Trust Models for RDF Data: Semantics and Complexity - AAAI2015

Trust Models for RDF Data: Semantics and Complexity
AAAI 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 ofTrust 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)

Introduction
The Resource Description Framework
Resource
Description
Framework
(RDF)
Resource
Description
Framework
(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
[G
utierrez, H
urtado,
and
Vaism
an
2007]
Time
Provenance
[Dividino et al. 2009]
Fuzzy
[Straccia 2009]
Trust
[Hartig 2009;
Tomaszuk, Pak,
and Rybinski 2013]
General annotations
[U
drea,Recupero,
and
Subrahm
anian
2010;
Zim
m
erm
ann
etal.2012]
Resource
Description
Framework
(RDF)

Introduction
Extensions of RDF
Trust
Resource
Description
Framework
(RDF)

Introduction
Why trust is important?
Due to the openess and decentralization of the Semantic Web, the
presence of incorrect and unreliable RDF data can negatively aﬀect
decision processes and cause economic damages.
By associating trust values to RDF data, some of these issues can be
mitigated.
Having trust values alone is not enough; making reasoning
problems tractable when dealing with the large volume of data
available on the Web is essential.

Introduction
Contributions

Trust Framework
Outline
1 Introduction
2 Trust Framework
3 Complexity
4 Conclusions

Trust Framework
Trustworthiness

Trust Framework
Trustworthiness
The trustworthiness of t is a
value indicating to what extent t is
believed or disbelieved to be true

Trust Framework
Trustworthiness
The trustworthiness of t is a
value indicating to what extent t is
believed or disbelieved to be true
A trust-enriched RDF graph (short: t-graph) is a pair G, w where G is an
RDF 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 associated
with any triple outside the domain is meant to denote that the trust
value of t is unknown;

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

Trust Framework
Trust Aggregation Functions

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

Trust Framework
Trust Aggregation Function - example
author
Untitled
author
genre
genre
0.8
0.7
John_Grisham A_Time_To_Kill
Legal_thriller
-0.2
Minimum trust aggregation function
fmin({w1(t) | t∈G1})= min{w1(t) | t∈G1}=-0.2.
Maximum trust aggregation function
fmax({w1(t) | t∈G1})= max{w1(t) | t∈G1}=0.8

Trust Framework
RDF - Simple Interpratation

Trust Framework
t-interpratation

Trust Framework
f-models
Given a trust aggregation function f , a t-interpretation is an f -model if
the value assigned via ¯σ to each interpreted triple is the result of the
function 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 Checking
Complexity
General Acyclic
RDF NP-complete in P
t-RDF NP-complete NP-complete

Complexity
Trust Aggregation Operators
Model Checking
Complexity
General Acyclic
RDF NP-complete in P
t-RDF NP-complete NP-complete
We focus on trust aggregation functions (f⊕) that can be built on top
of binary trust aggregation operators (⊕):
A trust (aggregation) operator ⊕ is the binary operator of an
Idempotent Commutative Ordered Monoid ([−1, 1] ∪ {φ}, ⊕, ) where
the partial order is deﬁned as v v if, and only if, v ⊕ v = v.

Complexity
Complexity
Concept Complexity
General Bounded treewidth
RDF
Model Checking NP-complete in P
Entailment NP-complete in P
Core coNP-complete in P
t-RDF
Model 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 data
that are not accurate.
Having trust values alone is not enough. Indeed, since RDF is the
backbone of the Semantic Web, making reasoning problems tractable
when dealing with such a large volume of data is essential.
We deﬁned a formal framework (and a prototype system) for
reasoning about trust values and by singling out islands of tractability
for classes of acyclic and nearly-acyclic graphs for the most basic
problems.

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

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 every
f⊕-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 with
G ⊆ G and such that: (i) G, w |= G , w ; and (ii) G, w |= G , w
holds ∀G ⊂ G .

Trust Models for RDF Data: Semantics and Complexity - AAAI2015

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