In this paper we investigate representation of the part-whole relationship in SNOMED CT. We discuss the current approach, based on “SEP” triples, and several translations of it, which involve DLs at different levels of expressivity. We intend that our analysis will concretely inform the SNOMED community about the important tradeoffs of expressivity for their ontology, and help with future decisions about the representation of the SNOMED CT's anatomical taxonomy.
A common pattern in knowledge representation is that a fault of a part is considered a fault of the whole. For example, a fault in the battery is a fault in the ignition system, and is a fault in the car. This pattern pervades common medical terminology: “Heart disease” includes diseases of any of the parts of the heart - muscle, valves, walls, etc. Gastrointestinal disease includes any disease of the stomach (gastrum) or any of the parts of the intestine. The same is true of procedures: fixing a heart valve is a kind of heart operation; repair of the retina is a kind of eye operation, etc.
However, the pattern does not always hold. “Amputation of the hand” means amputation of the entire hand. “Amputation of a ifnger” is not a kind of “Amputation of the hand” (although it is a kind of “Operation on hand”). Similarly, there are diseases that affect an entire organ, for example “pancarditis” means literally, “inflammation throughout (pan) the heart”.
In general, therefore, there is a requirement to represent two cases: 1.“Disorder/Procedure of A and/or any of its parts” and 2.“Disorder/Procedure of the entire A” where A is any anatomical structure.
In common medical language, the distinction is usually implicit. The distinction between the meaning of “Operation on hand” and “Amputation of hand” is left to the medical knowledge of the reader. It is only in unusual cases such as “pancarditis” (“inflammation throughout the heart”) that the distinction is made explicit in the language. However, when representing diseases and procedures formally, the distinction must be made explicitly and systematically.
Over the past twenty years, there have been at least three
mechanisms used to represent this pattern and the associated
distinctions:
1.Propagation across transitive properties - the property used for
“of”, usually “has locus”, is said to be inherited across the
property “part of”. In modern description logics this is achieved
by using property paths in subproperty axioms
Note that these three methods require different expressiveness in the
description logic:
1.Propagation across transitive properties requires property-paths,
which were not supported in early description logics and are not
part of the basic specification of the standard starting description
logic, ALC. They were originally thought to be intractable, but
have since been shown not only to be tractable
It also requires transitive properties but not property paths.
3.SEP triples can be implemented within the simplest possible
description logic, and does not require transitive properties,
disjunction or properties paths
The history of the use of these three methods and their variants
is intertwined with the development of description logics for use
with medical terminologies. The large description logic based
terminology, SNOMED CT
The purpose of this paper is to explore variants on the three
methods in the light of modern description logics, which has also
been investigated in
We view SNOMED’s set of class names C to be partitioned into:
Cn ∪ CS ∪ CE ∪ CP where CS ∪ CE ∪ CP are specific to (human) anatomy. We use XS for class names in CS, XE for class names in CE, and XP for class names in CP. We assume that in any occurrence of XS, XE, or XP in an axiom, ‘X’ refers to the same term, e.g., Heart.
The SEP “triple” approach represents parthood implicitly within
a class hierarchy
Ideally, a SEP triple is given for each anatomical entity, and every XS class (except that for the top anatomical class) is a subclass of some YP class.2
The heart has as part of it a muscular wall that contracts to pump blood out of the heart, and then relaxes as the heart refills with returning blood. This wall is called the myocardium. The heart and myocardium are illustrated in Figure 1.3 Applying SEP triples, MyocardiumS is a subclass of HeartP and HeartS is a subclass of BodyP. This means that a specific part of a myocardium or a whole myocardium is a part of some heart, a specific part of a heart or a 1 http://www.nlm.nih.gov/research/umls/Snomed/snomed main.html. 2 In SNOMED CT, however, the SEP triples are thus far incompletely populated. 3 http://texasheart.org/HIC/Topics/Cond/myocard.cfm whole heart is a part of some body, and furthermore, a specific part of a myocardium or a whole myocardium is a part of some body. These axioms are also illustrated in Figure 2, and given formally below:
Note that, in SNOMED-CT, we neither find disjointness axioms for classes XE and XP nor covering axioms for XS, XE, and XP, although both are assumed to be true under the SEP triple theory.
