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Ontology Language Comparisons

doug foxvog

16 September 2004

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Overview

• Numerous Ontology Languages

• Different Logical Formalisms

• Syntactical Form

• Language Features

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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

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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

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Languages

• RDF-S• OWL

– OWL-Full– OWL-DL– OWL-Lite

• WSML• DAML+OIL• SHOE• SWRL• …

• KIF• CycL• PowerLoom• FLORA-2• TRIPLE• OntoBroker (OXML)

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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

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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

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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

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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

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Language Features

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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

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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

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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

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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

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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

FunctionRelation whose value when applied is that of corresponding functional argument stripped from Functional Predicate

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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)

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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

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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

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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

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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

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Rules – Axioms

• Implication– Not: DAML+OIL, OWL, RDF-S

• Rule/Formula as Object– WSML-Core, TRIPLE, FLORA, CycL, Ontobroker

• Rule Exceptions– KIF, FLORA, CycL

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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)

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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

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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

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Questions?