Distributed Ontological Reasoning

1
Distributed Ontological Reasoning
International Doctorate School in Information and
Communication Technologies DIT - University of
Trento
PhD Dissertation Presentation
Andrei Tamilin

• Advisor
• Dr. Luciano Serafini, ITC-irst

1500 Thursday, February 1, 2007
2
Outline

• Part I Preliminaries
• Context, Problem, State of the Art, Thesis
  Approach
• Part II Theory
• Distributed Description Logics Framework
• Part III Algorithms
• Distributed Tableaux Algorithms, DRAGO Reasoner
• Part IV Applications
• Modular Ontology Representation and Reasoning
• Semantic Mapping Analysis Diagnosis and
  Repairing
• Semantic Mapping Analysis Entailment and
  Minimality
• PART V Conclusions
• Results, Future Directions

3
Part I Preliminaries
4
Semantic Web Context the Story so far

• 1992 world wide web (WWW) by Tim Berners-Lee
• Continuously grows
• Marked up for human consumption only
• Difficult to delegate processing to machines
• 2001 - the semantic web (SW), by Tim Berners-Lee,
  James Hendler and Ora Lassila
• Enrich the content with semantic metadata
• Common understanding of metadata via description
  of tags in a shared ontology
• Interoperability

5
Semantic Web Context the Story so far cont.

• 2003 SW is possible
• Representational languages RDF, RDFS, DAML, OIL,
  DAML-OIL, OWL
• Theory Description Logics (DL)
• Effective reasoning algorithms Tableau reasoning
• Practical inference systems FaCT, RACER, Pellet,
  
• Management tools plenty
• 2003 SW can work
• Ready to be applied to range of practical
  scenarios, when a single ontology is kept in mind

6
Problem Ontology Multiplicity

• SW Reality
• Everyone has own ontology
• Ontologies are heterogeneous
• Challenge
• How to interoperate?
• Solution
• Semantic mappings
• Reasoning support

7
SoA approach I Global Reasoning

• Construct an integrated global ontology for
  reasoning with available DL tools
• Benefits
• Stable theory and
• tools support from DL
• Drawbacks
• (i) unlikely to scale
• (ii) losing language and reasoning specificity
• (iii) losing privacy and autonomy of ontological
  knowledge

8
SoA approach II Distributed Query Answering

• Querying P2p network of local ontologies by
  applying query rewriting techniques
• Benefits
• Really distributed practical implementations
• Drawbacks
• (i) Not really full-fledged reasoning
• (ii) Difficult to evaluate soundness and
  completeness of algorithms

9
Thesis Approach Distributed Reasoning

• Logical reasoning through a combination, via
  mappings, of distributed local reasoners
• Benefits
• (i) scalable
• (ii) respects language specificity
• (iii) supports information hiding
• Revisited thesis problem
• Enable a distributed reasoning for multiple
  ontologies coupled by semantic mappings

10
Addressed Research Questions

• How do construct a logical theory to adequatly
  represent ontologies and mappings?
• How semantic mappings affect reasoning with
  multiple onotlogies?
• How to correctly and completely formalize the
  affection?
• How to construct and implement truly distributed
  reasoning procedure aware of mapping effects?
• How to demonstrate the feasibility of the theory
  and reasoning procedure?
• Requirement
• Compatibility with the current ontology
  technology

11
Thesis Contributions

• Elaboration of Distributed Description Logics
  framework (DDL)
• Extends DL
• Sound and complete characterization of reasoning
  in DDL in terms of operator
• Truly distributed tableaux decision algorithm
• Extends standard DL tableau
• Distributed prototype reasoner DRAGO
• Extends standard DL reasoner Pellet
• Evaluation of feasibility and adequateness
  through several semantic web working scenarios

12
Check Point

• What we have?
• Step forward
• How to logically formalize the setting of
  multiple ontologies interrelated by semantic
  mappings? (Part II - Theory)

13
Intuitions and Design Rationale
Theory desiderata

• multiple local representational languages
• local heterogeneous domains
• local semantics
• relations between objects of heterogeneous local
  domains
• subjectivity and directionality of mapping

14
DDL in 3 Passages

• Captures the case of multiple ontologies pairwise
  linked by directional semantic mappings
• Local ontologies correspond to DL knowledge bases
• Mappings correspond to bridge rules and
  individual correspondences

15
DDL Syntax

• A family of knowledge bases Kii?I, Ki in DLi

16
Example 1
O1
O2
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DDL Syntax cont.

• A family of description logics DLii?I
• A bridge rule from i to j is an expression of the
  form
• where X and Y are concepts of i-th and j-th
  onto

• An individual correspondence from i to j is an
  expression of the form
• where x and y are individuals of i-th and j-th
  onto

18
Example 2
O1
O2
19
DDL Syntax cont.

• A distributed knowledge base is a triple
• DKB ?Kii?I, Biji?j?I, Ciji?j?I?

