1. 1 Consistency Checking of Semantic Web Ontologies Kenneth Baclawski, Northeastern U. & VIS Mieczyslaw M. Kokar, Northeastern U. & VIS Richard Waldinger, SRI & Kestrel Paul A. Kogut, Lockheed Martin

2. 2 Overview Inconsistency UBOT Tools ConsVISor Snark Conclusions Future directions

3. 3 Consistency consistency agreement with what has already been done or expressed; conformity with previous practice [Webster] In logic: from P and not(P) can derive anything Inconsistency is a dangerous thing for autonomous agents! An inconsistent ontology means one part of the ontology does not agree with another

4. 4 Logical Consistency Definition: there exists a non-trivial model of the theory. If a theory is inconsistent then every logical statement can be proven true. Our Opinion:  One consistent ontology for Semantic Web – impossible  Consistent subsets of a set of ontologies – but need to know when a given set is inconsistent – need warnings  Every single ontology should be consistent – need checking

5. 5 Inconsistent Ontology: Example Recursive combination of expressions Elementary – constants, variables Operation – includes operators (e.g., +, *) Example: (x + y + 5)*(z + 3)*(a + b) Problem: at least twice more Operations than Expressions (cardinality constraint) more Expressions than Operations (subClass constraint) #Expression  #Operation  2*#Expression – inconsistency? Operation – either empty or infinite! Mistake: cardinality restrictions inverted (not uncommon) (UML syntax)

6. 6 What’s wrong with this ontology?

7. 7 [Enzyme]  [Protein]  [Chemical]  [Reaction]<[Enzyme] Thus Enzyme<Enzyme! […] – class cardinality

8. 8 UBOT - Ontology Engineering Tools DAML Ontology Engineer DAML ontologies UML GUI Consistency Reasoning Agent CRAVE Consistency checking results UML DAML Translation XMI models DAML ontologies Consistency checking results ConsVISor SpecwareSNARK DAML ontologies DAML ontologies BugVISor

9. 9 ConsVISor Input: URI for DAML ontology or annotation Processing: Prolog-based tool that checks ontologies against the DAML+OIL axiomatic semantic specification Output: list of error and warning messages Role:  help ontology engineers check ontologies  help website developers check DAML annotations Cannot check consistency of the language (DAML)

10. 10 ConsVISor Architecture DAML file daml20.pl Modified daml20.pl Final Messages d2p Prolog p2d

11. 11 NumIDMessage 1:0034 The classes http://quantlabs.com/vis/ont/vehicle.daml#WaterCraft and http://quantlabs.com/vis/ont/vehicle.daml#LandVehicle were declared to be disjoint, but they both contain http://quantlabs.com/vis/ont/vehicle.daml#avk3379.

12. 12 SNARK/Specware Specware (from Kestrel Institute)  Formal specifications  Based on category theory SNARK (from SRI)  Theorem prover (resolution, paramodulation, special unification, sorts, procedural attachments, extensibility with Lisp)  But may not terminate (when ontology is consistent)  Can check consistency of the language specification!

13. 13 Example (SNARK) ( (Type ?fp FunctionalProperty) (and (Type ?fp Property) (=> (and (PropertyValue ?fp ?s ?v1) (PropertyValue ?fp ?s ?v2)) (= ?v1 ?v2)))) ( (Type ?fp FunctionalProperty) (and (Type ?fp Property) (forall (?s ?v1 ?v2) (=> (and (PropertyValue ?fp ?s ?v1) (PropertyValue ?fp ?s ?v2)) (= ?v1 ?v2))))) Original axiom: Revised axiom Checking Consistency of DAML Axiomatization With the original axiom every property is functional Consequently, since rdf:Bag is both rdfs:Class and rdf:Resource rdfs:Class = rdf:Resource

14. 14 Checking Restriction w/SNARK daml:Restriction was used to state that one can have only one father (see [1]) SNARK was able to prove that there is at least one father for everybody But could not prove that there are no more than one The problem was in the DAML specification of cardinality restriction Specification has been revised [1] www.daml.org/2001/03/daml+oil-walkthru.html

15. 15 Conclusion Inconsistencies are not desirable although not easy to avoid It’s better to identify them and then decide how to treat them rather than ignore ConsVISor is available at http://vis.home.mindspring.com for checking consistency of your DAML ontologieshttp://vis.home.mindspring.com Can be used to find problems in an ontology, not necessarily inconsistencies and not necessarily all SNARK can find more, but will quit after some time SNARK can be used to check language specifications

16. 16 Current/Future Work Ontology Or Annotated Source DAML Axioms ConsVISor Bug Locations Explanations BugVISor Errors DAML Bug Ontology

17. 17 Current/Future Work (cont.) Integrate ConsVISor with Snark Investigate ways to address time complexity of consistency checking Make the integrated tool available on the web Analyze errors due to merging different ontologies Provide quantitative evidence of problems related to inconsistencies