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 Flatfile 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 filled with named classes. Additionally, we provide a semantics for open patterns in OWL. Our method is applicable to the OBO Flatfile 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 Flatfile Format and OWL, but extends OWL with an intuitive interface for designing ontologies us ing complex definition patterns. A prototypic implementation and test results are available at http://bioonto.de/obo2owl

1. Relational Patterns in OWL and their application to OBO Robert Hoehndorf1, Anika Oellrich1, Michel Dumontier2, Janet Kelso4, Heinrich Herre3, and Dietrich Rebholz-Schuhmann1 OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 1 1European Bioinformatics Institute, 2Carleton University, 3University of Leipzig, 4Max Planck Institute for Evolutionary Anthropology

3. Ontology Explicit specification of conceptualization specify meaning of terms in vocabulary formal ontology uses languages with explicit semantics to specify meaning axioms in FOL, OWL, etc OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 3

4. Biomedical Ontologies OBO - 100+ ontologies OBO Foundry common principles and criteria format: OBOF or OWL must use OBO Relation Ontology OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 4

5. OBO Flatfile Format Graph based language Nodes [term] represent categories [Term] id: CL:0000028 name: CNS neuron (sensuNematoda and Protostomia) is_a: CL:0000540 ! neuron relationship: develops_from CL:0000338 OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 5

6. OBOF examples Edges [typedef] represent relations [Typedef] id: develops_from is_transitive: true OBOF semantics not explicit One solution uses tailored FOL semantics Another uses fixed semantics for relations and relational statements OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 6

7. OBO Relationship Ontology Smith, 2005 FOL definitions for common relations C part_of C' if and only if: given any c that instantiates C at a time t, there is some c' such that c' instantiates C' at time t, and c *part_of* c' at t. weak axioms (reflexivity, transitivity, etc.) use of FOL and ternary relations: mapping to (decidable) OWL problematic OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 7

8. Horrocks OBO2OWL semantics Fixed semantics via mapping to OWL intersection, union, disjointness R(C,D) maps to C subClassOf R some D OBOF [Term] name: mouse relationship: has-part tail OWL mouse subClassOf has-part some tail OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 8

9. Critique Horrocks semantics does not use RO semantics but RO must be used for OBO Foundry ontologies Horrocks semantics sometimes inadequate Tailless-Mouse subClassOf lacks-part some Tail Should instead be: Tailless-Mouse subClassOf not(has-part some Tail) OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 9

10. Problem statement RO in FOL -> undecidable RO not integrated in OBOF no semantics for OBOF static translation of relations to OWL C subClassOf R some D-> inadequate develop OBOF semantics, preferably using decidable logic (OWL) OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 10

11. Proposal Observation: relation between classes defined through relations between instances R(C,D) <-> Def(C,D) C and D occur as variables in Def Idea: Pattern Definitions in OWL extend OWL with variables for classes use Manchester OWL syntax formulate relations using extended OWL syntax similar to OWL Pre-Processing Language (OPPL) OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 11

12. Extended OBOF syntax:OWLDEF [Typedef] id: CC-has-part name: has-part owldef: ?X subClassOf: has-part some ?Y every use of the relation CC-has-part in the OBOF is expanded to an OWL axiom in which the variables are filled by the classes between which the relation was asserted. [Term] id: Mouse relationship: has-part Tail gives: Mouse subClassOf has-part some Tail OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 12

13. integral-part-of integral-part-of(?X, ?Y): ?X part-of ?Y and ?Y has-part ?X Produces two OWL class axioms ?X subClassOf part-of some ?Y ?Y subClassOf has-part some ?X Which are transformed to one (?X and not (part-of some ?Y)) or (?Y and not (has-part some ?X)) subClassOfNothing OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 13

14. OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 14

15. OBO2OWL prototype extends OWL API to convert OBOF to OWL with owldef statements ?X and ?Y from the owldef statement are replaced by the corresponding term names inline axiom parser generates an OWL axiom API and web-interface at http://bioonto.de/obo2owl OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 15

16. OWL2OBO Extract relational patterns from OWL ontology Naïve: replace ?X and ?Y with all combinations of named classes are generated to fill variables in the relation patterns and generate OWL axioms from binary class relations Hermit used to prove axioms; keep track of those which could be inferred from asserted axioms Obtain list of theorems that can be added to OBO file OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 16

17. Evaluation Celltype Ontology 1253 is-a; 275 develops-from relations identified 9,497 is-a and 124,420 develops-from Malaria Ontology 3 realized-by Identified 56 realized-by Sequence Ontology Added 1 exonintegral-part-of transcript Now: all exons are part-of transcript and all transcripts has-partexon OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 17 Results @ http://bioonto.de/obo2owl

18. Open Problems intersection, union statements and relations have unclear semantics [Term] id: ID:A intersection_of: ID:B intersection_of: integral-part-of ID:C OWL class axiom (integral-part-of) intersected with class description -> invalid (A subClassOf B) intersected with C: is C intersected with A, B, both? no obvious solution: inherent problem in OBOF, needs to be addressed (by OBOF developers) OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 18

19. Advanced Applications n-ary relations between classes introduce variables ?X1, ..., ?XN example: has-quality-with-value(?X1, ?X2, ?X3): ?X1 subClassOf has-quality some (?X2 and has-value some ?X3) OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 19

20. Advanced Applications 2 open patterns as meta-properties of ontologies Consider the combinatorics of connecting chemical groups to base groups for high throughput chemical synthesis assert ?X subClassOf is-connected-to some ?Y semantics: all named classes in ontology satisfy the pattern: all classes can be connected to all other classes OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 20

21. Future Research integration with OPPL2 and use of OPPL2 to define relations formalization of further relations repository of frequently used relation definitions efficient conversion from OWL to OBO integration with OWL: use of annotation properties OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 21

22. Conclusion pattern approach as a simple interface to complex definitions flexible semantics based on conversion to OWL we implemented OBO RO in OWL current approaches have shortcomings open issues with intersection, union, etc http://bioonto.de/obo2owl OWLED2010:San Francisco:Relational Patterns in OWL and their application to OBO 22