S
K
C
An Algebraic Approach to
Articulate Ontologies for
Information Integration
February 2001
Gio Wiederhold
Stanford University
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What are Ontologies?
Ontologies list the terms and their relationships
that allow communication among partners in
enterprises (in machine-readable form)
Relationships determine meaning - parent, school, company
Databases use ontologies during design
in their E-R diagrams
(Implicitly)
and
represent the leaf nodes in their schemas
Knowledge-bases use ontologies (often implicitly)
add class definition (to hold instances), constraints,
and, sometimes, operations among the terms
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Functions of Ontologies
.
• Enable Precision in Understanding
People = designers, implementors, users, maintainers
Systems = implementors = users = maintainers
• Share the Cost of Knowledge Acquistion &
Maintenance
reuse encoded knowledge, remain up-to-date as domains change
• Enable Information Interoperation
Define the terms that link domains
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*
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Ancestors of Ontologies
 Lexicons:
 Taxonomies:
.
collect terms used in informtion systems
categorize, abstract, classify terms
 Schemas of databases: attributes, ranges, constraints
 Data dictionaries: systems with multiple files, owners
 Object libraries: grouped attributes, inherit., methods
 Symbol tables: terms bound to implemented programs
 Domain object models: (XML DTD): interchange terms
 . . . More Knowledge formalized
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Establishing Ontologies
.
Top-down:
–Commonly acceptable UPPER layers
Domain-specific
–Sharing tools
–Object based
Bottom-up
–Pragmatic, TASK-specific collections
–Database schemas and models
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Heterogeneity among Domains
If interoperation involves distinct
domains mismatch ensues
• Autonomy conflicts with consistency,
– Local Needs have Priority,
– Outside uses are a Byproduct
Heterogeneity must be addressed
• Platform and Operating Systems 
• Representation and Access Conventions 
• Naming and Ontology
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
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Semantic Mismatches
Information comes from many autonomous sources
• Differing viewpoints
(by source)
– differing terms for similar items
{ lorry, truck }
– same terms for dissimilar items
trunk(luggage, car)
– differing coverage
vehicles (DMV, AIA)
– differing granularity
trucks (shipper, manuf.)
– different scope
student museum fee, Stanford
• Hinders use of information from disjoint sources
– missed linkages
loss of information, opportunities
– irrelevant linkages
overload on user or application
program
• Poor precision when merged
Still ok for web browsing , poor for business & science
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Need for precision
More precision is needed as data volume increases
--- a small error rate still leads to too many errors
False Positives have to be investigated
( attractive-looking supplier - makes toys
apparent drug-target with poor annotation )
Information Wall
lost opportunities,
suboptimal to some degree
False positives = poor precision
typically cost more than
false negatives = poor recall
data errors
False Negatives cause
information quantity
adapted from Warren Powell, Princeton Un.
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Ontology Sharing
Three Alternatives
 Create a committee to define everybody’s terms
 Takes many years, until people are worn out
 Ignored when changes make deviation necessary
 Get all terms and put them into large model
[ Cyc, UMLS, Federated Schemas, . . . ]
 Can be rapid
 Ignores conflicts
 Hard to maintain (requires committee)
 Keep all Terms distinct, except where sharing
 Requires initial effort
 Empowers participants
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Proposed Language Solutions
Specify and define terminology usage: ontology
• Domain-specific ontologies XML DTD assumption
– Small, focused, cooperating groups
– high quality, some examples - genomics, arthritis, Shakespeare plays
– allows sharable, formal tools
– ongoing, local maintenance affecting users - annual updates
– poor interoperation, users still face inter-domain mismatches
• Cannot achieve globally consistency
– wonderful for users and their programs
– too many interacting sources
– long time to achieve, 2 sources (UAL, BA), 3 (+ trucks), 4, … all ?
– costly maintenance, since all sources evolve
– no world-wide authority to dictate conformance
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An unsolved problem
Common assumption in assembling and integrating
distributed information resources
• The language used by the resources is the same
• Sub languages used by the resources are subsets of
a globally consistent language
This assumption is provably false
Working towards the goal of globally consistency is
1. naïve -- the goal cannot be achieved
2. inefficient -- languages are efficient in local contexts
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General Ontologies?
