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Large-Scale Repositories of Highly Expressive Reusable Knowledge

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Foundation Technology and Lessons Learned from Community Interoperability Efforts Prof. Richard Fikes Knowledge Systems, AI Laboratory Computer Science Department – PowerPoint PPT presentation

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Title: Large-Scale Repositories of Highly Expressive Reusable Knowledge


1
Foundation Technology and Lessons Learned from
Community Interoperability Efforts
Prof. Richard Fikes Knowledge Systems, AI
Laboratory Computer Science Department Stanford
University
3/27/06
2
In the Knowledge Is The Power
  • Its not enough to be smart and clever
  • Knowledge is a fundamental enabler of intelligent
    behavior
  • Encoding knowledge requires extensive time
    expertise
  • The challenge is to enable
  • Rapid construction of large-scale knowledge bases
  • Knowledge encoding by large populations of domain
    experts
  • Customization of knowledge for specific tasks and
    methods
  • Address the challenge by developing
  • Libraries of multi-use knowledge bases
  • Tools for assembling knowledge bases from
    multi-use modules
  • Interoperable knowledge servers and tools
  • Methods for encoding knowledge on Web pages

3
Ontologies as KB Building Blocks
  • Typical KR languages are domain-independent
  • E.g, predicate calculus and frame languages
  • Do not provide a domain-specific vocabulary
  • KB construction therefore involves two steps
  • Define vocabulary to be used to represent the
    knowledge
  • Represent the knowledge using the defined
    vocabulary
  • Vocabulary is reused in many applications
  • Therefore, ontologies are the major form of
    multi-use knowledge

4
Impediments to Sharing and Reuse
  • Heterogeneous representation formalisms
  • Lack of knowledge-level communication conventions
  • Domain model mismatches

5
DARPA Knowledge Sharing Effort
  • Knowledge Standards Workshop March 1990
  • Sponsored by DARPA, NSF, and AFOSR
  • Launched a knowledge standards effort
  • A rebellion against standards
  • KRR conference 1991
  • The KIF of Death 1991
  • Effort changed to a Knowledge Sharing Effort
  • Funding provided by DARPA for several years

6
Impediments to Sharing and Reuse
  • Heterogeneous representation formalisms
  • Lack of knowledge-level communication conventions
  • Domain model mismatches

7
DARPA Knowledge Sharing Effort
  • Heterogeneous representation formalisms
  • Interlingua WG
  • Developed a first-order logic interlingua for
    exchanging knowledge
  • KIF (Knowledge Interchange Format)
  • Knowledge Representation System Specification
    (KRSS) WG
  • Developed a consensus-standard description logic
  • Lack of knowledge-level communication conventions
  • Domain model mismatches

8
Interlingua for Reusable KBs
...
Language 1
Language 2
Language n
K I F
9
DARPA Knowledge Sharing Effort
  • Heterogeneous representation formalisms
  • Interlingua WG
  • Developed an FOL interlingua for exchanging
    knowledge (KIF)
  • Knowledge Representation System Specification
    (KRSS) WG
  • Developed a consensus-standard description logic
  • Lack of knowledge-level communication conventions
  • External Interfaces WG
  • Developed knowledge-level communication protocols
  • KQML (Knowledge Query and Manipulation Language)
  • OKBC (Open Knowledge Base Connectivity)
  • Domain model mismatches

10
DARPA Knowledge Sharing Effort
  • Heterogeneous representation formalisms
  • Interlingua WG
  • Developed an FOL interlingua for exchanging
    knowledge (KIF)
  • Knowledge Representation System Specification
    (KRSS) WG
  • Developed a consensus-standard description logic
  • Lack of communication conventions
  • External Interfaces WG
  • Developed knowledge-level communication protocols
    (KQML, OKBC)
  • Model mismatches at the knowledge level
  • Shared, Reusable Knowledge Bases WG
  • Developed the concept of an ontology
  • A specification of a conceptualization (1993)
  • Developed an ontology representation language and
    library
  • Ontolingua

11
Interlinguas for Reusable KBs
...
Language 1
Language 2
Language n
K I F
  • Knowledge Interchange Format (KIF)
  • First-order logic with an Ascii syntax
  • Ontolingua An interlingua for ontologies
  • Monotonic frame language augmented by KIF axioms
  • Frame language defined as an ontology represented
    in KIF
  • Evolved into the OKBC knowledge model (as used in
    Protégé)

