1. 1 Ontology Language Comparisons doug foxvog 16 September 2004

2. 2 Overview Numerous Ontology Languages Different Logical Formalisms Syntactical Form Language Features

3. 3 Numerous Ontology Languages Most Computer Science fields have a few standard languages Ontologies expressed in many languages – Some languages merely for expression – Other languages for reasoning Concentrate on reasoning

4. 4 Term Hierarchies Taxonomy – Broader/Narrower Term OpenDirectory – 590,000 categories Subclass Hierarchy UNSPSC – 10,000 product types Multiple Hierarchies (via different predicates) WordNet – 152,000 synsets Hierarchies + Logical Languages Express Semantics Considered Ontologies Topic of Talk

5. 5 Languages RDF-S OWL – OWL-Full – OWL-DL – OWL-Lite WSML DAML+OIL SHOE SWRL … KIF CycL PowerLoom FLORA-2 TRIPLE OntoBroker (OXML)

6. 6 Logical Formalisms Description Logic: Roles, Classes, Individuals Propositional Calculus: ∨ ∧ ¬ Variables Subset without ¬ Subset without ∨ Subset without Variables Horn Clauses only First-Order Logic:  Higher-Order Logics Quantification over predicates Quantification over sets Cardinality: ThereExistExactly, ThereExistAtLeast, ThereExistAtMost Predicates as arguments

7. 7 Ontology Logic Types Restricted Description Logic – OWL-Lite, RDF-S, SHOE Description Logic – OWL-DL, DAML+OIL, SWRL(+) First-Order Logic – F-Logic, FLORA, OntoBroker, OWL-Full, TRIPLE Extended First-Order Logic – Power-LOOM Higher-Order Logic – CycL, KIF Three-valued Logic – Power-LOOM

8. 8 Propositional Calculus Includes: ∨ ∧ ¬ Variables Limitations for Computational Tractability Subset without ¬ Owl-Lite, RDF-S, SHOE Subset without ∨ OWL-Lite, RDF-S, OntoBroker Subset without Variables DAML+OIL, OWL, RDF-S Horn Clauses only: (A ∧ B ∧ … ∧ C  D) SHOE

9. 9 Closed World & Unique Name Assumptions Closed World Assumption – If it cannot be proved true, it is false. – In: TRIPLE – Optional settings: CycL, FLORA, KIF, PowerLoom Unique Name Assumption – Two things with different names are different. – In: PowerLoom, Ontobroker (not external term) – Default: TRIPLE – Optional: CycL

10. 10 Language Features

11. 11 Syntax LISP – CycL, KIF, PowerLoom PROLOG Extensions – F-Logic, FLORA, TRIPLE XML – DAML+OIL, OWL-Full, RDF-S, SHOE, SWRL Multiple – OntoBroker, OWL-DL, OWL-Lite, WSML-Core

12. 12 Ontology Language Components Named Terms – Class / Type / Concept / Category … – Individual / Instance – Relation / Predicate / Role / Attribute / … Reserved Operators; Special Symbols Variables Datatype Instances – Strings– Characters – Numbers– URIs, Dates, … Data Structures – Sets– Lists Statements

13. 13 Variables and Quantifiers Variables Imply Quantification Default to forAll in statement Default to either forAll or thereExists in Query Most Ontological Languages Include Variables Not in: DAML+OIL, OWL, RDF-S Existential Quantification Not in: FLORA-2, WSML-Core Anonymous/ Don’t-Care Variables Effectively Provide Existential Quantification In: CycL, FLORA-2 Qualified Number Restrictions (Cardinality) In: CycL, DAML+OIL, F-Logic, Ontobroker, OWL*, Power-LOOM, SWRL

14. 14 Class – Type – Category Concept – Collection Multiple Inheritance – All Class/Individual Distinction Not: KIF, F-Logic, TRIPLE Metaclasses Disallowed: OWL, DAML+OIL, SWRL Code support: CycL Class as argument Not: OWL-DL, OWL-LITE, DAML+OIL, SWRL Class & Role with Same Name OWL*, F-Logic, TRIPLE Disjoint Classes Not RDF-S, SHOE, WSML

