A survey on SPARQL query relaxation under the lens of RDF reification

3.1.1.RDF

RDF provides the data model in the form of a graph. It extends the linking structure of the web to use IRIs to name the relationship between things as well as the two ends of the link (this is usually referred to as a “triple”). An RDF triple is a fact represented as (s, p, o) ∈ (I ∪ B) × I × (I ∪ B ∪ L), where I is the set of IRIs, B is the set of blank nodes, and L is the set of literals. An RDF graph G is a set of RDF triples.

Figure 2 shows some RDF triples (Turtle syntax, on the left) and the corresponding RDF graph (on the right) that represent the knowledge about Maya, a student enrolled in the Semantic Web course teached by Patricia and who knows Peter.

Fig. 2.

Example of some RDF triples and the corresponding data graph.

3.1.2.SPARQL

SPARQL is a query language that enables the expression of queries across of RDF data sources. Several types of queries can be defined (SELECT, CONSTRUCT, ASK, and DESCRIBE). In this article we focus on SELECT queries.

The SPARQL semantics [35] is centered on matching graph patterns of the target data graph.

Queries can be distinguished by the shape of their BGPs into four types: star, chain, composite, and property path.

3.1.3.RDFS entailment

RDFS (RDF Schema) provides basic elements for the description of ontologies. Several RDFS concepts are included in OWL (Web Ontology Language) which is a more expressive language. RDFS constructs allow to define classes and associate properties. Properties define the relations between subject resources and object resources.

Query relaxation is frequently based on the entailment rules of RDFS1313 that we show in Table 2.

3.2.1.Triple pattern relaxation

Given two triple patterns tp and tp′, tp′ is a triple pattern logically derived from tp if one or more relaxation rules are applied to tp in order to produce tp′. Relaxation rules are frequently based on the RDFS entailment rules (see Table 2).

Typing relaxations using the domain and range can have several disadvantages. Adding types is not helpful if they already exist in the query. It is also not possible to use domain or range relaxations when there is a variable in the object and the subject because the links of the variables not being considered in the relaxation and other terms in the query will be lost (i.e., joins will be broken). In addition, applying these relaxations makes it hard to compare the relaxed triple pattern with the original one. Hence, measuring their similarity would need uncommon methods. For these reasons, typing relaxation is not frequently used and so it is not considered in the rest of this section.

The set of relaxed triple patterns can be represented by an acyclic relaxation graph. This graph can be a lattice-based partial order where the relation ≺ is a triple pattern relaxation. A relaxation step transforms tp into a relaxed triple pattern tp′ by replacing any element e∈tp by e′:tp′=tp∖e∪e′ where e′∈{≺sp,≺sc,≺s}.

Fig. 3.

Relaxation lattices of triple pattern tp. ≺sc is a class relaxation, ≺sp is a property relaxation and ≺s is a simple relaxation. In (a), type relaxation is applied to :c1 once (with superclass :c1’) then simple relaxation is used (with the variable ?c1). In (b), type relaxation is applied twice (with superclass :c2’ then super-superclass :c2”) then simple relaxation is applied (with variable ?c2). In (c), type relaxation is applied to :c1 (with superclass :c1’), property relaxation to :p (with the superproperty :p’), and simple relaxation to :c2’ and :p’ (with variables ?c and ?p.)

Fig. 4.

Relaxation lattice of a query Q that is composed of the triple patterns of Figs 3a and 3b.

Figure 3 shows three relaxation lattices of a triple pattern tp. The size of a relaxation lattice depends on the relaxation possibilities allowed by the hierarchy of the ontology and the number of elements that is possible to relax. In Fig. 3a, one element of tp can be relaxed once (the object) while in Fig. 3b, it can be relaxed twice. In Fig. 3c, two terms can be relaxed once (the predicate and the object). The bottom-right corner of Fig. 4, shows the class and property hierarchy used in these relaxation lattices.