12
Ontolingua A World Wide Web Service
  • A first generation ontology development
    environment (Dec. 94)
  • Usable via a standard Web viewer
    (ontolingua.stanford.edu)
  • Representation languages that facilitate
    widespread usability
  • Internal --
  • Knowledge Interchange Format (KIF)
  • Frame language ontology
  • OKBC programmatic interface
  • External --
  • Frame language augmented with KIF axioms and
    definitions
  • Fully cross-referenced html documents
  • On-line library of multi-use ontologies
  • A publication medium for ontologies
  • Ontology editor and browser
  • Assemble and extend library ontologies
  • Develop collaboratively

13
Example Definitions
  • LengthDimension
  • instanceOf PhysicalDimension
  • standardUnit Meter
  • LengthUnitOfMeasure
  • subclassOf UnitOfMeasure
  • unitDimension LengthDimension
  • Meter
  • instanceOf LengthUnitOfMeasure
  • Kilometer
  • instanceOf LengthUnitOfMeasure

  • If q is a physical quantity on the Length
    dimension, then the magnitude of q in Kilometers
    is the magnitude of q in meters divided by 1000.
  • (forall ((q PhysicalQuantity))
  • (implies (quantityDimension q
    Length)
  • (Magnitude q
    Kilometer (/ (Magnitude q Meter) 1000))))

14
Ontologies What Are They? Where's The Research?
Richard Fikes, Chair Professor, Computer
Science Knowledge Systems Laboratory Stanford
University Mark Fox Nicola Guarino Professor,
Industrial Engineering Research
Scientist Enterprise Integration
Laboratory Institute for Systems
Science University of Toronto and Biomedical
Engineering of the Italian National Research
Council William Mark Director, Architecture
Laboratory National Semiconductor Corporation
11/5/96
15
But, What Is An Ontology?
Specification of a conceptualization
Specification of a vocabulary
Object schema
Class-subclass taxonomy
Reusable domain theory
T-box
  • The portion of a knowledge base that does not
    change during problem solving.

16
KR Language Components
  • A logical formalism
  • Syntax for wffs
  • Vocabulary of logical symbols (e.g., AND, OR,
    NOT, implies, iff)
  • Interpretation semantics for the logical symbols
  • E.g., (implies A B) is true if and only if B is
    true or A is false.
  • An ontology
  • Vocabulary of non-logical symbols
  • Relations, functions, constants
  • Definitions of non-logical symbols
  • ???
  • A proof theory
  • Specification of the reasoning steps that are
    logically sound
  • E.g., From (implies S1 S2) and S1, conclude
    S2.

17
Ontologies in Representation Languages
  • KIF (Knowledge Interchange Format)
  • Logical formalism
  • ASCII S-expression syntax for WFFs
  • First-order logic semantics
  • Ontologies
  • Numbers, lists, sets,
  • OKBC (Open Knowledge Base Connectivity)
  • KIF plus a frame language ontology
  • Subclass-Of, Instance-Of , Value-Type,
    Slot-Cardinality,
  • OWL (Ontology Web Language)
  • RDF-S plus a description logic ontology
  • subclassOf, inverseOf, TransitiveProperty,
    Restriction,

18
Classical Definitions Are Not Enough
  • Definitions provide equivalent expressions
  • (forall (x1 xn) (iff (R x1 xn)
    ??x1,,xn)
  • E.g., (forall (x) (iff (bachelor x)
  • (and
    (man x) (not (married x))))
  • Defined symbols can be eliminated by replacement
  • Defined symbols are non-primitive symbols
  • KB is then expressed in terms of undefined
    symbols
  • Undefined symbols are primitive symbols
  • Undefined symbols are given meaning by axioms
  • E.g., (forall (x y) (not (and (on x y)
    (on y x)))
  • Thus, ontologies must have both definitions and
    axioms

19
Object-Oriented Languages Too Restrictive
  • Frames and description logics are popular
    ontology languages
  • They support definitional axioms of the form
  • (forall ((x R)) (and (P x) )) subclass
  • (forall ((x R) y) (and (implies (S y x)
    ?P y)) ) value type
  • (forall ((x R)) (and (exists (y)???S y
    x)) ) slot cardinality
  • They do not support
  • N-ary relations and functions
  • Standard properties of relations and functions
  • E.g., transitive, symmetric
  • Partial sufficient conditions
  • E.g., (forall (x) (implies (gt x 0) (R x))