15. 15 Relations – Predicates Roles – Properties – Attributes Relation – Predicate or Function Predicate Specifies interrelationship among meanings of terms. Value, when applied to arguments, is a truth value Binary Predicate – Two argument predicate Role/Property/Attribute Binary predicate applicable only to elements of a class Functional Predicate Predicate with single arg-n valid for other args fixed Functional Role/Property/Attribute Role with single arg2 valid for given arg1 Function Relation whose value when applied is that of corresponding functional argument stripped from Functional Predicate

16. 16 Relations Argument Type Constraints – Not in: OWL-Lite, KIF – For Attributes only: OWL-DL, OWL-Full Inter-argument Restrictions – In: OWL-Full, OWL-DL, CycL, F-Logic, FLORA, WSML Higher Arity Relations – In: FLORA-2, CycL, KIF, PowerLoom, SHOE, Ontobroker, TRIPLE (functions only) Variable Arity Relations – KIF, CycL, Triple (functions only)

17. 17 Relations Transitive Binary Relations – DAML+OIL, CycL, FLORA (Transitive Closure), WSML, PowerLoom, SWRL, OWL, Ontobroker Symmetric Binary Relations – CycL, FLORA, WSML, PowerLoom, SWRL, OWL, Ontobroker Inverse Binary Relations – WSML, PowerLoom, SWRL, OWL, KIF, Ontobroker Subrelations – By rule: KIF, TRIPLE

18. 18 Attributes Attribute Definition is Part of Class Definition Range Includes: – individuals – datatype instances Range Excludes – Relations – Classes – Statements Languages with Attributes also Limit other Relations’ Arguments – OWL, DAML+OIL, RDF-S, WSML-Core

19. 19 Functions & Functional Relations Functions, but no Functional Predicates – FLORA, TRIPLE Functional Predicates, but no Functions – OWL, Ontobroker Neither Functions nor Functional Predicates – RDF-S, WSML-Core, SHOE Functions and Functional Predicates – CycL, PowerLOOM, KIF, DAML+OIL, SWRL

20. 20 Relation Features Multiple Argument Constraints – RDF-S, OWL-Full, OWL-DL, DAML+OIL, CycL, TRIPLE, RDF-S (Constraint Disjunction!), WSML- Core Default Argument Values – FLORA, Ontobroker, CycL – By rule: KIF, TRIPLE Argument Cardinality Restrictions – OWL*, DAML+OIL, F-Logic, CycL, SWRL, Ontobroker, PowerLOOM

21. 21 Rules – Axioms Implication – Not: DAML+OIL, OWL, RDF-S Rule/Formula as Object – WSML-Core, TRIPLE, FLORA, CycL, Ontobroker Rule Exceptions – KIF, FLORA, CycL

22. 22 Equality Not – Not in: WSML-Core, SHOE, RDF-S, OWL-Lite – restricted: DAML+OIL (complimentOf) Different – OWL, CycL, – Individual: DAML+OIL – Datatype Values: SHOE, SWRL – Classes: SHOE Equals – Levels of Equality: CycL, FLORA – DAML+OIL (property, individual, class), TRIPLE, SHOE (datatype, class), SWRL (datatype, URI)

23. 23 Datatypes & Sets Datatype Support Arithmetic operations String operations (concatenate, replace, …) Comparisons Extent of Support Often not Described Extensional Sets OWL-FULL, OWL-DL, RDF-S, DAML+OIL, CycL, PowerLoom, KIF Expressible: TRIPLE

24. 24 Multiple Ontologies External Ontologies Import External Ontologies – OWL,RDF-S, DAML+OIL, WSML, TRIPLE, SHOE Specify Synonymous Term in External Ontology – CycL, Ontobroker Different Logical Worlds (Context/ Module/ Model/ Microtheory) in which to Reason Hierarchy of contexts – FLORA, TRIPLE, PowerLOOM, CycL

25. 25 Questions?