What's in an Attribute? Consequences for the Least Common Subsumer

TL;DR

This paper investigates how the interpretation of attributes as required or partial functions affects the existence and computation of the least common subsumer in Description Logics, revealing complexity differences and providing algorithms.

Contribution

It provides the first explicit analysis of attribute assumptions on the least common subsumer in DLs, correcting and extending previous results, and offers polynomial-time decision procedures.

Findings

LCS exists and is computable for partial attributes.

LCS may not exist or be exponentially large for required attributes.

Existence of LCS can be decided in polynomial time.

Abstract

Functional relationships between objects, called `attributes', are of considerable importance in knowledge representation languages, including Description Logics (DLs). A study of the literature indicates that papers have made, often implicitly, different assumptions about the nature of attributes: whether they are always required to have a value, or whether they can be partial functions. The work presented here is the first explicit study of this difference for subclasses of the CLASSIC DL, involving the same-as concept constructor. It is shown that although determining subsumption between concept descriptions has the same complexity (though requiring different algorithms), the story is different in the case of determining the least common subsumer (lcs). For attributes interpreted as partial functions, the lcs exists and can be computed relatively easily; even in this case our results correct and extend three previous papers about the lcs of DLs. In the case where attributes must have a value, the lcs may not exist, and even if it exists it may be of exponential size. Interestingly, it is possible to decide in polynomial time if the lcs exists.