Document lattices

If the information conveyed by the markup in a document can be identified with the set of inferences we can draw from that markup, as has been proposed in earlier work, then the sets of inferences licensed by documents form an infinitely large lattice, by means of which the relative information content of any two documents (equivalence, subsumption, contradiction, consistency) can be displayed visually. The sets of inferences licensed by markup can be used to test translations from one markup language to another for equivalence or information loss; a simple example using XHTML and CALS table markup illustrates the process.