1. The process of diagnosis by elimination in terms of probabilities is analysed mathematically.

2. A piece of evidence which is only associated with a small number of differential diagnoses is of particular importance.

3. To deal with a differential diagnosis, a feature is required which occurs commonly in a postulated diagnosis but rarely in its rivals, irrespective of its frequency in those already discriminated against.

4. By using this analysis, inadequate evidence may be identified, new tests developed, and their effectiveness assessed in a logical and efficient way.

5. The approach is illustrated by considering the differential diagnosis of localized right lower quadrant abdominal pain.

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