Directed acyclic graphs are commonly used to represent ontologies in the biomedical domain. They provide an intuitive means to formalize relations that hold between ontological categories. However, their semantics is usually not explicit. We provide a semantics for a part of the OBO Flat le Format by extending OWL with a method to express relational patterns. These patterns are OWL axioms with variables for classes. The variables can only be lled with named classes. Additionally, we provide a semantics for open patterns in OWL. Our method is applicable to the OBO Flat le Format, and provides a means to design OWL ontologies using complex ontology design patterns. Therefore, it leads not only to an integration of the OBO Flat le Format and OWL, but extends OWL with an intuitive interface for designing ontologies using complex de nition patterns. A prototypic implementation and test results are available at http://bioonto.de/obo2owl.
Directed acyclic graphs (DAG) have been a popular representation format for
biomedical ontologies. The original representation of the Gene Ontology (GO)
has been in the form of a DAG [
In the OBO Flat le Format, nodes represent ontological categories and edges
represent relations between these categories. The OBO Relationship Ontology
(RO) provides formal de nitions for commonly used relations between
ontological categories [
We developed an extension to the OBO Flat le Format and to the
Manchester OWL Syntax [
The OBO Flat le Format is a knowledge representation format that has been
developed for biomedical ontologies. The basic elements of the OBO Flat le Format
are typedef and term statements. Term statements de ne nodes in the DAG.
A node has an identi er and a name. Additionally, several restrictions can be
asserted for a node. In particular, the edges originating from the node are
speci ed in the node description. For this purpose, either the is a or relationship
statements are used. Edges represent relations between nodes. An example of a
term de nition taken from the Celltype Ontology (CL) [
Typedef statements specify the kinds of edges in the DAG. They represent the relation that is intended to be established between two nodes when an edge of a certain kind is used. An edge has an identi er and a name. Additionally, properties for the edges can be asserted, such as transitivity. A de nition of the develops from edge kind taken from the CL is: [Typedef] id: develops_from is_transitive: true
The intended meaning of the graph representations is that nodes represent
ontological categories and edges represent relations between these categories.
The OBO Relationship Ontology (RO) [
However, the semantics of the OBO Flat le Format is not explicit, and several
competing solutions have been proposed. One type of semantics is provided by
the RO, which uses a rst order semantics tailored to each relation type. Another
type of semantics uses a xed semantics for relations and relational statements
[
The latter kind provides a semantics for intersection, union and disjointness statements as well, using the corresponding operations for classes in description logics.
Although the rigid semantics for relational statements in the OBO Flat le
Format is adequate for many relation types, it fails in several cases. For example,
the relation lacks-part must not be translated using an existential assertion.
Similarily, the relation realized-by must use a universal quanti cation instead of
an existential one [
Both kinds of semantics are incompatible, and each has drawbacks. The rst does not provide a semantics for the OBO Flat le Format as a knowledge representation language, because it only provides a semantics for parts of the OBO Flat le Format, and this semantics depends on the used relations. New relations cannot easily be introduced or de ned. On the other hand, using a rigid semantics for relations does not correspond to the intuitions of ontology designers and often leads to assertions which are false within a domain.
This observation motivated us to develop and implement an extension to OWL that can be applied to solve the problems with the OBO Flat le Format, and is general enough to be applicable in other domains of knowledge representation using OWL. 3
To provide compatibility with the OBO Flat le Format, we focus on binary relations between classes rst and extend our method later. We introduce a new type in OWL which represents relational pattern speci cations.
To specify the intensions of binary relations between classes, we have
extended the Manchester OWL Syntax [
For example, we can de ne the pattern CC-part-of as ?X SubclassOf: part-of some ?Y where part-of is an OWL object property. Then we can apply the CC-part-of pattern to the primitive classes A and B, CC-part-of(A; B). The resulting OWL axiom is derived by substituting ?X with A and ?Y with B: A SubclassOf: part-of some B. In such a scenario, the patterns are never directly used within OWL for reasoning. Instead, the patterns provide a template for asserting OWL axioms.
More complex ontology design patterns5 can be asserting using di erent relational pattern de nitions. Table 1 lists a translation of the relational patterns in the RO to relational pattern de nitions.
