. Scrape into a bowl using a rubber spatula; cover and chill.
Bring cider to a boil in a medium, heavy saucepan over high heat; cook until reduced to 1/2 cup (about 20 minutes). Cool completely.
Combine the chilled yogurt, cider, and celery seeds in a large bowl, stirring yogurt mixture well with a whisk. Add the chopped apple, celeriac, and toasted pecans, tossing gently to coat. Serve salad on lettuce-lined plates.