DL-Lite is a family of Description Logics (DLs) whose aim is to capture some of the most popular conceptual modeling formalisms, such as Entity-Relationship model [4] and UML class diagrams1, while preserving the tractability of the most important reasoning tasks, such as ontology satisfiability and query answering of arbitrary (union of) conjunctive queries (ground and not ground). More specifically, reasoning over ontologies of the DL-Lite family, is LOGSPACE in data complexity, and can be entirely delegated to a standard DBMS technology. We refer here to DL-LiteA, the DL of the DL-Lite family that is closest to OWL 2.0. Note that DL-LiteA is in fact a fragment of OWL 2. As such, it is possible to restrict the syntax of OWL so that it captures DL-LiteA. Because of the lack of the space, we will not discuss further this topic. We provide an expressive query language for DL-LiteA ontologies, named SparSQL , whose syntax is inspired by both SQL and SPARQL3, one of the most popular W3C proposals as standard query language for OWL. Actually, SparSQL is an epistemic query language that implements the language EQL-Lite(UCQ) presented in [2]. Thus, query answering is in LOGSPACE and can be reduced to evaluate first-order logic queries over the ABox. Moreover, we stress the expressive power of DL-LiteA by presenting a series of features, that are beyond OWL and can be added to the language. Specifically, these features allow one to express data properties of object properties, denial and identification constraints, and they include a new ontology component, called the ECBox, which is a set of general form of constraints called EQL constraints, based on epistemic logics. Note that this is not the first attempt to add constraints to OWL. However, previous related work, e.g. [5], are technically and semantically incomparable with the approach presented in this paper. Notably, all the contributions discussed in this work are currently implemented within the MASTRO system, a tool for ontology representation and reasoning that has DL-LiteA as proprietary core language. The main feature of MASTRO is to reduce all reasoning tasks, such as consistency checking and query answering to the evaluation of standard SQL queries over a DBMS. Note that one of the major benefits of using 1 http://www.omg.org/uml/ 2 From now on we will refer to OWL 2.0, see http://www.webont.org/owl/1.1/. 3 We refer to http://www.w3.org/TR/2008/REC-rdf-sparql-query-20080115/ for details about SPARQL.
DBMS technologies, is to allow for using huge amounts of possibly pre-existing data,
to populate the ontology instances [
SparSQL It is well-known that open-world semantics, typically adopted to interpret DL ontologies, are essential for representing incomplete information, but make FOL queries over DL ontologies undecidable. To the best of our knowledge, the most expressive FOL fragment for which decidability of query answering has been proved in DLs, is the class of union of conjunctive queries (UCQs), which unfortunately, have limited expressive power.
Hence, a non monotonic epistemic query language, named EQL-Lite(Q) , was
introduced in [
In the following example, we illustrate SparSQL , the query language actually implementing EQL-Lite(UCQ) in MASTRO.
Example 1. Consider the following fragment of DL-LiteA ontology: SubClassOf(F emale P erson) DisjointClasses(F emale Male) ObjectPropertyDomain(MARRIES P erson) SubClassOf(P erson DataMinCardinality(1 SSN)) SubClassOf(Male P erson) ObjectPropertyRange(MARRIES P erson)
SymmetricObjectProperty(MARRIES)
The intensional level of the ontology asserts that males and females are disjoint sets of persons, where all persons have at least one social security number and can marry other persons. Moreover, it says that if a person x marries a person y , then also y marries x.
Suppose that we want to know if there is not any person that is not known be a male or a female. This query, not expressible through a UCQ, can be caught by the following boolean SparSQL query: VERIFY not exists (SELECT persons:x
FROM SparqlTable(SELECT ?x WHEREf?x rdf:type 0P erson0g) persons EXCEPT( SELECT males:x
FROM SparqlTable(SELECT ?x
WHEREf?x rdf:type 0Male0g) males UNION SELECT females:x FROM SparqlTable(SELECT ?x
WHEREf?x rdf:type 0F emale0g) females))
We now present some new features that are absent in OWL and can be added to DL-LiteA.
Extending the intensional level It is possible to extend DL-LiteA of object property
data, denial constraints and identification constraints, as formally introduced in [
Example 1 (cont.) The ontology of Example 1 can be enriched with the following axioms:
ObjectPropertyDataDomain(W eddingDate MARRIES) ObjectPropertyDataRange(W eddingDate rdf:date) KeyFor(SSN P erson) deny(q() MARRIES(X,X)) The new intensional axioms state that MARRIES is the domain of the object property data W eddingDate, while its range is date. Moreover, they state that SSN is an identifier for P erson, and that nobody is married with himself.
Adding epistemic constraints : the ECBox We present a new component of a DL-LiteA
ontology, called ECBox, consisting of a set of epistemic constraints, named EQL
constraints, formally introduced in [
An EQL constraint is a ECBox axiom used to guarantee that a certain condition is satisfied by the ontology. Specifically, the condition is expressed through a (boolean) SparSQL query.
Let us explain the need for introducing the ECBox. It is well-known that DL-LiteA, being conceived to keep data complexity of the main reasoning tasks within LOGSPACE, has renounced to express few constructs typically used in the ER (or UML) formalism, such as complete generalization and minimal cardinality (greater than 1) on relations. Hence, for example, it is not possible to assert in a DL-LiteA ontology that a person is either a male or a female (and nothing else). However, by weakening the semantics and using a EQLC with the boolean SparSQL query showed in Example 1, it is possible to guarantee that if the ontology with constraints is satisfiable, then a person is either a male or a female, in all the models of the ontology.
We presented a new query language, called SparSQL , that is an implementation of the
EQL-Lite(UCQ) epistemic query language presented in [
As future work we plan to follow two main directions. On one hand, we plan to investigate the use of SparSQL to query ontologies written in DLs, other than DL-LiteA, e.g. OWL-DL and RDFS. On the other hand, we plan to run experiments with actual users, in order to compare the usability of MASTRO with the other tools for ontology management reasoning that are currently available.