20
What Axioms Can Be In An Ontology?
  • No apparent distinction between
  • Definitional axioms and
  • Contingent facts
  • No rationale for excluding any axiom that is
  • Not a tautology
  • Satisfied by the intended interpretation in the
    conceptualization being represented

21
KR Language Components
  • A knowledge representation language consists of
  • A logical formalism
  • An ontology
  • Set of non-logical symbols defined or restricted
  • Definitions of non-primitive non-logical symbols
  • Axioms restricting the interpretation of
    primitive non-logical symbols
  • A proof theory
  • Ontologies are distinguished
  • Not by their form, but
  • By the role they play in representing knowledge

22
Whats Special About Ontologies?
  • Dont change during problem solving
  • Are particularly suited for compiling into
    tools
  • Intended to support multiple tasks and methods
  • Emphasis on properties that hold in all
    situations
  • Emphasis on classes rather than individuals
  • Need to satisfy a community of use
  • Emphasis on collaborative development
  • Emphasis on translation to multiple logical
    formalisms

23
Magnitude of Physical Quantities
  • Function Magnitude
  • The magnitude of a physical quantity in a given
    unit of measure
  • Defining axioms
  • If (Magnitude q u m) is true, then q is a
    physical quantity, u is a unit of measure, m is a
    real number, and q and u are of the same physical
    dimension
  • (forall (q u m) (implies (Magnitude q u m)
  • (and
    (PhysicalQuantity q)

  • (UnitOfMeasure u)

  • (RealNumber m)

  • (quantityDimension q (unitDimension u)))))
  • Quantities q1 and q2 are equal if and only if
    they are of the same physical dimension and their
    magnitudes are equal with respect to a unit of
    that dimension.
  • (forall ((q1 PhysicalQuantity) (q2
    PhysicalQuantity) qd1 qd2 su)
  • (implies (and (quantityDimension
    q1 qd1)

  • (quantityDimension q2 qd2)

  • (standardUnit qd1 su))
  • (iff ( q1 q2)
  • (and ( qd1
    qd2) (Magnitude q1 su (Magnitude q2 su))))))

24
Expressivity Demands Will Continue To Grow
  • Typicality conditions need to be included in
    ontologies
  • PhoneNumber(p,n) CallFrom(c,n) Typ(c) ?
    callBy(c,p)
  • StolenPhone(n) CallFrom(c,n) ? ?Typ(c)
  • Enables reasoners to draw provisional conclusions
    by hypothesizing typicality
  • Given PhoneNumber(Ramazi,703-659-2317)
    CallFrom(c1,703-659-2317)
  • Hypothesize (i.e., assume) Typ(c1)
  • Conclude CallBy(c1,Ramazi)
  • and inform user of assumptions made
  • In general, representations of uncertainty need
    to be in our ontologies

25
Interoperable Knowledge Representation for
Intelligence Support (IKRIS)
A challenge problem project on knowledge
representation sponsored by U.S. intelligence
agencies
Technical Team Leaders
Prof. Richard Fikes Dr. Christopher
Welty Knowledge Systems, Knowledge Structures
Group Artificial Intelligence Laboratory
(KSL) T. J. Watson Research Center Stanford
University IBM Corporation
Northeast Regional Research Center Leaders
Dr. Brant Cheikes (MITRE) Dr. Mark Maybury
(MITRE)
Government Champions
Steve Cook (NSA) Jean-Michel Pomarede
(CIA) John Donelan (CIA) John Walker (NSA)
2/7/06
26
Challenge Problems for the IC
  • DTO (Disruptive Technology Office) funds
    challenge problem projects
  • Focus is on problems that require collaboration
    to solve
  • DTO recognizes knowledge representation (KR) as a
    critical technology
  • IKRIS is addressing two KR challenges
  • Enabling interoperability of KR technologies
  • Developed by multiple contractors
  • Designed to perform different tasks
  • Interoperable representations of scenarios and
    contextualized knowledge
  • To support automated analytical reasoning about
    alternative hypotheses

