????????%20Logical%20Foundation%20of%20the%20Semantic%20Web

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???????? Logical Foundation of the Semantic Web
?? ??? Zhisheng Huang Vrije University
Amsterdam, The Netherlands huang_at_cs.vu.nl ?? ??
Wei Hu Southeast University whu_at_seu.edu.cn
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?????Schedule
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(No Transcript)
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??5???????(I)Lecture 5 Ontology Management
and Reasoning (I)

• ???????(Reasoning and Management of Ontologies)
• ????????(Reasoning with Inconsistent Ontologies)
• ???????????(Reasoning with Multi-version
  Ontologies)
• ?????????(Ontology Revision and Ontology
  Evolution)
• ????? (Conclusion and Discussion)

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Ontology Reasoning and Inconsistency Management
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?????????SEKT Project

• Semantically Enabled Knowledge Technologies
  (SEKT)
• A European research and development project
  launched under the EU Sixth Framework Programme.
• .

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Duration and Partners

• Three year project January 2004 December 2006.
• 13 partners
• ?? BT(????), Empolis GmbH, iSOCO(Spain), Kea-pro
  GmbH, Ontoprise, Sirma AI EOOD(Bulgaria),
  (SIEMENS?????)
• ?? Jozef Stefan Institute(Slovenia), Univ.
  Karlsruhe(Germany), Univ. Sheffield(U.K.), Univ.
  Innsbruck(O), Univ. Autonoma Barcelona(Spain),
  Vrije Universteit Amsterdam(The Netherlands)

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Case Studies

• Legal Domain (iSOCO)
• Telecom Domain (BT)
• Siemens

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SEKT Activities and Relationships
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Core Tasks WP3
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SEKT WP3 Architecture
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Inconsistency and the Semantic Web

• The Semantic Web is characterized by
• scalability,
• distribution, and
• multi-authorship
• All these may introduce inconsistencies.

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Ontologies will be inconsistent

• Because of
• mistreatment of defaults
• polysemy
• migration from another formalism
• integration of multiple sources
• (Semantic Web as a wake-up call for KR)

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Example Inconsistency by mistreatment of
default rules

• MadCow Ontology
• Cow ? Vegetarian
• MadCow ? Cow
• MadCow ? ? Eat.BrainofSheep
• Sheep ? Animal
• Vegetarian ? ? Eat. ? (Animal? PartofAnimal)
• Brain ? PartofAnimal
• ......
• theMadCow ?MadCow
• ...

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Example Inconsistency through imigration from
other formalism

• DICE Ontology
• Brain ? CentralNervousSystem
• Brain ? BodyPart
• CentralNervousSystem ? NervousSystem
• BodyPart ? ?NervousSystem

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Inconsistency and Explosion

• The classical entailment is explosive P, P
  Q Any formula is a logical  consequence of a
  contradiction.
• The conclusions derived from an inconsistent
  ontology using the standard reasoning may be
  completely meaningless

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Why DL reasoning cannot escape the explosion

• The derivation checking is usually achieved by
  the satisfiability checking.
• ? ? ? ? ?? is not satisfiable.
• Tableau algorithms are approaches based on the
  satisfiability checking
• ? is inconsistent gt ? is not satisfiable gt ?
  ?? is not satisfiable.

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Two main approaches to deal with inconsistency

• Inconsistency Diagnosis and Repair
• Ontology Diagnosis(Schlobach and Cornet 2003)
• Reasoning with Inconsistency
• Paraconsistent logics
• Limited inference (Levesque 1989)
• Approximate reasoning(Schaerf and Cadoli 1995)
• Resource-bounded inferences(Marquis et al.2003)
• Belief revision on relevance (Chopra et al. 2000)

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What an inconsistency reasoner is expected

• Given an inconsistent ontology, return meaningful
  answers to queries.
• General solution Use non-standard reasoning to
  deal with inconsistency
• ? ? the standard inference relations
• ? ?? nonstandard inference relations

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Reasoning with inconsistent ontologies Main Idea

• Starting from the query,
• select consistent sub-theory by using a
  relevance-based selection function.
• apply standard reasoning on the selected
  sub-theory to find meaningful answers.
• If it cannot give a satisfying answer, the
  selection function would relax the relevance
  degree to extend consistent sub-theory for
  further reasoning.

