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'''2 Summary Abox''' describes the propert … '''2 Summary Abox''' describes the properties of a ''canonical function'' '''f''' satisfying the converses of (1) and (3), and satisfying (4–6), and producing a summary Abox. Condition (6) is that "'''f'''(''a'') ≠ '''f'''(''b'') ∈ ''A’'' implies ''a'' is the only individual in ''A'' mapped to '''f'''(''a'') (same for ''b'')." This approach produces something very different than what model finders for, for example, first-order logic typically produce. The techniques that such model finders employ typically increase the domain size gradually, trying to find interpretations. Thus a model finder presented with ''a'' ≠ ''b'' and ''c'' ≠ ''d'' would probably find an interpretation with two domain of size two that mapped one name from each inequality to one domain element, and the other names to the other domain element (e.g., ''x'' = ''a'' = ''d'', and ''y'' = ''b'' = ''c''). More importantly, the results of such model finders, I think, could be considered summary Aboxes, though they would not be ''canonical'' summary Aboxes. How many of the techniques described in this paper could be applied to non-canonical summary Aboxes? (I recognize that in '''3 Abox Filtering''' the authors write, "we described filtering techniques on the original Abox first," but this is just "for the purpose of exposition.") is just "for the purpose of exposition.")
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