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MotivationResults

Summary

Constructive Reasoning for Semantic Wikis

Jakub Kotowski

LMU Munich

October 18, 2011

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Outline

MotivationThe KiWi ProjectAddressed Topics and Contributions

ResultsConceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

The KiWi ProjectAddressed Topics and Contributions

Outline

MotivationThe KiWi ProjectAddressed Topics and Contributions

ResultsConceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

The KiWi ProjectAddressed Topics and Contributions

KiWi - Knowledge in a Wiki

I An EU FP7 project

I March 2008 - March 2011

I KiWi 1.0 - semantic wiki / semantic software platform

I Employs advanced semantic techniques

I reasoning, semantic search, personalization, informationextraction

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

The KiWi ProjectAddressed Topics and Contributions

Requirements on a Semantic Wiki

I Social →I Emergent collaborationI Preference for free tagging rather than prede�ned schemes

I Read/write + social → work in progress, inconsistencies

I Semantic + read/write → reasoning in presence of updates

I Social + reasoning →I Reasoning updates have to be fastI Reasoning comprehensibleI Otherwise people lose interest

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

The KiWi ProjectAddressed Topics and Contributions

Outline

MotivationThe KiWi ProjectAddressed Topics and Contributions

ResultsConceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

The KiWi ProjectAddressed Topics and Contributions

A Conceptual Model of a Semantic Wiki[What the User Interacts With: ..., SemWiki 2009, Heraklion]

I Focus on the user's point of view

I Content

I Annotations

I Knowledge representation formalisms

I Structured tagsI Evaluation of structured tags

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

The KiWi ProjectAddressed Topics and Contributions

KWRL - The KiWi Rule Language[Social Vision of Knowledge Representation and Reasoning, SOFSEM 2010]

I A rule language based upon Datalog concepts

I Inconsistency-tolerant

I Aware of the conceptual model of a wiki

I Focused on annotations

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

The KiWi ProjectAddressed Topics and Contributions

Forward Chaining Revisited

I Materialization of Datalog programs

I Extended immediate consequence operators

I Useful for reason maintenance, explanation

I Support graphs

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

The KiWi ProjectAddressed Topics and Contributions

Incremental Reason Maintenance

[Reasoning as Axioms Change: ..., RR2011, Galway]

[A Potpourri of Reason Maintenance Methods. Submitted for publication]

I New algorithms for incremental reason maintenance

I Improve upon existing database and reason maintenancealgorithms

I Formally anchored in

I Support graphsI Extended immediate consequence operators

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

The KiWi ProjectAddressed Topics and Contributions

Implementation[A Perfect Match for Reasoning, Explanation, and Reason Maintenance: ..., SemWiki 2010]

I Incremental reason maintenance - KiWi 1.0

I Explanation - KiWi 1.0

I Interactive �explanation tree� renderingI Fast on demand �tooltip� explanations

I A graph database implementation

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Outline

MotivationThe KiWi ProjectAddressed Topics and Contributions

ResultsConceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Conceptual Model[What the User Interacts With: ..., SemWiki 2009, Heraklion]

I Content

I Content itemsI FragmentsI Links

I Annotation

I Informal: TaggingI Semi-formal:Structured tags

I Formal: RDF, OWL, ...

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Conceptual Model[What the User Interacts With: ..., SemWiki 2009, Heraklion]

I Content

I Content itemsI FragmentsI Links

I Annotation

I Informal: TaggingI Semi-formal:Structured tags

I Formal: RDF, OWL, ...

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Structured Tags

I A semi-formal �knowledge representation formalism�

I Users can proceed

I From simple free tagging: �apple� �orange� �strawberry�I To complex structured tags: �fruit:(apple, orange, strawberry)�

I Based on grouping �(...,...,...)� and characterization �...:...�

I Grouping groups similar, related tagsI Characterization names groups tagsI Already young children are able to group and name

I Cognitive science: Gestalt psychology, Prorotype theoryI Eleanor Rosch: Natural categories, 1973

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Structured Tags Evaluation

I A user study, 19 participants split into two groups, 8 hours

I Annotation with RDF vs Annotation with Structured tags

I Focus on ease of use, understandability, expressiveness

I Participants generally favoured structured tags, enjoyed usingthem more, made fewer errors

I Some participants created complex JSON-like structures

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Structured Tags Evaluation

I A user study, 19 participants split into two groups, 8 hours

I Annotation with RDF vs Annotation with Structured tags

I Focus on ease of use, understandability, expressiveness

I Participants generally favoured structured tags, enjoyed usingthem more, made fewer errors

I Some participants created complex JSON-like structures

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Stuctured Tags - Evaluation Results

I >70% participants felt understood introduction to s.t. (65%did not unterstand RDF introduction)

I S.tags more intuitive (∼80% vs. ∼25%), �restriction to triplestoo limiting�, ...