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New formal notions are needed

• New notions
• Accepted
• Rejected
• Overdetermined
• Undetermined
• Soundness (only classically justified results)
• Meaningfulness (sound never overdetermined)sou
  ndness

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Some Formal Definitions

• Soundness ? ?? gt???? (? consistent and
  ??).
• Meaningfulness sound and consistent (? ?? gt ?
  ?).
• Local Completeness w.r.t a consistent ? ??
  (?? gt ? ??).
• Maximality locally complete w.r.t a maximal
  consistent set ?.
• Local Soundness w.r.t.a consistent set ? ? ??
  gt ??).

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Selection Functions

• Given an ontology T and a query ?, a selection
  function s(T,?,k)returns a subset of the
  ontology at each step kgt0.

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General framework

• Use selection function s(T,?,k),with s(T,?,k) ?
  s(T,?,k1)
• Start with k0 s(T,?,0) ? or s(T,?,0) ??
  ?
• Increase k, untils(T,?,k) ? or s(T,?,k) ??
• Abort when
• undetermined at maximal k
• overdetermined at some k

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Inconsistency Reasoning Processing Linear
Extension
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Proposition Linear Extension

• Never over-determined
• May undetermined
• Always sound
• Always meaningful
• Always locally complete
• May not maximal
• Always locally sound

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Direct Relevance and K Relevance

• Direct relevance (0-relevance).
• there is a common name in two formulas C(?) ?
  C(?)?? ? R(?) ? R(?)?? ? I(?)? I(?)??.
• K-relevance there exist formulas ?0, ?1,, ?k
  such that ? and ?0, ?0 and ?1 , , ?k and
  ? are directly relevant.

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Relevance-based Selection Functions

• s(T,?,0)?
• s(T,?,1) ?? T ? is directly relevant to ?.
• s(T,?,k) ?? T ? is directly relevant to
  s(T,?,k-1).

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PION Prototype
PION Processing Inconsistent ONtologies http//wa
sp.cs.vu.nl/sekt/pion
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An Extended DIG Description Logic Interface for
Prolog (XDIG)

• A logic programming infrastructure for the
  Semantic Web
• Similar to SOAP
• Application independent, platform independent
• Support for DIG clients and DIG servers.

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XDIG

• As a DIG client, the Prolog programs can call any
  external DL reasoner which supports the DIG DL
  interface.
• As a DIG server, the Prolog programs can serve as
  a DL reasoner, which can be used to support
  additional reasoning processing, like
  inconsistency reasoning multi-version reasoning,
  and inconsistency diagnosis and repair.

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XDIG package

• The XDIG package and the source code are now
  available for public download at the website
  http//wasp.cs.vu.nl/sekt/dig/
• In the package, we offer five examples how XDIG
  can be used to develop extended DL reasoners.

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Answer Evaluation

• Intended Answer (IA) PION answer Intuitive
  Answer
• Cautious Answer (CA) PION answer is
  undetermined, but intuitive answer is
  accepted or rejected.
• Reckless Answer (RA) PION answer is accepted
  or rejected, but intuitive answer is
  undetermined.
• Counter Intuitive Answer (CIA) PION answer is
  accepted but intuitive answer is rejected,
  or vice verse.

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Preliminary Tests with Syntactic-relevance
Selection Function
Ontology Queries IA CA RA CIA IA () ICR ()
Bird 50 50 0 0 0 100 100
Brain (DICE) 42 36 4 2 0 85.7 100
MarriedWoman 50 48 0 2 0 96 100
MadCow 254 236 16 0 2 92.9 99
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Observation

• Intended answers include many undetermined
  answers.
• Some counter-intuitive answers
• Reasonably good performance

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Intensive Tests on PION

• Evaluation and test on PION with several
  realistic ontologies
• Communication Ontology
• Transportation Ontology
• MadCow Ontology
• Each ontology has been tested by thousands of
  queries with different selection functions.