 Have all the Knowledge together
+ simple for customers of KBs
– hard for owners of KBs
 Large KB will cover multiple domains
 created by a committee -- slow
 maintained by a committee -- costly
 Differences in level of abstraction -- efficiency
 homeowner: nail
 carpenter: sinker, brad, boxnail, . . .
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Structural Heterogeneity
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Domains and Consistency
.
• a domain will contain many objects
• the object configuration is consistent
• within a domain all terms are consistent &
• relationships among objects are consistent
Domain Ontology
• context is implicit
No committee is needed
to forge compromises *
within a domain
 Compromises hide valuable details
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SKC grounded definition
.
• Ontology:
a set of terms and their relationships
• Term:
a reference to real-world and abstract objects
• Relationship:
a named and typed set of links between objects
• Reference:
a label that names objects
• Abstract object:
a concept which refers to other objects
• Real-world object:
an entity instance with a physical manifestation
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Domain-specific Expertise
.
Knowledge needed is huge
• Partition into natural
domains
• Determine domain
responsibility and
authority
• Empower domain owners
• Provide tools
Consider interaction
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Society of
specialists
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An Ontology Algebra
A knowledge-based algebra for ontologies
Intersection
Union
Difference
create a subset ontology
keep sharable entries
create a joint ontology
merge entries
create a distinct ontology
remove shared entries
The Articulation Ontology (AO) consists of
matching rules that link domain ontologies
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Sample Operation: INTERSECTION
Result contains
shared terms
Source Domain 1:
Owned and maintained
by Store
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Terms useful
for purchasing
Source Domain 2:
Owned and maintained
by Factory
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INTERSECTION support
Articulation ontology
Terms useful
for purchasing
Matching
rules that use
terms from the
2 source domains
Store
Ontology
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Factory
Ontology
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Sample Intersections
Articulation
size = size
ontology
matching rules : color =table(colcode)
style = style
Anatomy
{. . . }
Shoe Factory
Shoe Store
• Shoes { . . . }
• Customers { . . . }
• Employees { . . . }
foot = foot
Employees
Nail (toe, foot)
...
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• Material inventory {...}
• Employees { . . . }
• Machinery { . . . }
• Processes { . . . }
• Shoes { . . . }
Department
Store
Hardware
Employees
Nail (fastener)
...
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Other Basic Operations
DIFFERENCE: material
fully under local control
UNION: merging
entire ontologies
Articulation
ontology
typically prior
intersections
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Features of an algebra
Operations can be composed
Operations can be rearranged
Alternate arrangements can be evaluated
Optimization is enabled
The record of past operations can be
kept and reused
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Sample Processing in HPKB
• What is the most recent year an – Problems resolved by SKC
OPEC member nation was on the
* Factbook – a secondary
UN security council (SC)?
source -- has out of date
– Related to DARPA HPKB
OPEC & UN SC lists
Challenge Problem
• Indonesia not listed
– SKC resolves 3 Sources
• Gabon (left OPEC 1994)
» CIA Factbook ‘96 (nation)
» OPEC (members, dates)
» UN (SC members, years)
– SKC obtains the
Correct Answer
» 1996 (Indonesia)
– Other groups obtained more,
but factually wrong answers
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* different country names
• Gambia => The Gambia
* historical country names
• Yugoslavia
» UN lists future security
council members
• Gabon 1999
needed ancillary data
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Interoperation via Articulation
At application definition time
– Match ontologies
– Establish articulation rules.
– Record the process
At execution time
– Query rewriting
– Optimization based on an Ontology Algebra.
For maintenance
–Regenerate rules using the stored
formulation
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Semi-automatic approach
Provide library of automatic match heuristics
•
•
•
•
•
Lexical Methods -- spelling
Structural Methods -- relative graph position
Reasoning-based Methods
Nexus 
Hybrid Methods
– Iterative/Non-iterative Methods
GUI tool to
- display matches and
- verify generated matches using human expert
- expert can also supply matching rules
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Articulation Generator
Being built by Prasenjit Mitra
Thesaurus
OntA
Phrase Relator
Context-based
Word Relator
Driver
Structural
Matcher
Ont1
Ont2
Semantic
Network
(Nexus)
Human Expert
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Lexical Methods
• Preprocessing rules.
