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Citation: Solimando, A., Jimenez-Ruiz, E. and Guerrini, G. (2017). Minimizing
conservativity violations in ontology alignments: algorithms and evaluation. Knowledge and
Information Systems, 51(3), pp. 775-819. doi: 10.1007/s10115-016-0983-3
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Under consideration for publication in Knowledge and Information Systems
Minimizing Conservativity Violations in
Ontology Alignments: Algorithms and
Evaluation
Alessandro Solimando
1
, Ernesto Jim
´
enez-Ruiz
2
, Giovanna Guerrini
1
1
DIBRIS, Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi; University of Genova; Italy
2
Department of Computer Science; University of Oxford; United Kingdom
Abstract. In order to enable interoperability between ontology-based systems, ontology match-
ing techniques have been proposed. However, when the generated mappings lead to undesired
logical consequences, their usefulness may be diminished. In this paper, we present an approach
to detect and minimize the violations of the so-called conservativity principle where novel sub-
sumption entailments between named concepts in one of the input ontologies are considered as
unwanted. The practical applicability of the proposed approach is experimentally demonstrated
on the datasets from the Ontology Alignment Evaluation Initiative.
1. Introduction
Ontologies play a key role in the development of the Semantic Web and are being used
in many diverse application domains, ranging from biomedicine to energy industry. An
application domain may have been modeled with different points of view and purposes.
This situation usually leads to the development of different ontologies that intuitively
overlap, but they use different naming and modeling conventions.
The problem of (semi-)automatically computing mappings between independently
developed ontologies is usually referred to as the ontology matching problem. A num-
ber of sophisticated ontology matching systems have been developed in the last years
[16, 71]. Ontology matching systems, however, rely on lexical and structural heuristics
and the integration of the input ontologies and the mappings may lead to many undesired
logical consequences. In [36] three principles were proposed to minimize the number of
potentially unintended consequences, namely: (i) consistency principle, the mappings
should not lead to unsatisfiable concepts in the integrated ontology, (ii) conservativity
Received xxx
Revised xxx
Accepted xxx
2 A. Solimando et. al
principle, the mappings should not introduce new semantic relationships between con-
cepts from one of the input ontologies, (iii) locality principle, the mappings should link
entities that have similar neighbourhoods.
These alignment principles have been actively investigated in the last years (e.g.,
[32, 33, 36, 54, 56, 57, 66]). Violations to these principles are frequent, even in the
reference mapping sets and the alignments generated by the best performing match-
ers of the Ontology Alignment Evaluation Initiative
1
(OAEI). Also manually curated
alignments, such as the UMLS Metathesaurus [5] (UMLS),
2
a comprehensive effort for
integrating biomedical knowledge bases, suffer from these violations [36]. The occur-
rence of these violations may hinder the usefulness of ontology mappings. The practical
effect of these violations is clearly evident when ontology alignments are involved in
complex tasks such as query answering [54, 78]. The undesired logical consequences
caused by violations can either prevent query answering, or cause incorrect results. In
order to reduce existing violations, alignment repair methods typically remove a subset
of the alignment, given that input ontologies are considered as immutable, a common
setting in ontology alignment repair scenarios.
It should be noted, however, the different nature of the alignment principles. Vio-
lations of the consistency principle, unlike violations of the conservativity and locality
principles, always lead to an undesired logical consequence (i.e., unsatisfiability of a
concept) and they should always be avoided. Conservativity and locality violations may
also lead to undesired logical consequences; however they may also represent false pos-
itives and reveal incompleteness in one of the input ontologies. In Section 8 we discuss
alternative approaches that suggest to fix the input ontologies instead of repairing the
alignment (e.g., [7, 48]).
In this paper we focus on the conservativity violations and we follow a “better safe
than sorry” approach (i.e., we treat violations as undesired consequences led by the
mappings). Conservativity violations are presented in two flavours, namely subsumption
violations and equivalence violations. The (potential) challenging number of conserva-
tivity violations requires to exploit the intrinsic characteristics of these two flavours,
that result in the development of different approaches for their repair. The detection
and correction of subsumption violations relies on the assumption of disjointness [67]
and it is reduced to a consistency principle violation problem; while equivalence vi-
olations are addressed using a combination of graph theory and logic programming.
These two methods are combined into a multi-strategy approach addressing both types
of violations. Our extensive evaluation supports the effectiveness of the individual and
combined approaches in the detection and correction of conservativity violations.
The present paper extends [74, 75] under the following aspects: all the experimental
evaluations provided here cover both reference alignments and alignments computed
by participating systems of the OAEI 2012–2014 campaigns, where previous papers
covered only the reference alignments of the OAEI. Compared to [75], the present article
fully details the proposed method, including a correctness proof of the technique for
adding disjointness clauses to Horn Propositional formulas, on which our technique
heavily relies. Furthermore, [75] only dealt with the subsumption violations flavour,
while in this paper we also cover in detail the equivalence violations flavour. Concerning
[74],
3
all the technical details and proofs are now provided. In addition, the results of
the evaluation of the two possible variants of our combined repair approach are now
1
http://oaei.ontologymatching.org/
2
Alignments from UMLS are extracted according to the method defined in [36].
3
This paper was presented in a workshop without formal proceedings.
Minimizing Conservativity Violations in Ontology Alignments 3
analyzed, as well as the results for the independent techniques in isolation, that can be
used as baseline results. Finally, an empirical assessment of the impact of our repair
methods on the alignment quality (in terms of precision, recall and f-measure) is now
provided.