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Summary

• we proposed a general framework for reasoning
  with inconsistent ontologies
• based on selecting ever increasing consistent
  subsets
• choice of selection function is crucial
• query-based selection functions are flexible to
  find intended answers
• simple syntactic selection works surprisingly
  well

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Extension

• Semantic Relevance Based Selection Functions
• K-extension
• Variants of over-determined processing
  strategies
• Integrating with the diagnosis approach

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Using Semantic Distances for Reasoning with
Inconsistent Ontologies

• Google distances are used to develop semantic
  relevance functions to reason with inconsistent
  ontologies.
• Assumption two concepts appear more frequently
  in the same web page, they are semantically more
  similar (relevant).

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Google Distances (Cilibrasi and Vitanyi 2004)

• Google distance is measured in terms of the
  co-occurrence of two search items in the Web by
  Google search engine.
• Normalized Google Distance (NGD) is introduced to
  measure the similarity/light-weight semantic
  relevance
• NGD(x,y) (maxlog f(x), log f(y)-log
  f(x,y))/(log M-minlog f(x),log f(y)
• where
• f(x) is the number of Google hits for x
• f(x,y) is the number of Google hits for the
  tuple of search items x and y
• M is the number of web pages indexed by Google.

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Semantic Distances

• Define semantic distances (SD) between two
  formulas in terms of semantic distances between
  two concepts/roles/individuals (NGD)

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Postulates for Semantic Distances
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Semantic Distances
Semantic distance are measured by the ratio of
the summed distance of the difference between two
formulae to the maximal distance between two
formulae.
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Proposition

• The semantic distance SD satisfies the properties
  Range, Reflexivity, Symmetry, Maximum Distance,
  and Intermediate Values.

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Example MadCow
NGD(MadCow, Grass)0.7229 NGD(MadCow,
Sheep)0.6120
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Implementation PION
PION Processing Inconsistent ONtologies http//wa
sp.cs.vu.nl/sekt/pion
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Answer Evaluation

• Intended Answer (IA) Query answer Intuitive
  Answer
• Cautious Answer (CA) Query answer is
  undetermined, but Intutitve answer is
  accepted or rejected.
• Reckless Answer (RA) Query answer is accepted
  or rejected, but Intutive answer is
  undetermined.
• Counter Intuitive Answer (CIA) Query answer is
  accepted but Intuitive answer is rejected,
  or vice versa.

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Syntactic approach vs. Semantic approach quality
of query answers
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Syntactic approach vs. Semantic approach Time
Performance
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Summary

• The run-time of the semantic approach is much
  better than the syntactic approach, while the
  quality remains comparable.
• The semantic approach can be parameterised so as
  to stepwise further improve the run-time with
  only a very small drop in quality.

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Summary (cont.)

• The semantic approach for reasoning with
  inconsistent ontologies trade-off computational
  cost for inferential completeness, and provide
  attractive scalability.

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Multi-versioning Why

• Change Recovery allow the possibilities for the
  developers to withdraw or adjust the changes to
  avoid unintended impacts.
• Compatibility Ontology users may prefer an
  earlier version with less resource requirement to
  a newer version with higher resource requirement.

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The Idea of Versioning

• Version Spaces
• Models resulting from changes are stored
  separately
• Models and change operations form a graphcalled
  Version Space
• Data is accessed through the right version

v4
v2
v5
v3
v1
v6
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Managing Version Spaces

• Idea Enable Administrator to ask questions about
  the version space
• Combine Reasoning
• Ontologies DL reasoner (RACER)
• Version Space Modal Logic
• Principle
• Each Ontology is a possible world
• Truth of statements in a state is determine by
  the DL reasoner

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Simplifying Assumptions

• Linear Time Temporal Logic
• Linear Version Space
• Operators
• Conjunction, Negation, PreviousVersion,
  AllPriorVersions
• Pre-defined Statement predicates
• Child-of, parent-of,
• Any other RACER function..

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Version Space

• Version space A version space S over an ontology
  set Os is a set of ontology pairs, namely, S ? Os
  Os.
• Linear version space S lto1, o2gt, lto2, o3gt,
  , lton-1, ongt such that oi ?oj for i? j.
• alternatively, we write
• S(o1, o2, , on)
• Linear ordering o lt o iff o occurs prior to
  o in the sequence S.