I S.tags more expressive (∼80% vs. ∼30%)

I ∼�S.tags seem better without prior knowledge of the domain�

I Complex s.tags are used often: ∼79% of all s.tags are complex

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Outline

MotivationThe KiWi ProjectAddressed Topics and Contributions

ResultsConceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Forward Chaining - Motivation

I Forward chaining �completes� a wiki w.r.t. user-de�ned rules

I Materialization allows users to see the �current state of a�airs�

I Explanations should be readily available

I Need for incremental updates of the materialization

I Forward chaining should provide additional information to helpsolve the incremental reason maintenance problem

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Forward Chaining - Motivation

I Forward chaining �completes� a wiki w.r.t. user-de�ned rules

I Materialization allows users to see the �current state of a�airs�

I Explanations should be readily available

I Need for incremental updates of the materialization

I Forward chaining should provide additional information to helpsolve the incremental reason maintenance problem

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Forward Chaining and Reason Maintenance

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Forward Chaining and Reason Maintenance

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Support Graphs

I Inspired by data dependency networks of reason maintenance

I Better capture the logical notion of a derivation (via s.g.homomorphisms)

I Provide a framework for comparison of the presented methods

I Support: (r ,σ) (r - rule, σ - substitution)

I A support is �an evidence that the head of the support is animmediate consequence of a rule and the body of the support�

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Support Graphs

I Inspired by data dependency networks of reason maintenance

I Better capture the logical notion of a derivation (via s.g.homomorphisms)

I Provide a framework for comparison of the presented methods

I Support: (r ,σ) (r - rule, σ - substitution)

I A support is �an evidence that the head of the support is animmediate consequence of a rule and the body of the support�

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Support Graphs

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Classical Semi-Naïve Forward Chaining

I TP - immediate consequenceoperator

I Standard Datalog set semantics

I Worst case time-complexityO(nk)

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

skTP : Support Keeping Immediate Conseq. Op.

De�nition

Let P be a de�nite range restricted program. The support keepingimmediate 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 .

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

skTP Semi-Naïve Forward Chaining

I Worst case time-complexity O(nk)

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

scTP : Support Counting Immediate Conseq. Op.

I A multiset operator: how many times is an atom derivedduring classical forward chaining?

I De�ned on the complete lattice P(HBP) (theorem)

I Lloyd's logic programming framework can thus be used

De�nition

Let P be a �nite de�nite range restricted program. The supportcounting 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) ]

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

scTP : Support Counting Immediate Conseq. Op.

I A multiset operator: how many times is an atom derivedduring classical forward chaining?

I De�ned on the complete lattice P(HBP) (theorem)

I Lloyd's logic programming framework can thus be used

De�nition

Let P be a �nite de�nite range restricted program. The supportcounting 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) ]

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

scTP Semi-Naïve Forward Chaining

I Worst case time-complexity O(nk)

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

scTP Example

scT 0

P= /0m

scT 1

P= [ a,b ]

scT 2

P= [ a,b,c ,c,d ,d ]

scT 3

P= [ a,b,c ,c,d ,d ,e ]

scT 4

P= [ a,b,c ,c,d ,d ,e,b ]

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

dcTP : Derivation Counting Immediate Conseq. Op.

I A multiset operator: how many derivations are there of anatom in the �xpoint?

I �Tracks� extended atoms: (a,D)

I De�ned on the complete lattice P(dHBP) (theorem)

I Lloyd's logic programming framework can thus be used

De�nition

Let P be a �nite de�nite range restricted program. The derivationcounting immediate consequence operator dcTP for P is themapping:

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 6= Biσ ,D =

⋃n

i=1Di ∪{Biσ} ].

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

dcTP : Derivation Counting Immediate Conseq. Op.

I A multiset operator: how many derivations are there of anatom in the �xpoint?