-Expert-generated seed rules.
e.g., (Match O1.President O2.PrimeMinister)
-Context-based preprocessing directives.
• Thesaurus - synonyms, relationships
• Distance of words as measure of
relatedness.
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Vehicle
sales
ontology
Vehicle
registration
ontology
Tools to create articulations
Suggestions
for articulations
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Combine ontology graphs
with expert selection
based on spelling,
graph matching, and
a nexus derived from
a dictionary (O.E.D.)
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Tools to create articulations
Graph matcher
for
Articulationcreating
Expert
Transport
ontology
Vehicle
ontology
Suggestions
for articulations
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continue from initial point
Also suggest similar terms
for further articulation:
• by spelling similarity,
• by graph position
• by term match repository
Expert response:
1. Okay
2. False
3. Irrelevant
to this articulation
All results are recorded
Okay’s are converted into articulation rules
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Candidate Match Repository
Term linkages automatically extracted from 1912 Webster’s dictionary *
* free, other sources
have been processed.
.
Based on processing
headwords  definitions
using algebra primitives
Notice presence
of 2 domains:
chemistry, transport
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Using the match repository
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Navigating the match repository
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Relative Arc Importance
• PageRank (Google) limitations
– node oriented
– high rank to words with little semantic value
» conjunctions, articles
The
» prepositions, pronouns
And
to
it
• Relative arc importance
– contribution of source rank to target rank
– vs ,t   ps / | as |
pt
es ,t
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ArcRank
• For All source s and target t nodes in graph
sort outgoing vs ,t j , rank by sorted order res (vs ,t j )
sort incoming vs ,t , rank by sorted order ret (vsi ,t )
i
for each arc es ,t compute mean( res (vs ,t ), ret (vs ,t ))
• In ranking
– Equal values take same rank
– Ranks numbered consecutively
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All Pairs Similarity
• Compute similarity value for all node pairs n,n'
product Pi of inbound arc importance vectors
product Po of outbound arc importance vectors
similarity = Pi  Po
• Similarity Matrix
– Initial state: nodes similar only to themselves
– Node substitution: terms replace similar ones
– Iterative convergence: bounded substitution
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Contents
» Examples
• Verb (Educate)
• Adverb (Ever)
• Proper Noun (Scotland -- undefined term
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Examples (Verb)
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Examples (Adverb)
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Examples (Proper Noun)
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Country Graphs
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To be matched to
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Knowledge Composition
Composed knowledge for
applications using A,B,C,E
Articulation
knowledge
Legend:
U
U
for
(A B) U
(B C) U
(C E)
Articulation
knowledge
(C E)
U
U : union
U
: intersection
Knowledge
resource
E
U
Knowledge
resource
A
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U
(B
C)
Knowledge
resource
B
Knowledge
resource
C
(C
U
U
Articulation
knowledge
for (A B)
D)
Knowledge
resource
D
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Primitive Operations
Model and Instance
Unary
• Summarize -- structure up
• Glossarize - list terms
• Filter - reduce instances
• Extract - circumscription
Binary
• Match - data corrobaration
• Difference - distance
measure
• Intersect - schem
discovery
• Blend - schema extension
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Constructors
• create object
• create set
Connectors
• match object
• match set
Editors
• insert value
• edit value
• move value
• delete value
Converters
• object - value
• object indirection
• reference indirection
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Future: exploiting the result
Result has links
to source
Avoid n2 problem of interpreter
mapping as stated by Swartout
as an issue in HPKB year 1
Processing & query evaluation
is best performed within Source
Domains & by their engines
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SKC Synopsis
• Research:
– Reliable query answers from heterogeneous,
imperfect data sources
• Sources:
– General: CIA World Factbook ‘96, UN-www, OPEC-www
Webster’s Dictionary, Thesaurus, Oxford English Dictionary
– Topical: OPEC, BattleSpace Sensors, Logistics Servers
• Client:
– DARPA High Performance Knowledge Base project
• Theory:
– Rule-based algebra
– Translation & Composition primitives
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Domain Specialization
• Knowledge Acquisition (20% effort) &
• Knowledge Maintenance (80% effort *)
to be performed by
• Domain specialists
• Professional organizations
• Field teams of modest size
autonomously
maintainable
Empowerment
* based on experience with software
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Innovation in SKC
•
•
•
•
No need to harmonize full ontologies
Focus on what is critical for interoperation
Rules specific for articulation
Tools for creation and maintenance
– Maintenance is distributed
» to n sources
» to m articulation agents
• Potentially many sets of articulation rules
is m < n2 , depends on semantic architecture density
a research question
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Backup Viewgraphs
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Summary
.