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Linear Time Logic LTLm

• Operators
• Boolean operators negation, conjunction, etc.
• Temporal operators (Backlooking operators)
• Prev? ? holds in the previous version
• P? ? holds in a prior version(Sometimes in the
  past)
• H? ? holds in all prior versions (Always in
  the past)
• ?S? ? always holds in the prior versions
  since ? holds in a prior version

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Linear Time Logic LTLm(F)

• Operators
• Temporal operators (forward-looking operators)
• Next ? ? holds in the next version
• F ? ? holds in a sequel version(Sometimes in
  the future)
• G? ? holds in all sequel versions (Always in
  the future)
• ?U ? ? always holds in all of the sequel
  versions until ? holds.

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Semantics
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Semantics

• S, o Prev ? iff lto, ogt ?S and S, o ?.
• S, o H ? iff ?olt o and S, o ?.
• S, o ? S ? iff ?o1, , on (lto1, o2gt, ,lton-1,
  ongt ? S and ono and S, oi ? and S, o1 ?

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Formal Properties

• H ? -gt P ?.
• H ? -gt Prev ?.
• Prev ? -gt P ?.
• Prev P ? -gt P ?.
• P P ? -gt P ?.
• H H ? -gt H ?.
• Prev Prev ? -gt P ?.

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Reasoning Queries

• ? ? holds in the current version
• ? ?? Prev ? ? holds in the current version but
  no in the previous version.
• ?? ?P? incompactible (with respect to ?).
• ? ? H?? ? holds only in the current version,
  it never holds before.

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Reasoning Query stable change

• Once ? is changed, it is never changed again.

?? S (H?).
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Change Accounting Only Twice

• ? is changed only twice.

?? S Prev(? S H??).
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Change Accounting Only N times

• Change(1, ?) df ?? S H?.
• Change(n, ?) df ?? S Prev(Change(n-1,??)),
• for n 2, 4, 6,,
• Change(n, ?) df ? S Prev(Change(n-1,?)),
• for n 3, 5, 7,,

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Reasoning Query last version I

• ? holds at the last version in which ? holds .

?? S (Prev(?? ?))
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Reasoning Query last version II

• ? holds at the last version in which ? does not
  hold before a version ? holds.

?? S (Prev(? S Prev(??? ?))).
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Retrieval Queries

• child, parent concept relation

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Relative Versioning

• Version0? ? ?. (the current version)
• Version-i? ? Prev(Version -(i-1) ?)

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Absolute Versioning

• Version(i,S)? ? Version i-n?
• where Sn

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Retrieval Query
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The MORE System

• Milestone 3.5 Software Prototype
• .
• Prototype MORE (Multi-version Ontology REasoner)
• MORE website http//wasp.cs.vu.nl/sekt/more

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The MORE System

• Functionality
• Temporal Reasoning Queries
• Ontology Comparison Queries
• Versioning Retrieval Queries
• Ontology Data format OWL and DIG
• Test Data
• BioSAIL ontologies (3 versions)
• SEKT legal case study ontologies (5 versions)

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Test Result Change Log
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Summary

• A framework of multi-version ontology reasoning
• Temporal logic approach
• Expressive power of LTLm
• Semantic differences on multi-version
  ontologies.

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Future Work

• Integrating MORE with ontology evolution (Dynamic
  logic approach).
• Hybrid logic approach for nominals
• Branching time version space.
• Merging time model (merging multiple ontologies).

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WP3.6 Inconsistency Diagnosis and Repair

• Software Prototypes
• DION Inconsistency Diagnosis and Repair
• Task Given an inconsistent ontology, locate
  possible sources of inconsistencies and offer the
  user (a knowledge engineer) to repair them.
• Prototypes DION/Mupster
• Using the pinpointing technology

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Pinpointing Technique

• MUPS Minimal unsatisfiability-preserving
  sub-TBox w.r.t. a concept
• MIPS Minimal incoherence-preserving sub-TBox
• MIPS-Core A non-empty intersection of n
  different MIPS
• Pinpoints are calculated from MIPS-Core. A
  pinpoint is a diagnosis in the sense of (Reiter
  1987)"A Theory of Diagnosis from First
  Principles.