I �Tracks� extended atoms: (a,D)

I De�ned on the complete lattice P(dHBP) (theorem)

I Lloyd's logic programming framework can thus be used

De�nition

Let P be a �nite de�nite range restricted program. The derivationcounting immediate consequence operator dcTP for P is themapping:

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 6= Biσ ,D =

⋃n

i=1Di ∪{Biσ} ].

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Properties of the Extended Immediate Conseq. Ops.

Theorem

Let P be a de�nite Datalog program. Then scTω

Pand dcTω

Pare

multisets with �nite multiplicities.

Theorem

Let P be a de�nite program. Then

HI (lfp(TP)) = HI (skTω

P) = HI (scTω

P) = HI (dcTω

P) is the unique

minimal Herbrand model of P.

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Properties of the Extended Immediate Conseq. Ops.

Theorem

Let P be a de�nite Datalog program. Then scTω

Pand dcTω

Pare

multisets with �nite multiplicities.

Theorem

Let P be a de�nite program. Then

HI (lfp(TP)) = HI (skTω

P) = HI (scTω

P) = HI (dcTω

P) is the unique

minimal Herbrand model of P.

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Outline

MotivationThe KiWi ProjectAddressed Topics and Contributions

ResultsConceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

The Reason Maintenance Problem

I Given

I P: a �nite (recursive) Datalog programI D: a subset of P to removeI Tω

P: the �old� �xpoint

I Compute

I Tω

P\D : the �new� �xpoint

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

The Reason Maintenance Problem

I Given

I P: a �nite (recursive) Datalog programI D: a subset of P to removeI Tω

P: the �old� �xpoint

I Compute

I Tω

P\D : the �new� �xpoint

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

The Reason Maintenance Problem

I Given

I P: a �nite (recursive) Datalog programI D: a subset of P to removeI Tω

P: the �old� �xpoint

I Compute

I Tω

P\D : the �new� �xpoint

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Related Work

I Belief revision - an epistemological approach

I Reason maintenance - a logical approach

I Belief revision and Reason maintenance are closely related

I Jon Doyle: Coherence and foundational approach

I Incremental view maintenance - a database approach

I DRed (derive and rederive)

I Staab, Volz, Motik adapted DRed for the Semantic Web, 2005

I PF (propagate and �lter)

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Related Work

I Belief revision - an epistemological approach

I Reason maintenance - a logical approach

I Belief revision and Reason maintenance are closely related

I Jon Doyle: Coherence and foundational approach

I Incremental view maintenance - a database approach

I DRed (derive and rederive)

I Staab, Volz, Motik adapted DRed for the Semantic Web, 2005

I PF (propagate and �lter)

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Related WorkI Belief revision - an epistemological approachI Reason maintenance - a logical approachI Belief revision and Reason maintenance are closely related

I Jon Doyle: Coherence and foundational approach

I Incremental view maintenance - a database approachI DRed (derive and rederive)

I Staab, Volz, Motik adapted DRed for the Semantic Web, 2005

I PF (propagate and �lter)

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Fixpoint Analysis

I U (unsure) - atoms that depend on sth. in D

I K (keep) - atoms that do not depend on sth. in D

I O (otherwise supported) - depend on sth. in D and have analternative derivation

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Reason Maintenance Without Support Graphs

I Compute U(overestimation)

I Determine K as Tω

P\U

I Compute Tω

P\D(K )

Theorem

TP\D(K )ω = Tω

P\D

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Computing the Set U (overestimation)

I Goal

I To use the old �xpoint as much as possible

I Solution

I A modi�cation of semi-naive forward chaining to use the old�xpoint and D as the ∆

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Computing the Set U (overestimation)

I Goal

I To use the old �xpoint as much as possible

I Solution

I A modi�cation of semi-naive forward chaining to use the old�xpoint and D as the ∆

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Computing the Set U (overestimation)

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Updating Rules

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Algorithm: Incremental Reason Maintenance WithoutSupport Graphs

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Summary

I The algorithm

I stays in de�nite Datalog if P is a de�nite Datalog programI uses the original program P

I DRed, PF, SVM alg. transform P into a bigger Datalogprogram with negation (12 rules → 60 rules)

I doesn't need a modi�cation to handle rule updatesI requires only a small modi�cation of classical forward chainingI recomputes only the a�ected part of a predicate's extensionI can be adapted to strati�ed normal programs as usual

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Algorithm: Incremental Reason Maintenance WithoutSupport Graphs

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Support Counting Reason Maintenance

Theorem

Let a ∈xm scTω

P. Then a ∈ O and a ∈ TP\D(K ) i�

x > |{t ∈ SU | head(t) = a}|.

