Constructive Reasoning for Semantic Wikis - PhD defense presentation

Motivation
Results
Summary
Constructive Reasoning for Semantic Wikis
Jakub Kotowski
LMU Munich
October 18, 2011
Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-log
Motivation
Results
Summary
Outline
Motivation
The KiWi Project
Addressed Topics and Contributions
Results
Conceptual Model and Structured Tags
Forward Chaining Revisited
Incremental Reason Maintenance

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Motivation
Results
Summary
The KiWi Project
Outline
Motivation
The KiWi Project
Results

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Motivation
Results
Summary
The KiWi Project
KiWi - Knowledge in a Wiki
An EU FP7 project
March 2008 - March 2011
KiWi 1.0 - semantic wiki / semantic software platform
Employs advanced semantic techniques
reasoning, semantic search, personalization, information
extraction

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Motivation
Results
Summary
The KiWi Project
Requirements on a Semantic Wiki
Social →
Emergent collaboration
Preference for free tagging rather than predened schemes
Read/write + social → work in progress, inconsistencies
Semantic + read/write → reasoning in presence of updates
Social + reasoning →
Reasoning updates have to be fast
Reasoning comprehensible
Otherwise people lose interest

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Motivation
Results
Summary
The KiWi Project
A Conceptual Model of a Semantic Wiki
[What the User Interacts With: ..., SemWiki 2009, Heraklion]
Focus on the user's point of view
Content
Annotations
Knowledge representation formalisms
Structured tags
Evaluation of structured tags

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Motivation
Results
Summary
The KiWi Project
KWRL - The KiWi Rule Language
[Social Vision of Knowledge Representation and Reasoning, SOFSEM 2010]
A rule language based upon Datalog concepts
Inconsistency-tolerant
Aware of the conceptual model of a wiki
Focused on annotations

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Motivation
Results
Summary
The KiWi Project
Materialization of Datalog programs
Extended immediate consequence operators
Useful for reason maintenance, explanation
Support graphs

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Motivation
Results
Summary
The KiWi Project
[Reasoning as Axioms Change: ..., RR2011, Galway]
[A Potpourri of Reason Maintenance Methods. Submitted for publication]
New algorithms for incremental reason maintenance
Improve upon existing database and reason maintenance
algorithms
Formally anchored in
Support graphs
Extended immediate consequence operators

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Motivation
Results
Summary
The KiWi Project
Implementation
[A Perfect Match for Reasoning, Explanation, and Reason Maintenance: ..., SemWiki 2010]
Incremental reason maintenance - KiWi 1.0
Explanation - KiWi 1.0
Interactive explanation tree rendering
Fast on demand tooltip explanations
A graph database implementation

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Motivation
Results
Summary
Outline
Motivation
The KiWi Project
Results

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Motivation
Results
Summary
Conceptual Model
[What the User Interacts With: ..., SemWiki 2009, Heraklion]
Content
Content items
Fragments
Links
Annotation
Informal: Tagging
Semi-formal:
Structured tags
Formal: RDF, OWL, ...

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Motivation
Results
Summary
Structured Tags
A semi-formal knowledge representation formalism
Users can proceed
From simple free tagging: apple orange strawberry
To complex structured tags: fruit:(apple, orange, strawberry)
Based on grouping (...,...,...) and characterization ...:...
Grouping groups similar, related tags
Characterization names groups tags
Already young children are able to group and name
Cognitive science: Gestalt psychology, Prorotype theory
Eleanor Rosch: Natural categories, 1973

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Motivation
Results
Summary
Structured Tags Evaluation
A user study, 19 participants split into two groups, 8 hours
Annotation with RDF vs Annotation with Structured tags
Focus on ease of use, understandability, expressiveness
Participants generally favoured structured tags, enjoyed using
them more, made fewer errors
Some participants created complex JSON-like structures

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Motivation
Results
Summary
Stuctured Tags - Evaluation Results
70% participants felt understood introduction to s.t. (65%
did not unterstand RDF introduction)
S.tags more intuitive (∼80% vs. ∼25%), restriction to triples
too limiting, ...
S.tags more expressive (∼80% vs. ∼30%)
∼S.tags seem better without prior knowledge of the domain
Complex s.tags are used often: ∼79% of all s.tags are complex

