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Ontology Language Comparisons

Explore various ontology languages and logical formalisms used in computer science, focusing on reasoning, term hierarchies, logical languages, and ontology logic types. This overview covers multiple hierarchies, hierarchies with logical languages, and ontology language components.

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Ontology Language Comparisons

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  1. Ontology Language Comparisons doug foxvog 16 September 2004

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

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

  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. 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. 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. 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. Language Features

  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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Questions?

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