The total size of the relaxation lattice is the cartesian product of the size of each element. The size of each element can be calculated as follows, where e is an element of a triple pattern:

3.2.2.Query relaxation

Let Q=X←P be a (conjuctive) query, where X=(x1,…,xn) is a tuple of variables and P is a graph pattern composed of triple patterns. X is called the head and P is the body. Given two queries Q and Q′, Q′ is a query logically derived from Q, denoted Q≺QQ′, if one or more relaxation rules are applied to Q in order to produce Q′. The set of relaxed queries can be expressed as a lattice-based partial order where the relation ≺Q is a query relaxation. This lattice is the product of the relaxation lattices of the triple patterns existing in the graph pattern. In this lattice structure, the original query is the lower bound and the query whose triple patterns contain only variables is the upper bound. Let Q=tp10∧⋯∧tpn0 be the original failing query with n triple patterns and Q′ be the set of relaxed queries {Q′=tp11∧⋯∧tpnm∣∃c∈[1,m]:c>0} where c counts the number of relaxations of each tp.

Figure 4 shows an example of a relaxation lattice of a query Q. The basic graph pattern of Q is composed of the triple patterns of Figs 3a and 3b. The relaxation distance between two queries is the number of relaxation steps applied to the most specific query to obtain the most general relaxed query. This lattice has five levels. Relaxed queries having the same distance from the original query are part of the same level. The size of a relaxation lattice is the product of the sizes of the relaxation lattices of its triple patterns. In this example, the lattice size is twelve. If the graph pattern is composed of several triple patterns and the relaxation possibilities of each triple pattern are important, then the size of the set of queries Q′ can be huge. One of the main challenges facing query relaxation approaches is how to choose the relaxed queries to be executed until efficiently obtaining k-relevant results.

3.2.3.Information content measures

Analysing all relaxed queries existing in the relaxation lattice of a query is time-consuming and unnecessary. Information content [38], is frequently used to compute the similarity of relaxed queries to the original query. That is, to avoid the execution of an important number of relaxed queries until obtaining k-relevant results, several approaches use statistical information about the concerned dataset, such as the number of entities per class and the number of triples per property. The goal is to generate and execute relaxed queries from the most to the least similar to the original query.

Suppose C is a set of concepts in an is-a taxonomy. The similarity between two concepts is how much they share information in common. Then, according to the standard argumentation of information theory [39], the information content of concept c can be quantified as the negative log-likelihood −logPr(c), where Pr(c) is the probability of finding an instance of concept c in a dataset which is computed as Pr(c)=|Instances(c)||Instances|. This implies that Pr(c) is monotonic over the taxonomy: if c1 is – a c2, then Pr(c1)⩽Pr(c2). E.g., Teacher is-a Person then Pr(Teacher)⩽Pr(Person).

Based on information content, [21,22] propose similarity measures between terms, triple patterns and queries. These measures are used by several works because they allow ranking relaxed queries from the most to the least similar in a total order of relaxed queries.

Similarity between terms The similarity between terms depends on their nature: class, property, constant, or variable. It is computed based on the instances of classes and properties in a dataset. Suppose that c′ is the superclass of c and p′ is the superproperty of p, then the similarity measures between terms can be defined as follows.

Similarity between triple patterns Given two triple patterns tp and tp′, such that tp≺tp′, the similarity of the triple pattern tp′ to the original triple pattern tp, denoted Sim(tp,tp′), is calculated as the average of the similarities between the terms of the triple patterns. The average is usually used to normalize the similarity scores and make them comparable across different terms of the triple pattern.

Where s, p, o, s′, p′ and o′ are the subject, predicate and object of the triple pattern tp and the relaxed triple pattern tp′ respectively. If tp′ and tp″ are two relaxations obtained from tp and tp′≺tp″ then Sim(tp,tp′)⩾Sim(tp,tp″).

Similarity between queries Given two queries Q and Q′, such that Q≺QQ′, the similarity of the relaxed query Q′ to the original query Q, denoted Sim(Q,Q′), is the weighted product of the similarity between triple patterns of the query:

Where tpi is a triple pattern of Q, tpi′ is a triple pattern of Q′, tpi≺tpi′, and wi∈[0,1] is the weight of triple patterns tpi. Weight can be specified by the user to take into account the importance of a triple pattern tpi in query Q. Thus Sim(Q,Q′)∈[0,1] is a function that defines a total order among relaxed queries.

This similarity function is monotone, i.e., given two relaxed queries Q′(tp1′,…,tpn′) and Q″(tp1″,…,tpn″) of the user query Q, if Q′≺QQ″ then Sim(Q,Q′)⩾Sim(Q,Q″).

