Trust Models for RDF Data: Semantics and Complexity - AAAI2015

Trust Models for RDF Data: Semantics and ComplexityAAAI 2015

Valeria Fionda1, Gianluigi Greco1

1Department of Mathematics and Computer Science, University of Calabria

Valeria Fionda, Gianluigi Greco ( Department of Mathematics and Computer Science, University of Calabria )Trust Models for RDF Data 1 / 28

Outline

1 Introduction

2 Trust Framework

3 Complexity

4 Conclusions


Introduction

Outline

1 Introduction

2 Trust Framework

3 Complexity

4 Conclusions


Introduction

The Resource Description Framework

Resource Description Framework

(RDF)


(RDF)

Formalization of the model

Systematic study of the complexity of entailment

Formalization of the concept of minimal representation (core) of an RDF graph

Study of the complexity of core computation

[Gutierrez et al. 2011]

Foundational aspects


Introduction

The Resource Description Framework


(RDF)


(RDF)

Formalization of the model

Systematic study of the complexity of entailment

Formalization of the concept of minimal representation (core) of an RDF graph

Study of the complexity of core computation

[Gutierrez et al. 2011]

Foundational aspects


Introduction

Extensions of RDF

[Gutie

rrez,

Hurtado,

and Vaism

an 2007] Time

Provenance

[Dividino et al. 2009]

Fuzzy [Straccia 2009]

Trust

[Hartig 2009; Tomaszuk, Pak,

and Rybinski 2013]

General annotations

[Udrea, Recupero,

and Subrahmanian 2010;

Zimm

ermann et al. 2012]


(RDF)


Introduction

Extensions of RDF

Trust


(RDF)


Introduction

Why trust is important?

Due to the openess and decentralization of the Semantic Web, thepresence of incorrect and unreliable RDF data can negatively affectdecision processes and cause economic damages.

By associating trust values to RDF data, some of these issues can bemitigated.

Having trust values alone is not enough; making reasoningproblems tractable when dealing with the large volume of dataavailable on the Web is essential.


Introduction

Contributions


Introduction

Contributions


Introduction

Contributions


Trust Framework

Outline

1 Introduction

2 Trust Framework

3 Complexity

4 Conclusions


Trust Framework

Trustworthiness

The trustworthiness of t is avalue indicating to what extent t isbelieved or disbelieved to be true

A trust-enriched RDF graph (short: t-graph) is a pair 〈G,w〉 where G is anRDF graph, and w is a real-valued trust function such that:

• dom(w) is a set of RDF triples;

• for each t ∈ dom(w), −1≤w(t)≤1 holds. The symbol φ associatedwith any triple outside the domain is meant to denote that the trustvalue of t is unknown;


Trust Framework

Trustworthiness






Trust Framework

Trustworthiness






Trust Framework

Trust Function - example


• for each t ∈ dom(w), −1≤w(t)≤1 holds.

w((A Time To Kill, author,John Grisham))=0.8


Trust Framework

Trust Function - example


• for each t ∈ dom(w), −1≤w(t)≤1 holds.

w((A Time To Kill, author,John Grisham))=0.8dom(w) = G \ {(A Time To Kill, genre, Legal thriller)}


Trust Framework

Trust Aggregation Functions

φ is a neutral element with respect to f , i.e., f (S) = f (S ∪ {φ})


Trust Framework




Trust Framework




Trust Framework




Trust Framework

Trust Aggregation Function - example

author

Untitled

authorgenre

genre

0.8

0.7

John_Grisham A_Time_To_Kill

Legal_thriller-0.2

Minimum trust aggregation functionfmin({w1(t) | t∈G1})= min{w1(t) | t∈G1}=-0.2.

Maximum trust aggregation functionfmax({w1(t) | t∈G1})= max{w1(t) | t∈G1}=0.8


Trust Framework

RDF - Simple Interpratation


Trust Framework



Trust Framework



Trust Framework

t-interpratation


Trust Framework

t-interpratation


Trust Framework

t-interpratation


Trust Framework

f-models

Given a trust aggregation function f , a t-interpretation is an f -model ifthe value assigned via σ̄ to each interpreted triple is the result of thefunction f on the trust values of the RDF triples mapped into it.


Trust Framework

f-models



Trust Framework

f -models



Complexity

Outline

1 Introduction

2 Trust Framework

3 Complexity

4 Conclusions


Complexity

Trust Aggregation Operators

Model CheckingComplexity

General Acyclic

RDF NP-complete in Pt-RDF NP-complete NP-complete

We focus on trust aggregation functions (f⊕) that can be built on topof binary trust aggregation operators (⊕):

A trust (aggregation) operator ⊕ is the binary operator of anIdempotent Commutative Ordered Monoid ([−1, 1] ∪ {φ},⊕,�) wherethe partial order � is defined as v � v ′ if, and only if, v ⊕ v ′ = v .


Complexity

Trust Aggregation Operators

Model CheckingComplexity

General Acyclic

RDF NP-complete in Pt-RDF NP-complete NP-complete

We focus on trust aggregation functions (f⊕) that can be built on topof binary trust aggregation operators (⊕):

A trust (aggregation) operator ⊕ is the binary operator of anIdempotent Commutative Ordered Monoid ([−1, 1] ∪ {φ},⊕,�) wherethe partial order � is defined as v � v ′ if, and only if, v ⊕ v ′ = v .


Complexity

Complexity

Concept ComplexityGeneral Bounded treewidth

RDFModel Checking NP-complete in P

Entailment NP-complete in PCore coNP-complete in P

t-RDFModel Checking NP-complete in P⊕-Entailment NP-complete in P⊕-Core coNP-complete in P


Conclusions

Outline

1 Introduction

2 Trust Framework

3 Complexity

4 Conclusions


Conclusions

Conclusions

Associating trust value to RDF data can prevent from the use of datathat are not accurate.

Having trust values alone is not enough. Indeed, since RDF is thebackbone of the Semantic Web, making reasoning problems tractablewhen dealing with such a large volume of data is essential.

We defined a formal framework (and a prototype system) forreasoning about trust values and by singling out islands of tractabilityfor classes of acyclic and nearly-acyclic graphs for the most basicproblems.


Download our prototype at http://trdfreasoner.wordpress.com

THANK YOU


http://trdfreasoner.wordpress.com

Reasoning Problems

⊕-Entailment:Let 〈G1,w1〉 and 〈G2,w2〉 be two t-graphs. Then, 〈G1,w1〉 ⊕-entails〈G2,w2〉 (denoted by 〈G1,w1〉 |= 〈G2,w2〉, if ⊕ is understood) if everyf⊕-model of 〈G1,w1〉 is also a f⊕-model of 〈G2,w2〉.

⊕-Core:Let 〈G,w〉 be a t-graph. A ⊕-core of 〈G,w〉 is a t-graph 〈G′,w〉 withG′ ⊆ G and such that: (i) 〈G,w〉 |= 〈G′,w〉; and (ii) 〈G,w〉 6|= 〈G′′,w〉holds ∀G′′ ⊂ G′ .


Trust Models for RDF Data: Semantics and Complexity - AAAI2015

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