27
Hypothesis Modeling and Analysis
  • Tools for modeling and analyzing alternative
    hypothetical scenarios
  • Models enable automated reasoning to accelerate
    and deepen analysis
  • Consistency and plausibility checking, deductive
    question-answering, hypothesis generation,
  • Requires sophisticated knowledge representation
    technology
  • Actions, events, abnormal cases, alternatives,
    open-ended domains,

28
Interoperable KR Technology
  • No one representation language is suitable for
    all purposes
  • Technology development necessarily involves
    exploring alternatives
  • Differing tasks require differing representation
    languages
  • So, modules using differing KR languages need to
    be interoperable
  • Requires enabling modules to use each others
    knowledge
  • The IKRIS approach to achieving interoperability
  • Select and refine a standard knowledge
    interchange language
  • Called IKRIS Knowledge Language (IKL)
  • Develop translators to and from IKL
  • Each system module will then
  • Use its own KR language internally
  • Use IKL for inter-module communication
  • Translate knowledge to and from IKL as needed

29
IKRIS Organization
  • Prime Contractor MITRE, Brant Cheikes and Mark
    Maybury
  • Technical Team Leads Fikes (Stanford KSL) and
    Welty (IBM Watson)
  • Working Groups
  • Interoperability Pat Hayes, University of West
    Florida
  • Chris Menzel, Michael Witbrock, John Sowa, Bill
    Andersen, Deb McGuinness,
  • Scenarios Jerry Hobbs, Information Sciences
    Institute
  • Michael Gruninger, Drew McDermott, David Martin,
    Selmer Bringsjord,
  • Contexts Selene Makarios, Stanford KSL
  • Danny Bobrow, Valeria de Paiva, Charles Klein,
    David Israel,
  • Evaluation Dave Thurman, Battelle Memorial
    Institute
  • Technology Transfer Paula Cowley, Pacific
    Northwest National Laboratory
  • Translation technology and example translators
    Stanford KSL
  • Government Champions
  • Steve Cook, John Donelan, Jean-Michel Pomarede,
    John Walker

30
IKRIS Project Schedule
  • Preparation January - April, 2005
  • Kickoff Meeting April 2005
  • Established working groups and their charters
  • Developed work plan and began work in each group
  • Working groups April 2005 through April 2006
  • Producing results and planning technology
    transfer
  • Evaluation January through September 2006
  • Iterative evaluation of workshop results
  • Second face-to-face workshop April 2006
  • Finalize and coordinate results of working groups
  • Finalize plans for technology transition and for
    completing evaluation
  • Technology transition April through September
    2006
  • Initiation of planned transition activities

31
FOL Knowledge Interchange Languages
  • KIF (Knowledge Interchange Format)
  • ASCII Lisp-style syntax
  • No formal model theory
  • Pre-WWW/XML/Unicode
  • Included a set theory, definition language, etc.
  • Subset became de facto AI/KR standard
  • Subset developed as a proposed ISO standard
  • CL (Common Logic)
  • Based on KIF
  • Formal model theory
  • Abstract syntax
  • Web savvy
  • In final stages of becoming an ISO standard
  • IKL (IKRIS Knowledge Language)
  • Variant of CL
  • Extensions include propositions

32
CLIF Syntax for IKL
  • Designed for use on an open network
  • Names are made globally unique by
  • Including a URI as part of the name
  • Using the XML namespace conventions to abbreviate
    names
  • Universal quantifiers can be restricted by a
    unary predicate
  • E.g., All humans own a car.
  • (forall ((x isHuman)) (exists ((y Car)) (Owns x
    y)))
  • Existential quantifiers can be restricted by a
    number
  • E.g., All humans have as parts 10 toes.
  • (forall ((x isHuman))
  • (exists 10 (y) (and (Toe y) (PartOf y
    x))))

33
Examples of CL/IKL Expressivity
  • Relations and functions are in the universe of
    discourse
  • E.g., (owlinverseOf parent child)
  • A relation or function can be represented by a
    term
  • E.g., (forall (x y r) (iff (r x y)
    ((owlinverseOf r) y x)))
  • Given the above axiom,
  • ((owlinverseOf Married) Uther Ygrain)
  • is equivalent to
  • (Married Ygrain Uther)
  • A unary relation could be allowed to take
    multiple arguments
  • So that, e.g.,
  • (isHuman Fred Bill Mary)
  • abbreviates
  • (and (isHuman Fred) (isHuman Bill) (isHuman Mary))

