Open Problems with Part-Whole Relations

Among attributes, a fundamental role is often played byvarious forms of part-whole relations, which contributeto describe the structure of composite objects. The rep-resentation of such a structural information usually re-quires a particular semantics together with specializedinference, but rarely do current modeling formalisms andmethodologies give it a specific, "first-class" dignity [Si-mons, 1987; Guarino, 1994].We have argued in [Artale et al., 1996] that part-whole relations should not be modeled by ordinary at-tributes in an Object-Oriented formalism like a De-scription Logic. This rules out simplifying approacheslike the one pursued by [Padgham and Lambrix, 1994;Lambrix, 1996] and [Speel and Patel-Schneider, 1994].They propose a simple extension of description logics,where part-whole relations do not have any particularsemantics with respect to standard roles. According tothese approaches, the reasoning involving parts is exter-nal to the standard description logic reasoning services.While terminological subsumption and instance recogni-tion are not affected by the particular meaning of thepart-whole roles, ad-hoc reasoning services are needed,like for example the computation of the transitive clo-sure for the special part-whole roles in the ABox (seesection 3).In this paper, we will refer to semantically deeper ex-tensions of description logics, and we will point out theexpressivity - see [Artale et al., 1996] for a discussionabout the conceptual modeling issues involving part-whole relations - and the computational problems ofsuch extensions in the current state of the art.