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Motivation
Results
Summary
Forward Chaining - Motivation
Forward chaining completes a wiki w.r.t. user-dened rules
Materialization allows users to see the current state of aairs
Explanations should be readily available
Need for incremental updates of the materialization
Forward chaining should provide additional information to help
solve the incremental reason maintenance problem

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Motivation
Results
Summary
Forward Chaining and Reason Maintenance

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Motivation
Results
Summary
Support Graphs
Inspired by data dependency networks of reason maintenance
Better capture the logical notion of a derivation (via s.g.
homomorphisms)
Provide a framework for comparison of the presented methods
Support: (r,σ) (r - rule, σ - substitution)
A support is an evidence that the head of the support is an
immediate consequence of a rule and the body of the support

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Motivation
Results
Summary
Support Graphs

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Motivation
Results
Summary
Classical Semi-Naïve Forward Chaining
TP - immediate consequence
operator
Standard Datalog set semantics
Worst case time-complexity
O(nk)

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Motivation
Results
Summary
skTP: Support Keeping Immediate Conseq. Op.
Denition
Let P be a denite range restricted program. The support keeping
immediate consequence operator skTP for P is the mapping:
skTP : P(sHBP) → P(sHBP)
skTP(F) = { s = (r,σ) ∈ sHBP | r = H ← B1,...,Bn ∈ P,
dom(σ) = var(r),body(s) ⊆ heads(F) }
where F ⊆ sHBP is a set of supports with respect to P.

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Motivation
Results
Summary
skTP Semi-Naïve Forward Chaining
Worst case time-complexity O(nk)

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Motivation
Results
Summary
scTP: Support Counting Immediate Conseq. Op.
A multiset operator: how many times is an atom derived
during classical forward chaining?
Dened on the complete lattice P(HBP) (theorem)
Lloyd's logic programming framework can thus be used
Denition
Let P be a nite denite range restricted program. The support
counting immediate consequence operator scTP for P is:
scTP: P(HBP) → P(HBP)
scTP(S) = [ Hσ ∈ HBP | ∃ s = (r,σ),
r = H ← B1,...,Bn ∈ P,
body(s) ⊆ root(S),dom(σ) = var(r) ]

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Motivation
Results
Summary
scTP Semi-Naïve Forward Chaining
Worst case time-complexity O(nk)

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Motivation
Results
Summary
scTP Example
scT0
P = /0m
scT1
P = [ a,b ]
scT2
P = [ a,b,c,c,d,d ]
scT3
P = [ a,b,c,c,d,d,e ]
scT4
P = [ a,b,c,c,d,d,e,b ]

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Motivation
Results
Summary
dcTP: Derivation Counting Immediate Conseq. Op.
A multiset operator: how many derivations are there of an
atom in the xpoint?
Tracks extended atoms: (a,D)
Dened on the complete lattice P(dHBP) (theorem)
Lloyd's logic programming framework can thus be used
Denition
Let P be a nite denite range restricted program. The derivation
counting immediate consequence operator dcTP for P is the
mapping:
dcTP(S) = [ (Hσ,D) ∈ dHBP | (∃s = (r,σ)),
dom(σ) = var(r),r = H ← B1,...,Bn ∈ P;
∀1 ≤ i ≤ n ∃Di (Biσ,Di) ∈m S;Hσ /∈ Di,
Hσ = Biσ,D = n
i=1 Di ∪{Biσ} ].

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Motivation
Results
Summary
Properties of the Extended Immediate Conseq. Ops.
Theorem
Let P be a denite Datalog program. Then scTω
P and dcTω
P are
multisets with nite multiplicities.
Theorem
Let P be a denite program. Then
HI(lfp(TP)) = HI(skTω
P ) = HI(scTω
P ) = HI(dcTω
P ) is the unique
minimal Herbrand model of P.

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Motivation
Results
Summary
The Reason Maintenance Problem
Given
P: a nite (recursive) Datalog program
D: a subset of P to remove
Tω
P : the old xpoint
Compute
Tω
PD: the new xpoint

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Motivation
Results
Summary
Related Work
Belief revision - an epistemological approach
Reason maintenance - a logical approach
Belief revision and Reason maintenance are closely related
Jon Doyle: Coherence and foundational approach
Incremental view maintenance - a database approach
DRed (derive and rederive)
Staab, Volz, Motik adapted DRed for the Semantic Web, 2005
PF (propagate and lter)