I �An atom a is derivable in the new �xpoint if not all itssupports belong to the unsure part of the old �xpoint�

Theorem

Let P be a de�nite range restricted program. Each support of an

atom g ∈ Tω

Pnot well-founded in G = SG(skTω

P) depends strongly

on the node labelled g in G.

I �Supports of an atom in U that aren't part of any derivationbelong to the unsure part of the old �xpoint�

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Support Counting Reason Maintenance

Theorem

Let a ∈xm scTω

P. Then a ∈ O and a ∈ TP\D(K ) i�

x > |{t ∈ SU | head(t) = a}|.

I �An atom a is derivable in the new �xpoint if not all itssupports belong to the unsure part of the old �xpoint�

Theorem

Let P be a de�nite range restricted program. Each support of an

atom g ∈ Tω

Pnot well-founded in G = SG(skTω

P) depends strongly

on the node labelled g in G.

I �Supports of an atom in U that aren't part of any derivationbelong to the unsure part of the old �xpoint�

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Support Counting Reason Maintenance

I In summary: a semi-naive way to compute the initial∆:

I ∆ := { a ∈ heads(SU) | a ∈xmscTω

Pand

x > |{t ∈ SU | head(t) = a}| }

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Support Counting for Non-Recursive Datalog Programs

I Non-recursive Datalog: overestimation phase not necessary

I Gupta, Katiyar, Mumick, JICSLP, 1992 - a counting algorithmfor non-recursive Datalog programs

I Counts �derivation trees�

I Alternative incremental algorithm that relies on countingsupports

I Counting supports is less expensive

I We de�ne the notion of �safeness� (safe atoms, safe rules) thatcan help determine situations in which a similar algorithm canbe applied even in the recursive Datalog case

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Support Counting for Non-Recursive Datalog Programs

I Non-recursive Datalog: overestimation phase not necessary

I Gupta, Katiyar, Mumick, JICSLP, 1992 - a counting algorithmfor non-recursive Datalog programs

I Counts �derivation trees�

I Alternative incremental algorithm that relies on countingsupports

I Counting supports is less expensive

I We de�ne the notion of �safeness� (safe atoms, safe rules) thatcan help determine situations in which a similar algorithm canbe applied even in the recursive Datalog case

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Support Counting for Non-Recursive Datalog Programs

I Non-recursive Datalog: overestimation phase not necessary

I Gupta, Katiyar, Mumick, JICSLP, 1992 - a counting algorithmfor non-recursive Datalog programs

I Counts �derivation trees�

I Alternative incremental algorithm that relies on countingsupports

I Counting supports is less expensive

I We de�ne the notion of �safeness� (safe atoms, safe rules) thatcan help determine situations in which a similar algorithm canbe applied even in the recursive Datalog case

Jakub Kotowski Constructive Reasoning for Semantic Wikis

institution-logo

MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Derivation Counting Reason Maintenance

I Simple when we have the dcTω

P�xpoint

I 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

I Rule updates requires a special algorithm

I Similar to the extended forward chaining algorithms - to�propagate� a rule change

I We also provide a �backwards� algorithm that requires lessspace (doesn't keep dependencies) and more time (to alwaysrecompute dependencies)

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Derivation Counting Reason Maintenance

I Simple when we have the dcTω

P�xpoint

I 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

I Rule updates requires a special algorithm

I Similar to the extended forward chaining algorithms - to�propagate� a rule change

I We also provide a �backwards� algorithm that requires lessspace (doesn't keep dependencies) and more time (to alwaysrecompute dependencies)

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Derivation Counting Reason Maintenance

I Simple when we have the dcTω

P�xpoint

I 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

I Rule updates requires a special algorithm

I Similar to the extended forward chaining algorithms - to�propagate� a rule change

I We also provide a �backwards� algorithm that requires lessspace (doesn't keep dependencies) and more time (to alwaysrecompute dependencies)

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Explanation

I Supports, dependencies can be used for explanation

I E.g. by rendering (interactive) support graphs

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Explanation

I Supports, dependencies can be used for explanation

I E.g. by rendering individual supports as tooltips

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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MotivationResults

Summary

Conceptual Model and Structured TagsForward Chaining RevisitedIncremental Reason Maintenance

Di�erent Algorithms for Di�erent Parts of Data

I Weaver, Hendler, ISWC 2009: Parallel materialization of the�nite RDFS closure for hundreds of mililons of triples

I RDFS data can be split in parts, their �xpoint can becomputed in parallel

I An application can choose which �xpoint (Tω

P, skTω

P, scTω

P,

dcTω

P) to compute for which part

I They provide

I At least the same information as the minimal Herbrand modelof P (a theorem)

I Di�erent space-time tradeo�s for reasoning, reasonmaintenance, explanation

I Di�erent explanation features (support counts, supports,dependencies, ...)