3.2.4.Relaxation based on the similarity of instances

Query relaxation based on the RDFS entailment can have effective results in queries over datasets where the hierarchies of classes or properties are rich. However, in some use cases, precise queries are posed for matching structured descriptions of resources in the RDF graphs. Relaxing these queries by replacing constants (that are actually resource instances) appearing in subjects or objects with similar resources is more appropriate than replacing them with variables (using simple relaxation). To measure the similarity among resources, similarity functions are needed to estimate the distance between resources. Different functions and methods can be used for computing the similarity between resources based on their type (numeric, string, date, etc.). For example, for dates, normalized distances can be used. For numeric values, euclidian distances can be employed, or a normalization or scaling process could also be applied to measure the relative position of one numeric value within a predefined range. String functions can be based on natural language techniques where lexical analysis is applied, like Jaccard similarity, Levenshtein distance, TF-IDF score, cosine similarity, etc.

3.3.1.Standard reification

Fig. 5.

Illustration of reification models with graph representations.

The standard reification method, proposed in the RDF primer standardized by W3C [28],1414^,1515 relies on the utilization of IRIs or blank nodes to represent each RDF statement that will be reified. Every statement is defined by three parts according to their roles in the reified statement (rdf:subject, rdf:predicate, and rdf:object). An identifier is assigned to each distinct RDF statement. This identifier is used as subject in the triple that represents the annotation. Figure 5a illustrates the graph representation of a reified statement in our example. A node, identified by the label s100, represents the reified statement (ex:John ex:enrolledIn ex:Semantic_Web). The two annotations (ex:enrolldate and ex:enrollpayment) use this node in the subject. The number of triples for standard reification is 4+n, where n represents the number of annotations. The RDF triples corresponding to this example, are presented in Listing 1a.

Listing 2a shows our example query with standard reification. This SPARQL query contains also four triple patterns that describe the RDF statement and two triple patterns that specify the metadata values using their related predicates. Queries of this reification model are typical subject star-shaped queries.

Listing 1.

Examples of RDF triples in different reification approaches.

Listing 2.

Example of SPARQL queries using different reification approaches.

3.3.2.Named graphs

Carrol et al. [4] extended the RDF data model to cover RDF graphs nameable by URIs. Named graphs were proposed to describe graphs with provenance information.1616 This approach considers pairs of the form (n,g), where n is an IRI that identifies the RDF graph g (n can be a blank node in some cases, or even omitted for a default graph). The graph identifier is used for the annotations. Figure 5b illustrates the idea of named graphs. One RDF graph is defined for the statement(s) to be annotated (g-100), and the annotations are defined into another RDF graph (g-101). This approach is very compact, 1+n quadruples (g,s,p,o) are needed for n annotations. Listing 1b shows the syntax used in named graphs. Listing 2b shows the query of our running example using named graphs (TriG syntax). Two graphs need to be accessed, the one that contains the statement and the second with the annotations. Each BGP contains is a subject star-shaped set of triple patterns.

3.3.3.N-ary relations

Traditionally, a triple links two resources through a relation or property. The n-ary relation model [33]1717 was proposed for relations that link a resource to more than one resource or value. This approach proposes to create a new class and n new properties to represent an n-ary relation. An instance of the relation is then an instance of this class. Ontologically the classes created in this way are called reified relations. The instance of a relation can be an IRI or a blank node. Figure 5c illustrates the n-ary relations model where a new class, named ex:Enroll_relation, is created and an instance of this class (ex:enroll_relation_1) is used as a reference for the reified statement. Additionally, ex:Semantic_Web is linked to this instance using the property ex:enroll_value. The same instance is then used for the annotations. This model results in 3+n triples as shown in Listing 1c, n being the number of annotations. Listing 2c shows our example query in n-ary relations. Queries with the n-ary relations approach are composite queries with a subject star-shaped set where the variable searches for the n-ary relation specified in the other part of the query (cf. Line 2).

3.3.4.Singleton properties

Instead of using new classes, the singleton properties approach [32] proposes to create a unique property for associating metadata. The new property is defined with the property singletonPropertyOf. Figure 5d shows the graph representation of this model for our example. In this representation, a new node is created to represent the new property (p-200). This property is linked to the original property via singletonPropertyOf. The same property is then used as subject for all annotations. This approach needs 2+n RDF triples to represent n annotations. Listing 1d shows our running example in RDF triples. An example of SPARQL query using singleton properties is shown in Listing 2d. A typical query using the singleton approach is a composite query. The particularity is that the chain part is with a predicate variable (cf. Line 2) that searches for instances (same subject variable in Line 3) of the property defined in the star-shaped part of the query.