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Motivation
Results
Summary
Fixpoint Analysis
U (unsure) - atoms that depend on sth. in D
K (keep) - atoms that do not depend on sth. in D
O (otherwise supported) - depend on sth. in D and have an
alternative derivation

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Motivation
Results
Summary
Reason Maintenance Without Support Graphs
Compute U
(overestimation)
Determine K as Tω
P U
Compute Tω
PD(K)
Theorem
TPD(K)ω = Tω
PD

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Motivation
Results
Summary
Computing the Set U (overestimation)
Goal
To use the old xpoint as much as possible
Solution
A modication of semi-naive forward chaining to use the old
xpoint and D as the ∆

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Motivation
Results
Summary
Computing the Set U (overestimation)
→

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Motivation
Results
Summary
Updating Rules

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Motivation
Results
Summary
Algorithm: Incremental Reason Maintenance Without
Support Graphs

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Motivation
Results
Summary
Summary
The algorithm
stays in denite Datalog if P is a denite Datalog program
uses the original program P
DRed, PF, SVM alg. transform P into a bigger Datalog
program with negation (12 rules → 60 rules)
doesn't need a modication to handle rule updates
requires only a small modication of classical forward chaining
recomputes only the aected part of a predicate's extension
can be adapted to stratied normal programs as usual

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Motivation
Results
Summary
Support Counting Reason Maintenance
Theorem
Let a ∈x
m scTω
P . Then a ∈ O and a ∈ TPD(K) i
x |{t ∈ SU | head(t) = a}|.
An atom a is derivable in the new xpoint if not all its
supports belong to the unsure part of the old xpoint
Theorem
Let P be a denite range restricted program. Each support of an
atom g ∈ Tω
P not well-founded in G = SG(skTω
P ) depends strongly
on the node labelled g in G.
Supports of an atom in U that aren't part of any derivation
belong to the unsure part of the old xpoint

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Motivation
Results
Summary
Support Counting Reason Maintenance
In summary: a semi-naive way to compute the initial∆:
∆ := { a ∈ heads(SU) | a ∈x
m scTω
P and
x |{t ∈ SU | head(t) = a}| }

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Motivation
Results
Summary
Support Counting for Non-Recursive Datalog Programs
Non-recursive Datalog: overestimation phase not necessary
Gupta, Katiyar, Mumick, JICSLP, 1992 - a counting algorithm
for non-recursive Datalog programs
Counts derivation trees
Alternative incremental algorithm that relies on counting
supports
Counting supports is less expensive
We dene the notion of safeness (safe atoms, safe rules) that
can help determine situations in which a similar algorithm can
be applied even in the recursive Datalog case

institution-log
Motivation
Results
Summary
Derivation Counting Reason Maintenance
Simple when we have the dcTω
P xpoint
Which dependencies contain an atom to be removed?
Invalidated :=
[ (a,S) | (a,S) ∈m dcTω
P , (∃d ∈ heads(D)) d ∈ S ] ∪m
[ (a, /0) | a ∈ heads(D) ]
return dcTω
P Invalidated
Rule updates requires a special algorithm
Similar to the extended forward chaining algorithms - to
propagate a rule change
We also provide a backwards algorithm that requires less
space (doesn't keep dependencies) and more time (to always
recompute dependencies)

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Motivation
Results
Summary
Explanation
Supports, dependencies can be used for explanation
E.g. by rendering (interactive) support graphs

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Motivation
Results
Summary
Explanation
Supports, dependencies can be used for explanation
E.g. by rendering individual supports as tooltips

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Motivation
Results
Summary
Dierent Algorithms for Dierent Parts of Data
Weaver, Hendler, ISWC 2009: Parallel materialization of the
nite RDFS closure for hundreds of mililons of triples
RDFS data can be split in parts, their xpoint can be
computed in parallel
An application can choose which xpoint (Tω
P , skTω
P , scTω
P ,
dcTω
P ) to compute for which part
They provide
At least the same information as the minimal Herbrand model
of P (a theorem)
Dierent space-time tradeos for reasoning, reason
maintenance, explanation
Dierent explanation features (support counts, supports,
dependencies, ...)
E.g. compute Tω
P if fast explanation is not needed

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Motivation
Results
Summary
Summary
Contributions
Omitted in this presentation
Most of structured tags evaluation details
KWRL
Batch updates, lazy evaluation
Implementation