• Algebra enables Interoperation by
dealing explicitly with differences by knowledge
identifying maintenance domains
keeping sources autonomous
• Assumes domain has a common ontology
composing domain ontologies requires the algebra
to manage the linkages where articulation occurs
processes are best executed within the domains
• Knowledge about articulation is disjoint
allows integration specialists to work independently
supports multiple intersections and views
• Maintenance is structured and partitioned
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Current Directions
• Experience with real world (imperfect) data
confirms validity of our approach
– Expert sources are better maintained than
general sources
– Rules applied to multiple sources provide
more reliable and accurate query results
– Component architecture enables scalable,
maintainable knowledge base development
• Developing proof of concept environment with
HPKB standard knowledge base connectivity
interface
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Components of Ontologies
.
• Vocabularies
• words as handles for classes and concepts
• from database schemas. textbooks, catalog
indexes
• identified with their domain or context
• Relationships
• meaning is primarily defined through relationships
 Employee of a Company; Nails in a Shoe
• Annotations
• material to clarify the meaning of the terms
• contributed by users as well as original authors
• best with some examples
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Status
September 1997
.
• Base HPKB funding from AFOSR
– New World Vistas
– some industrial co-funding
• Prior work supported through Commercenet
– support for common representation, an interlingua
• Acquiring ontologies that
–
–
–
–
are interesting to HPKB projects
not trivial, I.e., represent realistic activities
intersectable
Logistics: DoD CIM, CIA, Cyc, . . .
• Starting smart students
• Integrating into architecture managed by TFS
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Information Flow for Training Initiative
sample
scenarios
scenario
refinement
trainer /
controller
aggregation/
analysis/
evaluation
ISI scenario language
Scenarios
Objectives
tasks
explosion
doctrine
TRADOC
mediator
knowledge
base
Requirements
exercise
design
Legend
sources
scenario
justification
Data
collection
Probepoint
settings
draft 1
aggregation
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Interlingua(s)
Interlingua:
Query :
Object Exchange Model
Mediator Specification Language
OEM
MSL
{ OID, LABEL, TYPE, VALUE }
<document
{<author AUTHOR> <title TITLE>}:-
<biblioentry
{<author AUTHOR>}>@biblio
<inproceedings {<title TITLE>}>
@sybase
AND
AND
Equal(AUTHOR, “Jeff Ullman”)
Interlingua:
Query:
Knowledge Interchange Format
Knowledge Query and Manipulation Language
KIF
KQML
(PACKAGE :FROM ap001
:TO ap002
:CONTENT
(MSG
:TYPE query
:CONTENT-LANGUAGE KIF
:CONTENT (and (document (author@biblio ?a) (title@sybase ?t))
(eq “Jeff Ullman” ?a)))
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Support for KB-Algebra
• Ontolingua [Gruber, Fikes @ Stanford KSL]:
Repository for Domain Terminologies
Used for mechanical design, bibliographies, catalogs
• LOOM [MacGregor@ USC ISI]:
Classification-based Expert System
Helps in structuring and processing ontologies
• PROTÉGÉ [Musen@ Stanford MIS]
Reuse
• Penguin [Barsalou, Keller@ Stanford MIS, CIFE]:
Object manipulation based on Relational Algebra
Used for genetics laboratory, building design
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