3.3.5.RDF-star

Recently, [17]1818 proposed RDF-star and SPARQL-star, as an extension of RDF and SPARQL. The goal is to provide a compact alternative to standard RDF reification. RDF-star introduces quoted triple, which is a new kind of RDF term. A quoted triple is a triple used as the subject or object of another triple. A quoted triple is written using delimiters ≪ and ≫. The definition of quoted triple is recursive. That is, a quoted triple can itself have a subject or object component which is another quoted triple. Quoted triples can be asserted or not. If they are asserted then they exist as normal (asserted) triples. Figure 5e shows the graph representation of RDF-star with our running example. The quoted triple is inside the rectangular box which is directly linked to the annotations. Listing 1e shows the Turtle-star syntax.

SPARQL-star allows to bind a triple pattern enclosed in angle brackets as subject or object on other triple pattern. Our query example is shown in Listing 2e. This syntax shows that with this nesting-based approach, only one triple pattern is needed to search in a reified statement. It is hard to classify the shape of SPARQL-star queries. With our example query we can identify a subject star-shaped triple pattern in the enclosed angle brackets which is used for searching matchings with the given annotations.

At the time this paper was written, the RDF 1.21919 introduced the concept of Triple Terms that follows the simplicity of RDF-star while adding the capability to define an identifier. A triple term can be used as the object of a triple with the predicate rdf:reifies, where the subject of that triple is known as a reifier. This approach allows for indirect referencing of a triple term through its reifier.

3.3.6.Comparison of reification models

The described reification models differ in various criteria such as the number of triples (resp. triple patterns), flexibility, syntax support, and human understandability, etc.

Several works studied different reification methods and compared them according to several criteria. To mention a few, [18] focused on Wikidata and its representation in RDF using reification based on n-ary relations, standard reification, singleton properties and named graphs. [11] realized an analysis of standard reification, named graphs, n-ary relations, singleton properties, companion properties (proposed in that paper) and RDF-star in its early stages. [26] experimentally analysed the behaviour of standard reification, singleton properties, named graphs, and RDF-star over a knowledge graph with a huge number of annotations (over 70% of the used RDF dataset). [25] compared standard reification, n-ary relations, RDF-star and Qualifiers [18] (the reification model proposed for Wikidata) for three consumer scenarios: knowledge exploration, systematic querying, and embeddings for graph completion. [34] proposed REF, a benchmark (dataset and set of queries) to analyse reification models. To illustrate the utility of the benchmark, authors analysed querying performance, storage efficiency and usability on a single triplestore using three reification models (standard reification, singleton properties and RDF-star). [1] proposed StarBench (as an extension to REF), a benchmark for testing the SPARQL-star support and runtime performance. Their analysis highlighted limitations in loading the data, query parsing, correct evaluation of SPARQL-star queries, as well as contrasting query execution performance across all tested engines.

Results suggest that there is no outright winner for all comparison aspects. Standard reification and named graphs appear to have good performance. Singleton properties frequently produces poor performances. This is likely due to the high number of unique properties, and indexes of triplestores are usually not optimized with that in mind. Finally, it appear that RDF-star should be more efficiently implemented, as it is becoming part of the RDF 1.2 specification.

The next section surveys SPARQL query relaxation approaches. Even though they have proven their efficiency, RDF reification poses significant challenges and raises open questions. Is it pertinent to relax terms introduced to employ various methods of statement-based reification? Is it crucial to distinguish the part of a query that searches for annotations from the one that searches for data? Can annotation values be relaxed similarly to traditional description values? Does the higher number of triples and triple patterns necessary to describe annotations have a performance impact on query relaxation approaches?

4.1.1.Extension of the OPTIONAL clause with a RELAX clause

Hurtado et al. [23,24,36] propose a RELAX clause as a generalization of the OPTIONAL clause of SPARQL for conjunctive queries. These works use four types of relaxation: type relaxation, property relaxation, typing relaxation (using the domain and range rules), and simple relaxation. Simple relaxation includes dropping triple patterns (similar to the OPTIONAL clause of SPARQL), replacing constants with variables, and breaking join dependencies. Breaking join dependencies consists in generating new variable names for a variable that appears in multiple triple patterns. These works perform the breadth-first traversal of the relaxation lattice of a query and return the answers in a ranking order according to the relaxation distance. But the queries that are on the same relaxation level are not distinguished.

