Upload
chloe-henry
View
222
Download
2
Tags:
Embed Size (px)
Citation preview
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
Languages
• RDF-S• OWL
– OWL-Full– OWL-DL– OWL-Lite
• WSML• DAML+OIL• SHOE• SWRL• …
• KIF• CycL• PowerLoom• FLORA-2• TRIPLE• OntoBroker (OXML)
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
FunctionRelation 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?