The approach can be restricted to unary or extended to n-ary relational patterns. Unary patterns require a single variable symbol, while n-ary relational patterns use the variable symbols ?X1, ?X2, ?X3, etc. For such an application, the OBO Flat le Format would have to be extended to accommodate n-ary relation. 4
The patterns themselves contain the free variables ?X1,...,?XN. In some cases, it
may be useful to use open patterns themselves as meta-properties of an OWL
ontology. In such a case, the open variables are universally quanti ed. However,
the common interpretation of quanti cation over classes is second order, where
the quanti er ranges over the powerset of the universe. This results in
undecidability of class satis ability. We provide a decidable semantics for open relational
pattern de nitions, where the quanti er ranges only over named classes in the
signature of the OWL ontology. We use description logic syntax [
The semantics of a description logic theory over a signature = (C; R; A),
with C a set of concept symbols (including > and ?), R a set of relation symbols
and A a set of individual symbols, is given by an interpretation I. The
interpretation I consists of a non-empty set U I and an interpretation function , such
that for every Ci 2 C, (Ci) U I , (Ri) U I U I for every Ri 2 R and
(a) 2 U I for every a 2 A. The interpretation function is inductively extended
in the usual way. Using standard description logic notation [
= U I (C u D) = C
\ D (9R:C) = fa 2 U I j9b:(a; b) 2 R ^ b 2 C g
Using a higher-order logic, the interpretation of free class variables such as ?X and ?Y will map to a subset of the powerset of U I : (?X) 2 P(U I ). Universal quanti cation over these free variables would then range over the full powerset of U I . In particular, satis ability of terminological axioms6 that contain class expressions involving ?X or ?Y would have to consider the powerset of U I .
For the relational pattern de nitions, we adopt a di erent approach where it is not necessary to use the full powerset in the interpretations of the class variables. Instead, the variable symbols ?X1,..., ?XN are interpreted with an extension of one of the atomar classes from the signature . If is nite, then 5 http://ontologydesignpatterns.org 6 Terminological axioms in description logics are of the form C v D or C D with C and D being concept expressions, or R S with R and S being relationship (role) expressions. satis ability of terminological axioms in OWL extended with ?X and ?Y will be trivially decidable.
Formally, let T be a description logic theory over the signature = (C [ f?X1; :::; ?XN g; R; A) and I be an interpretation with the interpretation function and a domain U I, and P (U I) = fCi jCi 2 Cg. Then (?X1) 2 P (U I ),..., (?XN ) 2 P (U I ).
This restriction leads to decidability of the satis ability problem for terminological axioms (if is nite): satis ability of a terminological axiom involving ?X1,..., ?XN can be decided by verifying the satis ability of the terminological axioms that arise through substituting ?X,..., ?XN with all atomar concept symbols in . Since the signature = (C; R; A) is nite, jCjN terminological axioms must be veri ed for satis ability to decide the satis ability of one open relational pattern de nition involving ?X1,..., ?XN. 5 5.1
Due to the decidability of satis ability of terminological axioms, the de nition schema for relations in the OBO Flat le Format can be employed in two directions: from OBO to OWL and from OWL to OBO. We have already described how relations can be de ned and translated to OWL using a relational pattern de nition. Based on these de nitions, new relations between categories in the OBO Flat le Format can be extracted from an OWL knowledge base. Therefore, these de nitions can also serve as a method for an extended form of reasoning using the OBO Flat le Format.
The OBO Flat le Format provides a means to express relations between classes, yet it does not provide a way to de ne the relations themselves. We use relational pattern de nitions in our extended syntax to de ne relations between classes in the OBO Flat le Format. For this purpose, we extend the Typedef environment in the OBO Flat le Format to include the de nition of relations. For example, to de ne the relation CC-has-part, we would use the following Typedef statement in the OBO Flat le Format: [Typedef] id: CC-has-part name: has-part owldef: ?X SubClassOf: has-part some ?Y According to our semantics, every use of the relation CC-has-part in the OBO Flat le Format is expanded to an OWL axiom in which the variables are lled by the classes between which the relation was asserted. For example, the statement that every mouse body has some tail as part in the OBO Flat le Format would be: [Term] id: Mouse_body relationship: has-part Tail Using the OWLDEF method, Mouse body and Tail ll ?X and ?Y, respectively. The resulting OWL axiom would be
Although most relations in biomedical ontologies follow an existential
allsome pattern, some relations must be formalized di erently. In particular the
relation integral-part-of from the RO [
subclassOf Nothing This statement is logically equivalent to asserting both axioms ?X SubclassOf: part-of some ?Y and ?Y SubclassOf: has-part some ?X.
The patterns we de ne can not only be used to expand relations between classes into complex OWL statements, but also to convert a complex OWL ontology into a set of relations between classes. For this purpose, let L be the set of named classes in the signature of an OWL ontology. Then, for each pair (x; y) of classes x; y 2 L, we replace ?X with x and ?Y with y in the relational pattern de nitions, and use OWL reasoning to verify whether the resulting OWL axiom is true in the OWL ontology. If the resulting axiom is true in the OWL ontology, the relation between the classes x and y holds and we can add this information to the OBO Flat le Format. This approach is superior to syntactic transformations of OWL to OBO, because it accounts for the semantics of the relations, and makes the inferences that can be drawn from them available in the OBO format.