It is worth noting that the approach introduced in [23] focused on single triple pattern queries or simple chain queries. [24] extends their relaxation approach by addressing graph patterns (using the product of the relaxation lattices of the graph pattern). Then, [36] extended the application of ontology-based relaxation from graph patterns to property path queries. To do this, authors convert a property path query into a chain query. Once a chain query is obtained, the query relaxation is done as usual. For instance, the property path ex:friendOf/ex:knows of our running example will produce two triple patters, and ex:friendOf will be relaxed to ex:knows. This will interestingly result in obtaining extra answers. In our example dataset, this relaxation will return the student Maya who knows Peter, who in turn, knows Alice.

The RELAX clause proposed in these works has interesting constraints. A triple pattern whose predicate term is in the RDFS vocabulary cannot be relaxed except for type-triple-patterns (i.e., triple patterns having rdf:type in the predicate). This kind of triple pattern will be relaxed only with Rule 4 (rdfs9) of Table 2, where a class is replaced by a superclass in the object. Applied to our running example, the metadata part of our example query would not be relaxed except for the triple pattern tp6. Thus, tp6 can be specified as RELAX{?statement rdf:type rdf:Statement}. In that case, the rdf:Statement class will be relaxed with its superclass rdf:Ressource. This relaxation is semantically useless because numerous things are instances of rdf:Resource (all entities in subjects and objects). See Q9 in the Appendix A.5.

We remark that the works by Hurtado et al. propose theoretical concepts and algorithms but do not include experimental evaluations of their contributions.

4.1.2.Ranking model based on Bayesian networks

Huang et al. [20] propose an approach to rank the relaxed queries according to their similarities to the original user query, and an original method to compute similarity values using Bayesian networks. The goal is to identify a set of relaxed queries to obtain k-relevant answers. This work considers type relaxation, property relaxation, typing relaxation and simple relaxation. It focuses on relaxing predicates and objects within the context of subject star-shaped queries to find similar entities.

The similarity of a relaxed query to the original query is measured based on the difference of their estimated results, i.e., their selectivity, or more concretely Pr(c) (see Section 3.2.3). The main contribution lies in estimating selectivity by considering the correlation among properties that describe entities. The selectivity of a query depends on the joint probability distribution over the values of the properties whose entities match the query. But the possible combinations of values of properties would be exponential. Therefore, this work uses Bayesian networks as an appropriate structure to divide the joint probability distribution into several distributions of fewer variables by using the conditional independence assumption. The structure of these Bayesian networks is learned using the K2 algorithm [5]. Since the number of possible structures grows exponentially as a function of the number of variables, this process may be costly and it is done offline, previous to the online query processing.

This approach allows to discard relaxed queries with empty results. Our first observation is that as this approach focuses on star-shaped queries, the data part of our example query will be analyzed separately from the (related) metadata part (reification). Triple patterns like tp6 can be relaxed leading to uninteresting results. The advantage is that the ranking strategy will calculate a low similarity when this triple pattern relaxation is considered. A limitation of the ranking strategy is that it does not distinguish between queries that return the same number of results. For instance, Q12 and Q17 of our running example will not be distinguished because they return the same number of answers (see Appendix A.5).

Experimental setup The experiments conducted use Jena2121 and the Lehigh University Benchmark (LUBM) [16]. LUBM relies on a university domain ontology with numerous properties and classes. The experiments involve five star queries, each comprising three or four triple patterns. To compute k-relevant approximate answers, an algorithm based on best-first search is implemented, with the parameter k set to specific values.

Evaluation Experimental results show that this relaxation strategy can avoid some unneccessary relaxations by considering the real data distribution, i.e., relaxations giving empty results are avoided. However, the experiments carried out do not present a comparison with other state-of-the-art contributions. Thus, there is no confirmation of the better performance brought by this work compared to other contributions.

