Approximate Unification in the Description Logic $$\mathcal {FL}_0$$

Extensions of unification modulo ACUI

“…Approximate unification has been considered for FL 0 (Baader et al, 2016), but with measures that differ from the ones employed in the present paper for ACUI and ACUIG. Basically, instead of constants, the sets that one needs to consider there are sets of words, and the measures employed in (Baader et al, 2016) take the length of these words into account: violations caused by long words are counted as less important than violations caused by shorter words. In addition, in (Baader et al, 2016) only a single equation is considered, and thus measures counting the number of violated equations have not been considered there.…”

“…Basically, instead of constants, the sets that one needs to consider there are sets of words, and the measures employed in (Baader et al, 2016) take the length of these words into account: violations caused by long words are counted as less important than violations caused by shorter words. In addition, in (Baader et al, 2016) only a single equation is considered, and thus measures counting the number of violated equations have not been considered there. It would be interesting to see how approximate unification w.r.t.…”

“…In addition to the fact that ACUI is a theory investigated extensively in unification theory and in set unification, our interest in this theory is motivated by the fact that this theory is a common subtheory of the equational theories corresponding to the Description Logics FL 0 (Baader, 1996) and EL (Baader et al, 1999). Unification in DLs (Baader and Morawska, 2009;Baader and Narendran, 2001) was introduced as a novel inference problem that can be used to detect redundancies in knowledge bases, and approximate variants (Baader et al, 2016) were investigated in order to increase the recall of these approaches. The decidability and complexity results for unification in FL 0 and EL respectively shown in (Baader and Narendran, 2001) and (Baader and Morawska, 2009) are restricted to the setting without a background TBox.…”

“…The formal meaning of when a substitution approximately (i.e., "almost") solves a unification problem is formalized using distance measures between terms that are tailored towards the equational theory E in question. Approximate unification with constants in FL 0 was investigated in Baader et al (2016) w.r.t. two such measures.…”

“…two such measures. In contrast to approaches that try to speed up reasoning by employing approximate inference techniques (Pan et al, 2016), this work (Baader et al, 2016) uses approximation as a way to extend the range of admissible solutions to a unification problem. In the present paper, we consider approximate unification with constants in ACUI w.r.t.…”