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Applying Debugging within SeKT

• Debugging for Learning complex ontologies (UKA)
• Given natural language text
• Calculate complex (OWL) ontology
• this ontology might be inconsistent
• Strategy
• learn as many axioms as possible, and
• debug those that lead to logical contradictions

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Debugging for Learning (more)

• UKA developed methods for learning disjointness
  axioms from free-text.
• Ontology can become inconsistent
• Conceptually correct inconsistency
• Incorrectly learned axiom
• Debugging can help solve the latter
• MIPS (from learned axioms only) contains at least
  one axioms with a mistake.
• Pinpoint suggests a way of correcting

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Debugging for learning (example)

• The problems are already on a simpler level what
  is a correct disjointness statement.
• UKA tested agreement on added disjointness
  statements for PROTON.
• Even on expert level -gt inconsistencies!
• Debugging can explain!
• Let us see an example
• Even in the most expert level, there are three
  unsatisfiable concepts
• ltunsatisfiableConcept ontology"proton_100_all.owl
  " number"3"gt ltcatom name"http//proton.semantic
  web.org/2004/12/protonuReservoir"/gt ltcatom
  name"http//proton.semanticweb.org/2004/12/proton
  uHarbor"/gt ltcatom name"http//proton.semanticwe
  b.org/2004/12/protonuCanal"/gt lt/unsatisfiableCon
  ceptgt

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Debugging for Learning (ex cont)

• A minimal incoherent subterminology(MIPS)
  Facility ! WaterRegion Reservoir isa
  HydrographicStructure Reservoir isa Lake
  HydrographicStructure isa Facility Lake isa
  WaterRegion
• There are two pinpoints (i.e. possible errors)
  Facility ! WaterRegion andHydrographicStructur
  e isa Facility
• Experts have to decide which one is faulty!

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Debugging for Learning (ex cont)
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Debugging Evaluation of Prototypes

• Evaluation of MUPSter and DION showed
• Comparable runtimes
• DION more flexible, expressive and easy to adapt
• .

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DION

• Queries on MUPS/MIPS/Core/Pinpoints
• Data Format Support DIG/OWL
• Integration with RACER/KAON2
• Platform Support Windows/Linux
• Graphical User Interface DION Testbed
• Ontology Data Pre-processing more fine-grained
  debugging
• Example A ? D1 ?D2 gt A ? D1, A ? D2

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DION Testbed
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Ontology Evolution
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AGM Postulates for Belief Revision
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Postulates for Contraction
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Levi and Harper Identities
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Problems for Ontology Revisions

• Many description logics (including OWL DL) are
  not AGM-compliant
• Problem (implicit) negation and base recovery
  postulate

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Variants of Inconsistencies in SW

• Schlobach at el.(IJCAI03) Incoherence
  unsatisfiable concept in Tbox
• Huang at el. (IJCAI05) Classical sense of
  logical inconsistency
• Haase at el. (ISWC05) Example in a footnote.

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Incoherence and Inconsistency

• Unsatisfiable concept in a Tbox its
  interpretation is empty in any interpretation of
  Tbox
• Incoherent Tbox there exists unsatisfiable
  concept
• Incoherent Ontology its Tbox is incoherent
• Inconsistent Ontology there exists no models

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Example I Coherent and Inconsistent Ontology
disjoint
C1
C2
a
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Example II Incoherent and Inconsistent Ontology
disjoint
C1
C2
C3
a
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Example III Incoherent and consistent Ontology
disjoint
C1
C2
C3
b
a
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Example IV Inconsistent (and coherent?)
Ontology
disjoint
C1
C2
a
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Consistency Negation
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Coherence Negation
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Example
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New Postulates for Ontology Revision
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New Postulates for Ontology Changes
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Levi and Harper Identities
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Summary

• Framework accounts for negation, inconsistency
  and change for DL-based ontologies for management
  of dynamic ontologies.
• Proposed negations achieve the Harper identity
  and Levi identity for ontology changes
• Distinction between incoherence and inconsistency
  provides us two different approaches covering
  different needs in different application scenarios

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???PION

• ???????????Variants of extension strategies
• ???????ODP??Variants of over-determined
  processing strategies
• ??PION?????????? Integrating with the diagnosis
  approach

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Questions and Discussions