4.1.3.Relaxation strategies based on information content

[21,22] proposed the query similarity measures introduced in Section 3.2.3. [22] proposes and evaluates three query relaxation strategies: Best First Strategy (BFSR), Optimized Best First Strategy (OBFSR) and Batch-based Relaxation Strategy (BR). These strategies are based on the best-first traversal strategy of the query relaxation lattice and execute the relaxed queries in a ranking order according to similarity measures to generate the k-relevant answers for a query.

Although these algorithms rank relaxed queries based on similarity scores, distinguishing between relaxed queries can still be challenging. Consider two relaxed queries generated by simple relaxation. Despite both queries may yield distinct answers, it would be difficult to distiguish them if they have same similarity measures (see last line of Table 10 in the Appendix A.4).

Experimental setup These algorithms were evaluated using Jena TDB.2222 [22] constructed a dataset using LUBM. Seven queries were designed to conduct experiments that evaluate the performance of BFSR, OBFSR and BR algorithms with the increase of k (number of approximate answers). Three types of queries are used in these experiments: star queries, chain queries, and composite queries.

Evaluation Experiments showed that when the user asks for few answers, BR will behave as OBFSR and BFSR. OBFSR is more efficient than BFSR since it prunes the lattice and saves more time. However, no difference in results quality is observed according to the type of queries used in the experiments. This means that the type of queries do not have an impact on the quality of results obtained by these strategies. The experiments carried out do not present a comparison with other state-of-the-art contributions.

4.1.4.Query relaxation strategies based on failure causes

Fokou et al. [10] present three approaches that focus on optimizing the relaxation process by investigating the failure causes of relaxed queries. Authors argue that executing relaxed queries in a similarity-based ranking order lacks of efficiency because queries are relaxed without identifying their failure causes. The failing sets of triple patterns in a query are called Minimal Failing Subqueries (MFS). Identifying the MFSs (i.e., the set of MFS) of a query is an NP-hard problem. In [9,29], authors propose efficient methods to computate the MFSs of a failing query. Discovering MFSs of a query Q roughly consists in (1) finding an MFS of Q, (2) computing the maximal queries not containing the MFS determined in the first step, and (3) repeating the first two steps until no more MFS are found. [10] proposes three different strategies based on failing subqueries, MFS-Based Search (MBS), Optimized MFS-Based Search (O-MBS), and Full MFS-Based Search (F-MBS). These strategies rank relaxed queries based on the similarity function described in Section 3.2.3. The three proposed strategies use different levels of information about failing queries.

Experimental setup These three algorithms were implemented in Java using Jena TDB and Virtuoso.2323 Datasets were generated with LUBM. Seven queries are used in the evaluation experiments, where these queries include the main query patterns (star, chain, and composite).

Evaluation According to the experiments, O-MBS is the best strategy since it minimizes the computation time and the number of executed queries in most cases. O-MBS is a good compromise between MBS and F-MBS. However, these experiments do not show a comparison between these proposed algorithms and other state-of-the-art contributions.

4.1.5.Relaxing failing queries based on the hitting set problem

Mebrek et al. [29] introduced an approach named CADER for handling failing queries. Unlike all previous proposed relaxation techniques, CADER relaxes the constraints of a query only by eliminating triple patterns. It does not use any ontology-based relaxation or query similarity. However, this approach also aims to optimize the relaxation process by studying the failure causes of the relaxed queries similar to the works described in Section 4.1.4 but in different manner. It involves two main steps: (1) determining the MFSs, and (2) exploring these failing subqueries to compute the set of maximal succeeding subqueries (XSSs). The basic idea of identifying MFSs consists in decomposing the initial query into the smallest subqueries (one triple pattern) and evaluating those queries until finding the largest queries with empty answers. In [10], the idea is to start with queries having the largest number of triple patterns and progressively move to those with the smallest number. The iterative browsing performed by CADER is more efficient since it reduces the exponential search space, resulting in the evaluation of fewer queries. If a query fails to give answers, then all its proper superqueries will fail. Consequently, evaluating these superqueries becomes unnecessary. Regarding the second step, this approach models the query relaxation problem as a hitting set problem. Given a collection of subsets (i.e., answers calculated in the step 1), the hitting set problem is finding the smallest subset that intersects (hits) every set in the collection. This is performed by discovering the MFSs and searching for their hitting sets which correspond to the complement set of XSSs. Hence, the set of succeeding queries are the set of maximal subqueries that succeed to give answers, and these queries are just generated by eliminating some triple patterns from the original query (the MFSs).