34
Examples of CL/IKL Expressivity
  • A unary relation could be allowed to take
    multiple arguments
  • So that, e.g., (isHuman Fred Bill Mary)
  • abbreviates
  • (and (isHuman Fred) (isHuman Bill) (isHuman
    Mary))
  • We might call such relations Predicative
  • E.g., assert (Predicative isHuman)
  • What it means to be Predicative could be
    axiomatized as follows
  • (forall (r) (if (Predicative r)
  • (forall (x y z) (iff (r x y z)
  • (and (r x)
    (r y) (r z))))))
  • Predicative itself could be Predicative
  • (Predicative Predicative)
  • allowing such abbreviations as
  • (Predicative isHuman isAnimal isFish)

35
Examples of CL/IKL Expressivity
  • Sequence names
  • Allows a sentence to stand for an infinite number
    of sentences, each obtained by replacing each
    sequence name by a finite sequence of names
  • A sequence name is any constant beginning with
  • E.g., the general axiom for Predicative is as
    follows
  • (forall (r) (if (Predicative r)   
    (forall (x y ...) (iff (r x y ...)
  • (and (r x)
    (r y ...))))))
  • Function list and relation isList are
    predefined as follows
  • (forall (...) (isList (list ...)))

36
Extending CL to Include Propositions
  • Goal Support representation of contextualized
    and modal knowledge
  • Achieved by making propositions first-class
    entities in IKL
  • Refer to them by name, quantify over them, have
    relations between them and other entities, define
    functions that apply to them,
  • The operator that is used to denote propositions
  • that takes a sentence as an argument
  • E.g., (that (Married Ygrain Uther))
  • A that expression denotes the proposition
    expressed by its argument
  • E.g., (that (Married Ygrain Uther))
  • is a name, denoting the proposition that Ygarin
    and Uther are married
  • Issue When are two propositions equivalent?
  • E.g., does (and a b) name the same proposition as
    (and b a)?
  • IKL provides a propositional equivalence
    relation, but does not build it in

37
Interoperable Scenarios
  • IKRIS is addressing two KR challenges
  • Enabling interoperability of KR technologies
  • Developed by multiple contractors
  • Designed to perform different tasks
  • Interoperable representations of scenarios and
    contextualized knowledge
  • To support automated analytical reasoning about
    alternative hypotheses
  • Developing an interoperable representation for
    processes
  • Includes
  • Time points, time intervals, durations, clock
    time, and calendar dates
  • Events and relationships that overlap in time and
    interact
  • Process constructs, preconditions, states, etc.

38
An Interlingua for Processes
39
The Scenarios Ontology
  • The Scenarios Working Group is producing an IKL
    ontology
  • Inter-theory vocabulary
  • Bridging axioms to other vocabularies
  • Trigger axioms for making optional
    representational commitments
  • The inter-theory vocabulary includes
  • The OWL time ontology
  • Terminology for clock time, calendars, intervals,
    points, etc.
  • Terms such as the following to describe
    processes
  • Event
  • EventType
  • State
  • StateType
  • Eventuality
  • EventualityType
  • FluentFor
  • Subevent
  • Precondition
  • PreconditionToken
  • Effect

40
The Scenarios Ontology
  • Example bridging axioms to Cyc for Event and
    EventType
  • For every EventType x, there is a Cyc subclass
    of cycEvent that has the same instances as x
  • (forall ((x EventType)))
  • (exists (y) (and (cycgenls y cycEvent)
  • (forall (e) (iff
    (cycisa e y)

  • (instanceOf e x)))))))
  • For every subclass y of CycEvent, there is an
    EventType that has the same instances as y
  • (forall (y) (if (cycgenls y cycEvent)
  • (exists (x) (and (EventType x)
  • (forall (e)
  • (iff
    (cycisa e y)

  • (instanceOf e x)))))))

41
The Scenarios Ontology
  • Example bridging axioms to Cyc for Event and
    EventType
  • For every EventType x, there is a Cyc subclass
    of cycEvent that has the same instances as x
  • For every subclass y of CycEvent, there is an
    EventType that has the same instances as y
  • In Cyc, EventTypes are classes and classes are
    individuals
  • The inter-theory is neutral on the issue
  • A commitment can be made on this issue using a
    triggering axioms
  • If the TypesAreClasses trigger is true,
    EventTypes and the subclasses of CycEvents are
    equivalent
  • (forall (x) (if (TypesAreClasses)
  • (iff (cycgenls x cycEvent)
    (EventType x))))