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DDL Semantics
Each local ontology Ki is locally interpreted on
a local interpretation domain
Components

• family of local interpretations
• K1, K2, K3, K4, K5, K6, K7
• I1, I2, I3, I4, I5, I6, I7
• family of domain relations rij from i to j
• rij? ?Ii x ?Ij

A distributed interpretation (DI) of a DKB
?Iii?I, riji?j?I?
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DDL Semantics with Holes
Problem if some of local ontologies are
inconsistent (no classical interpretation) then
automatically distributed interpretation does not
exist and thus the whole system is
inconsistent Solution introduce a special
interpretation, called a hole (H), which provides
a model even for classically inconsistent local
ontologies Distributed interpretation revisited
consists of family of local (classical DL)
interpretations or holes
22
Satisfiability of Distributed Knowledge Base

• DI?Iii?I,riji?j?I? satisfies
  DKB?Kii?I,Biji?j?I,Ciji?j?I?
• DI DKB
• If
• all Ki are satisfied (according to standard DLs
  approach), i.e., Ii Ki
• all bridge rules Bij and
• all individual correspondences Cij are
  satisfied

23
Into-bridge rule Satisfiability
DI
rij(XIi) ? YIj
iX jY if
?Ii
?Ij
rij(XIi)
rij
XIi
YIj
24
Onto-bridge rule Satisfiability
DI
rij(XIi) ? YIj
iX jY if
?Ii
?Ij
rij
YIj
rij(XIi)
XIi
25
Individual correspondence Satisfiability
yIj?rij(xIi)
DI
ix jy if
?Ii
?Ij
xIi
rij
yIj
rij(xIi)
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Reasoning in DDL
Inference tasks are the same as in classical DL.
Difference not only local knowledge bases but
also mappings should be satisfied

• Satisfiability iX is satisfiable wrt DKB
• if there exist a DI such that DI DKB and
  XIi?0

• Subsumption iX is subsumed by iY wrt DKB, iC
  D,
• if for every DI of DKB and XIi ? YIj

• Instantiation ia is instance of iC wrt DKB,
  iC(a),
• if there exist a DI such that DI DKB and
  aIi?CIi

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Check Point

• What we have?
• DDL logic for representation of ontologies and
  semantic mappings
• Reasoning in DDL - depends not only on local
  ontologies, but also on mappings
• Step forward
• What are the possible effects of mappings on
  reasoning?

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1) Subsumption Propagation
DKB ??T1, Ø?, ?T2, Ø ?, B12, Ø ?
T1
T2
B
H
isSubsumed
A
G
?
GI2 ? r12(AI1)
r12(BI1) ? HI2
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2) Assertion propagation
DKB ??T1,A1?, ?T2,A2?, B12,C12?
T1
T2
B
H
isInstanceOf
isInstanceOf
A1
A2
b
h
hI2 r12(bI1)
r12(BI1) ? HI2
?
30
Effects of Mappings

• Knowledge propagation
• Mappings from a source ontology i to a target
  ontology j constitute a semantic channel from i
  to j which allows ontology j to access and import
  knowledge from ontology i in form of subsumption
  axioms and concept membership assertions
• Directionality
• Mappings from i to j support knowledge
  propagation only in such a direction from i
  towards j

31
Check Point

• What we have?
• DDL logic for representation of ontologies and
  semantic mappings
• Reasoning in DDL - depends not only on local
  ontologies, but also on mappings
• Mappings result in propagating knowledge across
  local ontologies
• Step forward
• How to correctly and completely characterize
  effects of mappings? Are these the only effects
  possible? (Part III - Algorithms)

32
Characterizing Subsumption Propagation
Given DKB12 ??T1, Ø?, ?T2, Ø ?, B12, Ø
? Bridge operator B12T1?T2 adsorbs
essentially all inferences (subsumption axioms)
possible from interactions in B12
Theorem (soundness and completeness)
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Characterizing Assertion Propagation
Given DKB12 ?K1, K2, B12, C12? Individual
correspondence operator C12(A1) encapsulates
propagated assertion axioms Combined propagation
operator BC12(K1) ?B12, C12?
Theorem (Soundness and Completeness)
34
Check Point

• What we have?
• DDL logic for representation of ontologies and
  semantic mappings
• Reasoning in DDL - depends not only on local
  ontologies, but also on mappings
• Mappings result in propagating knowledge across
  local ontologies
• Propagation can be correctly and completely
  captured by propagation operators
• Step forward
• How to define the (distributed) decision
  procedure?