By applying CADER on the motivating example, it will identify the MFS of the original failing subquery that was determined in Section 4.1.4 (i.e., {tp4.tp7.tp8.tp10}). Then it will discover the set of XSS which is a set of subqueries excluding the triple patterns that are in the discovered MFS. So, the set of relaxed queries are the 4 subqueries that exclude the triple patterns tp4, tp7, tp8, and tp10.

Experimental setup CADER has been implemented in Java with the Jena library. The experiments are carried out using datasets from DBpedia and LUBM. Several experiments were performed to compare the proposed approach with the LBA and MBA algorithms proposed in [9]. Queries of varying types (star, chain, and composite) were generated over the DBpedia and LUBM dataset. The LUBM tested queries were borrowed from [9].

Evaluation CADER behaves the best regardless the types of queries in terms of execution time.

4.1.6.Query relaxation using property paths and SHACL constraints

Lahmam Bennani et al. [2] propose two original predicate relaxations. The first one, relaxes a predicate to a predicate+, where + is a property path operator. The second one relaxes a predicate with another predicate based on the same domain and range constraints. The idea is to relax a property with another whose domain or range includes the subject or object in the triple pattern. To generate this relaxation, the SHACL constraints language [27] is used because it provides more expressive domain and range constraints than RDFS. Similarities are computed like in Section 3.2.3. This work explicitly uses weights to give priority to some triple pattern relaxations. However, the similarity is set to 0 when relaxing predicates using domain and range restrictions and to 1 when relaxing to a property path. This gives property path relaxations more preference. Simple relaxation is not used in this work. Only predicates and objects are relaxed. Suppose that there exist two constraints that say that only a student can enroll in a course and only a teacher can enroll in an employee meeting. In that case, SHACL shapes can be defined for identifying these constraints and defining the allowed domain and range of the predicate related to enroll. This approach will work on relaxing the predicate while still satisfying these constraints.

In addition, predicates will be transformed into property paths (for example, ex:teaches+, ex:knows+, etc.).

Experimental setup This work was evaluated over a dataset named Brick which its ontology is composed of building representations. A set of basic conjunctive queries were defined for this dataset. In the experiments, two scenarios are considered. In the first scenario, all the weight values for computing the similarity measure are 1, while in the second scenario, there is a willingness to relax a set of triple patterns in the original query. As a result, lower weights are assigned to some triple patterns to prioritize relaxation over these specific patterns.

Evaluation Experimental results show that a relaxation time less than 1 ms was observed for most of the queries. However, these experiments do not present a comparison with other state-of-the-art contributions. Furthermore, the results of the two considered scenarios for weight assignments demonstrated that assigning weights could facilitate the retrieval of more answers at lower levels of the relaxation graph.

4.1.7.License-aware query relaxation

Moreau et al. [30] proposes FLiQue, a license-aware query processing strategy that uses query relaxation to deal with contradictions among licenses. This is the only relaxation approach among the proposed works that deals with license conflicts in a federation of SPARQL endpoints. When two or more licensed datasets participate in evaluating a (federated) query, to be reusable, the query result must be protected by a license compliant with each license of the involved datasets. If a license conflict is detected, FLiQue dynamically discards datasets of conflicting licenses. As this solution may generate an empty query result, the original user query is relaxed with ontology-based relaxation technique (O-MBS proposed in Section 4.1.4). Thus, given a SPARQL query and a federation of licensed datasets, the goal is to guarantee a relevant and non-empty query result whose license is compliant with each license of involved datasets. The challenge is to limit the communication cost when the relaxation process is necessary. To reduce the overhead induced by the distributed query relaxation process, FLiQue uses data summaries, statistics, and descriptions of data. It uses a compatibility graph of licenses that can be produced with CaLi [31], a lattice-based model for license orderings. FLiQue searches for licenses that are compliant with each license of the datasets that can participate in the query evaluation. Subfederations that avoid license conflicts are defined if no compliant license exists in the original federation. If no subfederation can execute the query, then the O-MBS approach is used to produce and propose relaxed queries. This work does not propose a new query ranking strategy (queries are ordered by similarity like in O-MBS), but it is able to propose queries ordered by their licenses, from the less to the most restrictive license.