42
Interoperable Contextualized Knowledge
  • IKRIS is addressing two KR challenges
  • Enabling interoperability of KR technologies
  • Developed by multiple contractors
  • Designed to perform different tasks
  • Interoperable representations of scenarios and
    contextualized knowledge
  • To support automated analytical reasoning about
    alternative hypotheses

43
Contextualized Knowledge is Pervasive
  • The circumstances surrounding a specific activity
  • E.g., In this conversation, the suspect refers
    to Faris.
  • A published document
  • E.g., Based on the schedule, the Holland Queen
    will arrive in Boston sometime on April 29, and
    depart there sometime on May 1.
  • An intelligence report
  • E.g., Pakes is listed, according to a certain
    source, on the crew roster of the Holland Queen.
  • A database
  • E.g., Pakes is assumed, based on certain records,
    to not be a citizen of USA.
  • An assumption
  • E.g., Pakess presence on board the Holland Queen
    is assumed to be typical (i.e. he does not behave
    abnormally).
  • A set of beliefs
  • E.g., In the belief system of Abu Musab al
    Zarqawi, democracy is evil.

44
Interoperable Contextualized Knowledge
  • IKRIS is producing
  • A context logic with a formal model theory
  • Called IKRIS Context Logic (ICL)
  • Recommended ways of using the logic for IC
    applications
  • E.g., to represent alternative hypothetical
    scenarios
  • Methodology for translating into and out of IKL
  • Methodology for automated reasoning

45
Context Logic
  • In McCarthys context logic
  • Contexts are primitive entities
  • Propositions can be asserted with respect to a
    context
  • (ist c ?) means that proposition ? is true in
    context c
  • E.g., (ist CM (forall (x) (implies (P x) (G
    x)))) (ist C0 (P Fred))
  • How can automated reasoning be done with ist
    sentences?
  • E.g., assert ( CM C0) and derive (ist C0 (G
    Fred))
  • Contextualize constants rather than sentences
  • Constants in ist sentences are interpreted with
    respect to the context
  • E.g., Fred in (ist C0 (P Fred)) is interpreted
    with respect to C0
  • Replace each constant with a function of the
    context and the constant
  • E.g., (forall (x) (implies (P (iso CM x)) (G
    (iso CM x))))
  • (P (iso C0 Fred))
  • Use a first-order reasoner to make deductions

46
KANIs Hypothesis Graph
S9 The event is at Select Gourmet Foods.
N3
New hypothesis added by the analyst
47
Conflict Detected by KANI
48
Tools for Helping Resolve Inconsistencies
Event will not occur on April 30
Pakes is not a participant
Event is not a face-to-face meeting
Event is not in Atlanta
Pakes is not in Boston on April 30
49
Evaluation and Tech Transfer
  • Evaluation
  • Goals
  • Demonstrate the practical usability of results on
    IC-relevant problems
  • Provide functionality goals, scoping, and
    feedback for results
  • Evaluation will be informal using sample IC tasks
  • Tests will include
  • Round trip translations into and out of IKL
  • Inter-system knowledge exchange using IKL.
  • Tech Transfer
  • Goal Transition results into DTO programs and
    the IC at large
  • Producing showcase presentations of results for
    transition audiences
  • Being advised and facilitated by our government
    champions and MITRE

50
IKRIS Summary
  • IKRIS is enabling progress to be made on
    significant KRR problems
  • We are addressing two KR challenges relevant to
    the IC
  • Enabling interoperability of KR technologies
  • Developed by multiple contractors
  • Designed to perform different tasks
  • Interoperable representations of scenarios and
    contextualized knowledge
  • To support automated analytical reasoning about
    alternative hypotheses
  • Initial versions of the technical results have
    been completed
  • For more information, check out the IKRIS Web
    site
  • http//nrrc.mitre.org/NRRC/ikris.htm

51
Biggest Challenge Translators
...
Language 1
Language 2
Language n
IKL
  • Translating into a less expressive language is
    necessarily incomplete
  • Translating into the ontology of the target
    language can be arbitrarily difficult
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