Representing the difference between mandatory and essential parts and wholes

As mentioned earlier, there is more in the pipeline about part-whole relations than only the taxonomy of types of part-whole relations and the RBox Compatibility service [1]. There are a lot of issues in representing parts, wholes, and part-whole relations—in particular in bio(medical) ontologies and conceptual data models. One of them is the distinction between the plain mandatory constraint on the participation of the part (whole) in the part-whole relation and the stronger notion of essential part (whole). Informally, they deal with representing that “the part must be part of some whole” versus “the part must be part of the same whole”. A classical example is the difference between how your heart is part of your body versus how your brain is part of your body: your heart is replaceable and as long as you have some heart in your body you’ll be fine (well, continue to exist), whereas this is different for your brain[1]. This, again, is different from parts that a whole normally has (or is supposed to have), such as two eyes and two kidneys in case of a human: without the eyes, you still can live healthily without medical intervention, whereas without the kidneys, you will die if there’s no possibility for regular dialysis—hence, there is somehow a difference in modality on the participation of the parts and wholes in the part-whole relation.

To represent this sort of difference, one can resort to adding existence and necessity [2], but also assess it along the temporal dimension. To say that a part is essential to a whole, then throughout its entire lifetime, the whole has exactly that part related through only that part-whole relation. This does not say anything about the part, though: that part might well have existed before the whole or continue to exist after the whole ceased to exist as a whole. Vice versa, if a whole is essential to the part, then that part cannot survive as is without that whole it is part of. Of course, this can be combined so that the part and the whole are mutually essential.

To represent this talk about “before”, “after”, and “during” in the setting of essential parts and wholes, one can add time t to the predicates, add an ordering over time points (chronons) t1, …, tn, and construct long formalizations to represent precisely the temporal constrains over the objects participating in the part-whole relation as well as over the part-whole relation itself. With an eye on potential for implementation, however, we chose to take the well-studied Description Logic language DLRus and its corresponding ERvt temporal conceptual data modeling language (see [3] for the latest comprehensive treatment of both) so as to capture succinctly the set of constraints for mandatory and essential parts and wholes. A rather dense, DL-readership-oriented, paper has just been accepted for DL’08 that presents this solution [4], which I’ll try to render in a brief digest-format in the following paragraph and give a few realistic examples afterward.

DLRus is an expressive temporal description logic with the Until and Since operators and can capture most of the common conceptual data modeling languages, such as n-aries, cardinality restrictions, sub-relations, disjointness, covering etc. ERvt is, roughly, EER with extra constructs for the time aspects and for each ERvt conceptual model, there is an equi-statisfiable DLRus knowledge base.

In [3] you will find explanation on inclusion of the notion of status classes (well-known in temporal information systems), where some instance o can be member of Scheduled-C, Active-C, Suspended-C, or Disabled-C, with Active-C denoting the usual class C in a conceptual model (or call it concept C in DL terminology, universal C in an OBO Foundry ontology, whichever). There is a range of implications to ensure correct behaviour of the status classes, such as if an object is member of Suspended-C then it first must have been member of C. If we entertain ourselves with a particular instance o1 of the Papilionoidae, then when o1 is member of Caterpillar, we might as well make o1 also member of the Scheduled-Butterfly class and of the Disabled-Egg class (if it is interesting to do so, is another topic). We can do the same for relations; i.e., in [4] we extend ERvt by introducing the notion of status relations (from §3 onwards, including an informal description). Applying that to the partof relation, we get Scheduled-partof, Active-partof, Suspended-partof, and Disabled-partof. For the axioms that deal with essential participation, we first have that the partof relation cannot be suspended, and subsequently add axioms to say that the lifetime of the part (or whole) either starts before that of the whole (or part) or at the same time, and if the part (whole) finishes at the same time or if the part (whole) can outlive the whole (part). Thus, there are eight combinations of the possible constraints, which are drawn in an illustrative figure as well (Fig.3): four for essential parts and four for essential wholes (theorems 1 and 2). That’s it.

With this addition of status relations, we can represent a lot more than only the distinction between mandatory and essential parts and wholes—for quite realistic information, actually. For instance, we would like to say in a medical ontology or conceptual data model intended for development of a transplant database that all transplanted hearts must have been part of some other human. Put differently, and at the instance-level for illustrative purpose, such a constraint would enforce that if a heart h1 as member of Heart is partof p2 that is member of class Human and this partof is member of Active-partof, then there must be a human p1 that is member of DisabledHuman (i.e., p1 has died, assuming that a person cannot live without having a heart) and there must be a relational instance (tuple) of partof that relates h1 and p1 that is member of Disabledpartof. For kidney transplants, we can amend this to say that p1 is member of either Human or Disabled-Human (one could have donated just one kidney). For planning purposes, we can have donors in the transplant database whose organs are scheduled to become part of another human, i.e., the parts and wholes are both in their respective active classes, but a partof relation is member of Scheduledpart of relating the organ to a prospective recipient. Further, if we drop the standard essential part (whole) to less restrictive cases so that the objects and relations may become suspended some time during their lifespan, we can keep track of, say, some car engine e1 at the car mechanic who has removed it from the car c1 for maintenance purposes, but this e1 surely is supposed to be reinstalled in that car c1. And so forth.

Now, before running off to go forth and play with, e.g., the temporalised relations in the RO [5], some of those (like derivation), as well as other options, have already been addressed in [3] under the heading of so-called “evolution constraints”. And a caveat is that the full DLRus is undecidable[2], but there’s ongoing work on temporalising the well-behaved computationally nice DL-lite and some subsets of DLRus are in Exptime (see the last section of [3] for a summary).

[1] Keet, C.M., Artale, A. Representing and Reasoning over a Taxonomy of Part-Whole Relations. Applied Ontology, in print.
[2] Guizzardi, G. Ontological foundations for structural conceptual models. PhD Thesis, Telematica Institute, Twente University, Enschede, the Netherlands. 2005.
[3] Artale, A., Parent, C., Spaccapietra, S. Evolving objects in temporal information systems. Annals of Mathematics and Artificial Intelligence (AMAI), 2007, 50(1-2), 5-38.
[4] Artale, A., Keet, C.M. Essential and mandatory part-whole relations in conceptual data models. 21st International Workshop on Description Logics (DL’08 ), 13-16 May 2008, Dresden, Germany.
[5] Smith, B., Ceusters, W., Klagges, B., Koehler, J., Kumar, A., Lomax, J., Mungall, C., Neuhaus, F., Rector, A.L., Rosse, C. (2005).
Relations in biomedical ontologies. Genome Biology, 2005, 6:R46.

[1] Other subtopics, such as optional parts, amount of parts, or parts that a whole should have are not further considered in [4].

[2] Who cares? At least now we know what we need to represent the distinction between mandatory and essential parts and wholes… as well as several other cases with part-wholes relations.


2 responses to “Representing the difference between mandatory and essential parts and wholes

  1. Pingback: BFO’s specific and generic dependence and generalising progress in essential and mandatory parts « Keet blog

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