The SEP triples approach is iteratively applied along what is considered a partonomic hierarchy, for example for the anterior myocardium under the SEP triple for myocardium. The subsumption relationships are explicit, as given, but their reading is implicit; in particular, there is no ‘part of’ property that links XE and XP. However, transitivity of the subsumption relation implies the transitivity of this implicit part of reading, and so transitive parthood entailments are determined by subsumption reasoning. We refer to the SEP triple approach from SNOMEDCT described so far and sketched in Figure 2 as the Current SEP Triple Approach (A). In the following sections we discuss several alternative approaches to representing part-whole relations and discuss their relative expressivity.
On how approach A applies to subsumption reasoning for disorders, take for example a disorder specified in some anatomical location that is given as some class XS. Carditis is an inflammation that is located in some specific part of a heart, or a whole heart, therefore HeartS.4 These axioms and entailments are illustrated in Figure 3.5
In SNOMED CT, there are numerous disorders defined in terms of their location. For instance, Myocarditis is inflammation that is located in some specific part of a myocardium or a whole myocardium, therefore, MyocardiumS.
As illustrated in Figure 3, because MyocardiumS is a subclass of HeartS, the location for Myocarditis is also HeartS, and further, Myocarditis is a subclass of Carditis. We provide the DL representation for these findings and the corresponding inferences:
A disorder that occurs at some location that is specified as a class XE, however, does not have such inferred subclasses. For example, Pancarditis is a disorder that is characterized by inflammation and is specified as being located in the entire heart and not just some part of the heart, therefore HeartE. Recall that Myocarditis is located in some specific part of the myocardium or the entire myocardium, therefore MyocardiumS. As illustrated in Figure 4, it is accurately not entailed that Myocarditis is a subclass of Pancarditis:
4 When there is any question, SNOMED CT uses the Structure class. 5 Inferred relationships are given as dotted arcs.
MyocardiumS and MyocardiumP are also defined in this manner, and the following axiom connects the two triples:
Therefore MyocardiumE and MyocardiumP are subclasses of the expression ∃part of.HeartE. Because Myocarditis is an inflammation located in MyocardiumS, and by inference HeartS, it appropriately follows that Myocarditis is a subclass of Carditis. 3.2
Alternative Approach 2 Alternative Approach 2 (A2) is based on modifications to A1 which is obtained by the following steps: 1.Remove all axioms of the form XE v XS and XP v XS. 2.Replace all connecting axioms of the form XS v YP
(where X and Y are different) with X v ∃part of.Y. 3.Replace every occurrence of XS of a class name in CS with X t ∃part of.X and every occurrence of XE of a class name in CE with X.
Applying step (2) in A2, the connecting axiom for our running example classes is:
And by applying (3) to an inflammation disorder that is located in the entire heart, we apply the X class, Heart:
By the connecting axiom, every myocardium is a part of some heart, and because part of is transitive, every part of some myocardium is a part of some heart. Because Myocarditis is an inflammation of the myocardium or some part, both of which are parts of the heart, as in the prior two approaches, Myocarditis is a subclass of Carditis. 3.3
Alternative Approach 3 Alternative Approach 3 (A3) repeats Step (1) from A2, applies the proper part of property as a subproperty of part of, and includes the following steps for the connecting axiom and treatment of class names in CS and CE: 2.Replace all connecting axioms of the form XS v YP
(where X and Y are different) with X v ∃proper part of.Y. 3.Replace every occurrence of XS of a class name in CS with ∃part of.X, and every occurrence of XE of a class name in CE with X.
A3 differs from A2 in three important respects. First, for (3) part of.X replaces X t part of.X; second, part of here is defined as reflexive, where it is assumed irreflexive in A2 (and A1); and third, Step (5) introduces a left identity axiom which is necessary because it allows us to infer:6
∃part of.Myocardium v ∃proper part of.Heart and subsequently:
Applying (2) the connecting axiom for Myocardium and Heart is:
But, different from A2, applying (3) for our example disorders results in:
By the connecting axiom, along with (4) and the transitivity
of part of, as was the case for A, A1, and A2, Myocarditis is an
inferred subclass of Carditis. Note that by this approach, that (5) in
connection with (4) leads to cycles (as described in
Alternative Approach 4
Alternative Approach 4 (A4) introduces the has locus entire
property, a subproperty of has locus, which expresses when a
ifnding is located in some XE class. This approach was first
introduced in
A4 also repeats (4) and (5) from A3, while including an additional step:
A4 differs from A3 in two respects. First, in (3) A4 treats X— instead of ∃part of.X—as a replacement for XS, and employs the has locus entire property. Second, for A4 in (6) a right identity axiom is applied, where the has locus property is “transitive over” the part of relation.