I E.g. compute TωP

if fast explanation is not needed

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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MotivationResults

Summary

Summary

I Contributions

I Omitted in this presentation

I Most of structured tags evaluation detailsI KWRLI Batch updates, lazy evaluationI Implementation

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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MotivationResults

Summary

Contributions Summary

I Requirements on a Semantic Wiki

I Conceptual model

I Emphasis on the user's point of view and annotationsI Structured tags

I Structured tags user study

I Comparison to RDF w.r.t. to manual annotation anduser-friendliness

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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MotivationResults

Summary

Contributions Summary

I KWRL - The KiWi Rule Language

I A rule language about annotations based upon Datalogconcepts

I Aware of the conceptual model of the Wiki

I Thus provides a more concise syntax for rules aboutannotations

I Employs value invention suitable for annotations and LinkedData

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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MotivationResults

Summary

Contributions Summary

I A set of forward chaining algorithms

I Keep additional information about atoms for use in

I ExplanationI Reason maintenance

I Described declaratively in the classical way

I Naive algorithms �same� as classical forward chainingI Properties proven in the Lloyd's logic programming framework

I New multiset Datalog semantics

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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MotivationResults

Summary

Contributions Summary

I A set of reason maintenance algorithms

I For TωP

I Smaller programs than DRed, PF, SVZ, without negation,including rule updates

I For scTωP

I Further improves upon our algorithm for TωP

I A special alg. for non-recursive programs, more e�cient thanexisting

I Safeness - to optimize algorithms for recursive programs

I For dcTωP

I More extensive immediate explanations, fast reasonmaintenance

I Backwards algorithm to recompute dependencies on demand

I Di�erent space-time tradeo�s, suitability for explanation

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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MotivationResults

Summary

Contributions Summary

I Support graphs

I A formal framework encompassing all the described methods,uni�ed description

I Enables easier comparison of the described methodsI A notion of derivation such that

I # of derivations is always �nite even in recursive Datalog(theorem)

I - as opposed to the method of Gupta, Katiyar, MumickI clear relation to well-foundedness of reason maintenance

I Implementation

I Batch updates, lazy evaluationI Graph database

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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MotivationResults

Summary

Thank you

Thank you

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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Appendix Publications

Publications I

F. Bry, M. Eckert, J. Kotowski, and K. Weiand.What the User Interacts With: Re�ections on ConceptualModels for Sematic Wikis.SemWiki 2009, Heraklion, Greece

J. Kotowski, F. Bry, and S. Brodt.Reasoning as Axioms Change �- Incremental View MaintenanceReconsidered.RR2011, Galway, Ireland

J.Kotowski, F.Bry, N. Eisinger.A Potpourri of Reason Maintenance Methods.Submitted for publication

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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Appendix Publications

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 ReasonMaintenance: OWL 2 RL and Semantic Wikis. SemWiki 2010,Hersonissos, Greece, short paper, demo.

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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Appendix Publications

scTP Semi-Naïve Forward Chaining

I Worst case time-complexity O(n2k)

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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Appendix Publications

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)

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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Appendix Publications

dcTP

I Dependency of an atom: a set of atoms that are in aderivation of that atom

I dcTPderives multisets of extended atoms: pairs (a,D) whereD is a dependency of a

I The worst case time complexity of semi-naive forward chainingwith 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})]

Jakub Kotowski Constructive Reasoning for Semantic Wikis

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Appendix Publications

Wikis to Semantic Wikis

I Web - 1989 - 1994, read only, vision: read/write

I Wiki - 1995, Ward Cunningham, a read/write web

I Web 2.0 - 2004, AJAX technologies, social web

I Semantic Web - 2001, �adds semantics� to the Web

I Semantic Wikis - 2004, read/write social semantic webapplications

Jakub Kotowski Constructive Reasoning for Semantic Wikis