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Motivation
Results
Summary
Contributions Summary
Requirements on a Semantic Wiki
Conceptual model
Emphasis on the user's point of view and annotations
Structured tags
Structured tags user study
Comparison to RDF w.r.t. to manual annotation and
user-friendliness

institution-log
Motivation
Results
Summary
KWRL - The KiWi Rule Language
A rule language about annotations based upon Datalog
concepts
Aware of the conceptual model of the Wiki
Thus provides a more concise syntax for rules about
annotations
Employs value invention suitable for annotations and Linked
Data

institution-log
Motivation
Results
Summary
A set of forward chaining algorithms
Keep additional information about atoms for use in
Explanation
Reason maintenance
Described declaratively in the classical way
Naive algorithms same as classical forward chaining
Properties proven in the Lloyd's logic programming framework
New multiset Datalog semantics

institution-log
Motivation
Results
Summary
A set of reason maintenance algorithms
For Tω
P
Smaller programs than DRed, PF, SVZ, without negation,
including rule updates
For scTω
P
Further improves upon our algorithm for T
ω
P
A special alg. for non-recursive programs, more ecient than
existing
Safeness - to optimize algorithms for recursive programs
For dcTω
P
More extensive immediate explanations, fast reason
maintenance
Backwards algorithm to recompute dependencies on demand
Dierent space-time tradeos, suitability for explanation

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Motivation
Results
Summary
Support graphs
A formal framework encompassing all the described methods,
unied description
Enables easier comparison of the described methods
A notion of derivation such that
# of derivations is always nite even in recursive Datalog
(theorem)
- as opposed to the method of Gupta, Katiyar, Mumick
clear relation to well-foundedness of reason maintenance
Implementation
Batch updates, lazy evaluation
Graph database

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Motivation
Results
Summary
Thank you
Thank you

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Appendix Publications
Publications I
F. Bry, M. Eckert, J. Kotowski, and K. Weiand.
What the User Interacts With: Reections on Conceptual
Models for Sematic Wikis.
SemWiki 2009, Heraklion, Greece
J. Kotowski, F. Bry, and S. Brodt.
Reasoning as Axioms Change - Incremental View Maintenance
Reconsidered.
RR2011, Galway, Ireland
J.Kotowski, F.Bry, N. Eisinger.
A Potpourri of Reason Maintenance Methods.
Submitted for publication

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Publications II
F. Bry, J. Kotowski.
Social Vision of Knowledge Representation and Reasoning.
SOFSEM 2010
F. Bry, J. Kotowski.
A Perfect Match for Reasoning, Explanation, and Reason
Maintenance: OWL 2 RL and Semantic Wikis. SemWiki 2010,
Hersonissos, Greece, short paper, demo.

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scTP Semi-Naïve Forward Chaining
Worst case time-complexity O(n2k)

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Leveraging the Existing Fixpoint
(the edge relation)
edge(S,D) → reach(S,D)
edge(S,I),reach(I,D) → reach(S,D)
edge(a,b) → reach(a,b)
edge(a,b),reach(b,D) →
reach(a,D)

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dcTP
Dependency of an atom: a set of atoms that are in a
derivation of that atom
dcTPderives multisets of extended atoms: pairs (a,D) where
D is a dependency of a
The worst case time complexity of semi-naive forward chaining
with dcTP: O(n2k)
dcT
0
P = /0m
dcT
1
P = [(a, /0),(b, /0)]
dcT
2
P = [(a, /0),(b, /0),(c,{a}),(c,{b}),(d,{a}),(d,{b})]
dcT
3
P = [(a, /0),(b, /0),(c,{a}),(c,{b}),(d,{a}),(d,{b}),(e,{c,d,a}),
(e,{c,d,b}),(e,{c,d,a,b}),(e,{c,d,a,b})]
dcT
4
P = [(a, /0),(b, /0),(c,{a}),(c,{b}),(d,{a}),(d,{b}),(e,{c,d,a}),
(e,{c,d,b}),(e,{c,d,a,b}),(e,{c,d,a,b}),(b,{e,c,d,a})]

institution-log
Wikis to Semantic Wikis
Web - 1989 - 1994, read only, vision: read/write
Wiki - 1995, Ward Cunningham, a read/write web
Web 2.0 - 2004, AJAX technologies, social web
Semantic Web - 2001, adds semantics to the Web
Semantic Wikis - 2004, read/write social semantic web
applications

Constructive Reasoning for Semantic Wikis - PhD defense presentation

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