The remainder of the paper is organised as follows. Section 2 summarises the basic
concepts and definitions we will rely on along the paper. In Section 3 we introduce
our motivating scenario. Section 4 formally states the problem of computing repairs
for equivalence violations and presents an algorithm to solve such violations. Section 5
describes the method and algorithm to solve subsumption violations. Section 6 details
additional properties of the proposed methods. In Section 7 we present the conducted
evaluation. A comparison with relevant related work is provided in Section 8. Finally,
Section 9 gives some conclusions and future work lines.
2. Preliminaries
In this section, we provide the necessary definitions and notions that will be used in
the subsequent sections. Section 2.1 briefly introduces OWL 2 and the main elements
in an ontology. In Section 2.2 we give a formal definition of ontology mapping and on-
tology alignment (adapted from [17]) with their semantics. In Section 2.3 we precisely
define the semantic consequences imposed by ontology alignments, and we formalize
the consistency and conservativity principles. Finally, Section 2.4 covers the necessary
preliminaries about graph theory.
2.1. Ontologies and OWL 2
Ontologies play a key role in the development of the Semantic Web and are being used
in many diverse application domains, ranging from biomedicine to energy industry.
The most widely used ontology modelling language is the OWL 2 Web Ontology Lan-
guage [11], which is a World Wide Web Consortium (W3C) recommendation [84].
Description Logics (DL) are the formal underpinning of OWL 2 [3, 30].
An OWL 2 ontology O is equipped with a signature Sig(O), that is a vocabulary
of legal names for the entities appearing in the ontology. Sig(O) is composed by the
disjoint union of four finite sets: (i) N
C
, a set of unary symbols called named concepts,
(ii) N
R
, a set of binary symbols called named object properties, (iii) N
D
, a set of bi-
nary symbols called data properties, (iv) N
I
, a set of constant symbols called named
individuals.
OWL 2 ontologies can be seen as a set of axioms that are conformant to the syn-
tactic rules and constraints imposed by their underlying DL language [30], and built
using the elements of the signature. The classification of O, denoted as Cl(O), corre-
sponds to the result of the computation, performed using an OWL 2 reasoner, of the full
subsumption/subconcept relation between its named concepts (i.e., elements of N
C
).
Classification is therefore the subset of the logical closure of an ontology O s.t. each
axiom is of the form A v B, where A, B ∈ N
C
(O) and O |= A v B.
2.2. Ontology Mappings and Alignments
Ontology Mappings. In Definition 2.1 we provide the definition of ontology mapping
(also called match or correspondence).
4 A. Solimando et. al
Definition 2.1. Consider two input ontologies O
1
, O
2
, and their respective signature
Sig(O
1
) and Sig(O
2
). A mapping between entities of O
1
, O
2
is a 4-tuple he, e
0
, r, ci
such that e ∈ Sig(O
1
) and e
0
∈ Sig(O
2
), r ∈ {v, w, ≡}
4
is a semantic relation, and
c is a confidence value. Usually, the real number unit interval (0 . . . 1] is employed for
representing confidence values. Mapping confidence intuitively reflects how reliable a
mapping is (i.e., 1 = very reliable, 0 = not reliable).
Ontology Alignment. Definition 2.2 introduces the notion of alignment.
Definition 2.2. An alignment M between two ontologies, namely O
1
, O
2
, is a set of
mappings between O
1
and O
2
.
The main format to represent mappings have been proposed in the context of the
Alignment API, and it is called RDF Alignment [12]. This format is the standard for
the well-known OAEI campaign. In addition, mappings are also represented as standard
subclass and equivalence DL axioms. When mappings are expressed through OWL 2
axioms, confidence values are represented as OWL 2 axiom annotations [35]. The rep-
resentation through standard OWL 2 axioms enables the reuse of the extensive range of
OWL 2 reasoning infrastructure that is currently available. We adopt this representation,
and in the remainder of the paper we consider alignments as set of OWL 2 axioms.
Definition 2.3 introduces the notion of aligned ontology, resulting from the integra-
tion of two input ontologies, through an alignment between them.
Definition 2.3. Let O
1
, O
2
be two (input) ontologies, and let M be an alignment be-
tween them. The ontology O
M
O
1
,O
2
= O
1
∪ O
2
∪ M is called the aligned ontology w.r.t.
O
1
, O
2
, and M.
O
M
O
1
,O
2
is simply called the aligned ontology when no confusion arises. Note that
we assume that the signature of the aligned ontology is always the union of the signa-
tures of the input ontologies. When the input ontologies are clear from the context we
employ the abbreviated notation O
M
.
Given that each mapping is translated into an OWL 2 axiom, the aligned ontology is
again an OWL 2 ontology. Note that alternative formal semantics for ontology mappings
have been proposed in the literature, such as those proposed by Zimmermann et al.
in [87], and the semantics associated to the so-called bridge rules, in the context of
distributed description logics [6, 55].
2.3. Semantics of the Integration and Principles for Ontology Alignments
This section introduces the semantics of the integration, and provides a formal charac-
terization of the consistency and conservativity principles in ontology alignment.
Semantic Consequences of the Integration. The ontology resulting from the integra-
tion of two ontologies O
1
and O
2
via an alignment M may entail axioms that do not
follow from O
1
, O
2
, or M alone. These new semantic consequences can be captured
by the notion of deductive difference [46, 47].
Intuitively, the deductive difference between O and O
0
, w.r.t. a signature Σ, is the set
of entailments constructed over Σ that do not hold in O, but do hold in O
0
. The notion
4
We exclude disjointness from the semantic relations given that most of the available systems do not compute
this relation. Negative constraints are typically harder to identify and assess than positive ones [20].
