A concept satisfiability procedure that expands concept labels into a graph, branches on disjunctions, creates witnesses for existential restrictions, propagates universal restrictions along existing edges, and tests for a tableau clash. General TBoxes require global constraints and a termination device such as direct blocking in description logic.
A test that stops further witness generation at a node when an appropriate earlier ancestor already represents its required pattern of labels. The exact test depends on the logic and tableau calculus. An isolated root has no ancestor and is not directly blocked.
An explicit contradiction in a node label, such as both and , or . Opposite universal restrictions alone cause no clash when there are no successors.
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