We implemented the expansion and the contraction of relational patterns in
two separate software libraries and applications. The rst Java library is an
extension of the Manchester OWL API [
Table 1. OWLDEF implementation of selected relations. de nition, ?X and ?Y from the owldef statement are replaced by the corresponding term names (see 5.1). After the replacement, we use the OWL API's Manchester syntax inline axiom parser to generate an OWL axiom from the resulting statement. Each axiom is added to the OWL ontology in addition to the axioms generated by the transformation from OBO to OWL implemented in the Manchester OWL API.
Second, we provide a prototypical implementation to extract relational
patterns from an OWL ontology so that they can be converted back to the OBO
Flat le Format. For this purpose, an OWL ontology is read using the Manchester
OWL API [
To evaluate our method we applied it to the Celltype Ontology (CL) [
The CL contains 1253 is-a and 275 develops-from statements, i.e., 1528 axioms that restrict CL categories using one of these two relations. We classify the generated OWL ontology using the Hermit OWL reasoner. Based on the classi ed OWL ontology, we attempt to prove the two patterns for each pair of named classes in the ontology. We use the Hermit reasoner to perform these inferences. Using this approach, we identify 9,497 is-a and 124,420 developsfrom statements that we add to the OBO Flat le represenation of the CL. This shows that OWL reasoning can be used to infer new relations in OBO ontologies.
Since the CL only uses is-a and develops-from, our conversion is
similar to other OBO-to-OWL conversion methods. Therefore, we further
evaluated our method with the Malaria Ontology and the Sequence Ontology (SO)
[
There are several methods and tools available to convert ontologies in the OBO
Flat le Format to OWL [
Although this pattern is appropriate for a majority of currently used relations
in OBO and OBO Foundry ontologies, it fails in several cases. Table 1 lists
several such cases. In particular, the integral-part-of and has-integral-part
relations in the RO require a di erent translation to OWL. Further relations
that are used in OBO ontologies include the realized-by relation between a
function or disposition and a process. Several complex relations such as
hasfunction-realized-by [
To the best of our knowledge, there are no conversion tools available that are compatible with the RO in that they apply the de nition patterns of the RO in the conversion. Similarily, the OWL implementation of the RO does not coincide with the de nitions of the RO relations in rst order logic. We are also not aware of an implementation of the RO in OWL that implements or approximates the de nition patterns the RO attempts to provide.
Our prototypical implementations serve to demonstrate our method. In the
future, we plan to use the OPPL formalism [
The OWLDEF method provides a exible way to de ne relations using complex OWL statements. However, it interferes with other parts of the OBO Flat le 7 http://oppl2.sourceforge.net Format. In particular disjointness, intersection and union statements do not interoperate well with the OWLDEF method. To illustrate the problem, consider the following de nition of a category in the OBO Flat le Format: [Term] id: ID:1 intersection_of: ID:2 intersection_of: integral-part-of ID:3 The di culty is that integral-part-of ID:3 is not a class description when the OWLDEF method is used. Instead, ID:1 integral-part-of ID:3 would translate into one OWL axiom but axioms cannot be disjoint from classes (ID:2) in OWL. This shows a fundamental limitation of the OBO Flat le Format, because it is not obvious what an intersection statement together with an integral-partof relation is intended to mean.
However, the current translations of the OBO Flat le Format to OWL do not provide an adequate semantics for this statement either, because the relation integral-part-of is not appropriately translated. One possible solution would be to disallow the use of relational statements in intersection, disjointness or union statements, and allow only class names as arguments. However, it is subject to future research to provide a semantics for these statements in combination with the OWLDEF method. 6.3
OWL relational pattern de nitions can be applied to unstructured RDF data to
provide a semantic layer and an interpretation of relations used in RDF stores.
One application would be to apply our method to Linked Data [
We developed a novel semantics for a fragment of the OBO Flat le Format by explicitly incorporating relational de nition patterns in the OBO Flat le Format. A de nition pattern is an OWL axiom with variables for OWL classes. Our approach leads to a exible OWL-based semantics for several biomedical ontologies. Motivated by the problem of nding an adequate semantics for the OBO Flat le Format, we developed an extension to OWL that is general enough to be applicaple in many domains. It provides a means to incorporate ontology design patterns in the ontology development process, leading to an intuitive interface to otherwise complex logical statements. 8
We thank three anonymous reviewers for valuable comments on this manuscript.
We acknowledge funding from the Institute for Medical Informatics, Statistics and Epidemiology at the University of Leipzig, the Max Planck Institute for Evolutionary Anthropology and the European Bioinformatics Institute.