35
Desiderata
D
D
Tab1
Tab7
D
Tab2
D
D
Tab3
Tab6
D
D
Tab4
Tab5
DTabi Tabi computation of propagation
operators
36
Distributed SHIQ-T-box Tableaux

• DTabj
• SHIQ-tableau expansion rules
• bridge expansion rule
• Intuition
• Compute a backward version of bridge operator

37
Intuitive Run
Is jD is satisfiable wrt DKB?
DTabj(D)
x L(x) D
Bij
Standard tableau expansion rules
y
L(y) G,

Clash
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Algorithms Properties

• Theorem (Termination) For any distributed T-box
  and for any SHIQ concept X, DTabj(X) terminates
  (in a cyclical knowledge bases a blocking is
  used satisfiability request never generates
  itself).
• Theorem (Soundness and completeness) jX is
  satisfiable in a distributed T-box if and only if
  DTabj(X) can generate a complete and clash-free
  completion tree.
• Generalization (Application to parallelization)
  Each request to foreign tableaux procedures is
  independent from others and thus can run
  independently in parallel

39
Distributed SHIQ-A-box tabelaux

• DTabj
• SHIQ-tableau expansion rules
• bridge expansion rule
• Individual correspondence expansion rule
• Intuition backward versions of bridge and
  individual correspondence operators

40
Check Point

• What we have?
• DDL logic for representation of ontologies and
  semantic mappings
• Reasoning in DDL - depends not only on local
  ontologies, but also on mappings
• Mappings result in propagating knowledge across
  local ontologies
• Propagation can be correctly and completely
  captured by propagation operators
• Inference procedure can be implemented on top of
  standard DL tableau
• Step forward
• Implementation

41
DRAGO Vision
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DRAGO Architecture
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Implementation

• OWL ontologies
• C-OWL semantic mappings
• Distributed Reasoner is an extension to open
  source OWL Reasoner Pellet

http//sra.itc.it/projects/drago
44
Check Point

• What we have?
• DDL logic for representation of ontologies and
  semantic mappings
• Reasoning in DDL - depends not only on local
  ontologies, but also on mappings
• Mappings result in propagating knowledge across
  local ontologies
• Propagation can be correctly and completely
  captured by propagation operators
• Inference procedure can be implemented on top of
  standard DL tableau
• DRAGO - implementation of DDL inference engine
• Step forward
• Applications (Part IV)

45
1) Modular Ontology

• Addressed the problem of enabling modular
  ontology construction from existing ontological
  modules
• Basic idea
• view available ontologies as modules
• use bridge rules and individual correspondences
  as means for accessing and importing knowledge
  from ontological modules
• use distributed reasoning for composing modular
  ontology

46
Modular Ontology Example
O0
47
Modular Ontology Evaluation
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Modular Ontology Evaluation

• Does it scales?
• What about performance?

49
2) Mapping Debugging

• Addressed the problem of errors in semantic
  mappings and developed automatic method for
  diagnosis and repairing errors
• Basic idea
• encode semantic mappings in DDL and further see
  the affect of mappings on ontologies they connect
• detect changes in subsumption hierarchies of
  mapped ontologies using distributed reasoning
• treat changes as symptoms caused by incorrect
  mappings
• Claim
• correct mapping should not cause changes in
  mapped ontologies

50
2) Mapping Debugging Example
O1
O2
? r12(Regular_PaperI1)
RegularI2
PaperI2 r12(PaperI1)
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2) Mapping Debugging Evaluation

• Applied to sets of semantic mappings generated by
  real matching systems
• Evaluation demonstrated a high precision of
  repairing (70-100), although keeping the space
  for improving recall (20-50)
• DDL adequately captures semantic mappings

52
3) Mapping Minimization

• Addressed the problem of filtering redundant
  (entailed) parts of mappings to construct compact
  (minimal) representation
• Basic idea
• encode semantic mappings in DDL
• similarly to subsumption and entailment in DL
  define entailment of bridge rules
• one by one pick a bridge rule and if remaining
  mapping entails it remove it
• proceed until all rules verified.

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3) Mapping Minimization Example of Entailment
O1
O2
r12(ReviewerI1) ? PersonI2
r12(External_ReviewerI1) ?
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3) Evaluation To minimize or not to minimize?
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Final Check Point

• What we have?
• DDL logic for representation of ontologies and
  semantic mappings
• Reasoning in DDL - depends not only on local
  ontologies, but also on mappings
• Mappings result in propagating knowledge across
  local ontologies
• Propagation can be correctly and completely
  captured by propagation operators
• Inference procedure can be implemented on top of
  standard DL tableau
• DRAGO - implementation of DDL inference engine
• DDL and DRAGO applied to several working scenarios

56
Future Works

• Extensions, optimizations, applications
• support of heterogeneous mappings
• role-to-concept mappings
• concept-to-individual
• looking for optimizations in distributed tableaux
  algorithm and in its DRAGO implementation
• improving the results of already started
  applications

57
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