Applying (2) the connecting axiom for Myocardium and Heart is the same as for A3. Different from all other alternative approaches, applying (3) for our example disorders results in:
Also applying (3) to an inflammation disorder that is located in the entire heart yields:
which prevents erroneous propagation via the right identity axiom. By the connecting axiom, along with (4) and (5), the same inferences hold for our example disorders, primarily that Myocarditis is a subclass of Carditis. 4
In Section 1 we introduced three major methods for representing
part-whole relationships, by applying: (1) transitive properties (2)
6 A left identity axiom can be formalized in OWL2 as a property chain
axiom.
7
In general, there is a modeling choice between treating a generalized ‘part of’ property as reflexive or irreflexive. In A1 and A2 the part of property corresponds to the latter choice, and is assumed irreflexive. It is only assumed because in OWL2 we cannot assert that a transitive property is irreflexive, but we can assert that a transitive property is reflexive. Therefore we can also introduce approaches (as shown for A3 and A4) which correspond to the former choice, where ‘part of’ is reflexive, which can be therefore be applied—directly and without disjunctions—for representing the XS class expression. In these approaches a subproperty proper of, again assumed irreflexive, is also introduced for representing the XP class expression; subsequently cyclic role chains are required in order for the respective ontologies to entail correct subclasses of the pattern ∃proper part.X.
Also, an important distinction between the approaches A3 and A4 is that while A4 has the same approach as A3 for translating and thus representing SEP class expressions (via patterns ∃part of.X and ∃propert part of.X for Structure and Part expressions, respectively), A4 has a different approach for inheritance of properties along a partonomy. For A4 the inheritance is through a right identity axiom, while for A3 it is through the transitivity of part of. 5
A major difference between the current approach, A, and the alternative approaches, A1 - A4, is that the former offers only a propositional representation and the latter offer a relational representation of parthood. A does not model partonomic structure, but rather partonomic “level”. By modeling partonomic structure explicitly via the part of property we can make explicit statements of how part of interacts with other properties (i.e., laterality): ∃ hasLat.Left v (∀ part of.(∃ hasLat.> ⇒ ∃ hasLat.Left)) says that, if something has a left laterality, then, what it is a part of, if this ’whole’ has a laterality at all, it has a left laterality. Modelling this kind of interaction requires an explicit part of - which then can, of course, be used in sub-role and inverse role axioms as well.
It is reported by users of SNOMED-specific browsers that SEP triples are cumbersome to browse and search through. We suggest that this problem can be addressed by providing more intuitive labels. In the context of user navigation, it is simply a rendering issue. It is for this reason we do not necessarily recommend against the A or A1 approach. Nevertheless, A1 - A4 do provide the benefit of allowing a user to explicitly query parts, for A queries require knowledge of the SEP class hierarchy.
In preliminary performance testing, A1 performed the worst for classification across all the DL reasoners we tested. This is no doubt attributable to the inclusion of disjuncts in the class definitions, and corresponding unfolding performed by the reasoner. Despite this, A1 has utility as a representation used for mapping between ontologies that use the propositional approach and those that use the relational approach. Clearly, formulations that include the part of property facilitate ontology modularity, merging, and enrichment where A1 can serve as a bridge.
In future work we will empirically measure classification and query performance for these different SNOMED ontology formulations approaches across several DL reasoners. Furthermore, we will apply an evaluation framework across the formulations for various types of information requests. In that work we will address what kinds of information requests are expressible as OWL class expressions, and which require a more expressive query language.
This work was supported by the National Science Foundation (NSF Grant IIS-1107011) in conjunction with IJCAI 2011. We would like to give thanks to Luigi Iannone for assistance in using the OPPL scripting toolkit and useful advice for using the OWLAPI for the translation work. We would also like to give thanks to Kent Spackman and the reviewers for their helpful feedback.