From: Peter F. Patel-Schneider (pfps@research.bell-labs.com)
Date: 11/30/01
OK, lets try a different example where the non-entailment is even more obvious. peter Problem: Determine whether (type X ?ubc) (unionOf ?ubc ?lbc) (first ?lbc b) (rest ?lbc ?lc) (first ?lc c) (rest ?lc nil) DAML+OIL-entails (type X ?uabc) (unionOf ?uabc ?labc) (first ?labc a) (rest ?labc ?lbc) (first ?lbc b) (rest ?lbc ?lc) (first ?lc c) (rest ?lc nil) NB: DAML+OIL-entailment is not yet fully defined. Let's just say, for now, that a DAML+OIL interpretation is an RDFS interpretation with the obvious extra semantic conditions, taken from the DAML+OIL model theory. Solution: It does not entail. There are interpretations that satisfy the first knowledge base where the denotation of a is not in any list, i.e., the extension of the denotation of ``first'' does not contain any pairs whose second element is the denotation of ``a''. These interpretations do not satisfy the second knowledge base. QED
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