The FLiQue approach can be applied to our example and its behaviour would be similar as for O-MBS. The difference is that FLiQue can be also used in a federation of endpoints and can deal with the exponential number of possibilites wich depend on the instances of each dataset.

Experimental setup FLiQue was implemented in Java using Jena and CostFed [41], an index-assisted federated engine for SPARQL endpoints which relies on a join-aware triple-wise source selection by considering URI prefixes. The conducted experiments for the evaluation of FLiQue use Virtuoso endpoints and LargeRDFBench [40], a benchmark for a federation of SPARQL endpoints. This benchmark contains 32 federated queries (14 simple queries, 10 complex queries, and 8 large queries). Queries were executed over a federation of 11 interlinked endpoints.

Evaluation The experiments aim to demonstrate FLiQue’s ability to preserve licenses during federated query processing. For every query, experiments were carried out to compare the time to get the first result of the query with and without FLiQue. FLiQue shows a constant overhead due to checking the license conflicts. According to the experimental results, FLiQue succeeds in limiting the communication costs during the relaxation of federated queries whose results set cannot be licensed. However, LargeRDFBench is not ideal for this evaluation since the benchmark queries contain a lot of variables and very few classes. In addition, the potential for relaxation is poor due to the short depth of the hierarchies of the ontologies concerned by LargeRDFBench datasets.

4.2.1.Statistical language model relaxations

Elbassouni et al. [7] see the query relaxation problem as the entity-relationship-oriented counterpart of query expansion in traditional keyword-search settings. It uses NLP techniques, particularly statistical language models, to relax queries. This is performed by learning the probability of word occurence. In the same way, probability of occuring two entities together in the same triple in the dataset, is learned. Then similar entities are detected based on this statistics. This work proposes to rewrite triple patterns using similar entities and similar relations. Similarities are calculated using the entity descriptions existing in the knowledge graph. Each entity generates a document containing the triples where the entity appears as subject or object. Each relation generates also a document containing the triples where the relation appears as predicate. Then unigrams and bigrams are defined from each document. Unigrams correspond to all entities, and bigrams correspond to all entity-relation pairs. Language models are then estimated by combining unigrams and bigrams using linear interpolation smoothing from the corpus (i.e., the knowledge graph). The language model of each entity or relation becomes a probability distribution. The distance between the language models of every pair of entities allows to identify similar entities. The similarity score between any two distributions is computed using Jensen-Shannon divergence. Thus, for each entity, this approach computes a ranked list of similar entities. This processing is conducted offline prior to online query processing. Three types of relaxations are proposed: (1) replacing entities (subjects or objects) and properties with other related entities and properties, (2) replacing entities and properties with variables, and (3) removing triple patterns or making them optional. External information sources could be also used in this work to relax entities and predicates.

In our query example, the course ex:Semantic_Web can be replaced with the course ex:Databases by estimating their statistical language models. This estimation can be done from some common information about these two courses in the dataset, such as that both are taught by ex:Patricia. Concerning RDF reification, reified triples may induce errors because, for instance, in standard reification the subject is an identifier not an entity. But, it is possible that in a query relaxation, the subject of triple patterns like tp6 be replaced by another identifier with similar reification.

Experimental setup The effectiveness of this relaxation approach was evaluated in two experiments. The first one evaluated the quality of relaxations of entities and relations. The second one evaluated the quality of the final results obtained from the original and relaxed queries. The experiments were conducted over two datasets. The first dataset was derived from the LibraryThing community, and the second dataset was derived from a subset of the Internet Movies Database (IMDB).

Evaluation Experiments based on human evaluations were conducted to evaluate the quality of the relaxations and relaxed query results. Evaluators studied the quality of these relaxations and how close they were. The same was carried out for the relations. The evaluators agreed with the ranking results of the entity and relations relaxations. indicating the good performance of this contribution in relaxing entities and relations. This work does not report a comparision with other approaches.

4.2.2.Relaxations of heterogenous resources descriptions

Hogan et al. [19] focus on entity-lookup queries using similarities of RDF terms. They address vague queries executed over heterogenous and incomplete data. Vague means that the query issuer may be not sure about the query constraints. When queries yield no results, this approach proposes rewriting them with similar constraints. This work introduces a generic framework to calculate distance scores between resources based on their structured descriptions. This process is conducted offline before online query processing. The target queries are subject-star shaped queries where only objects are relaxed. The framework maps entity values to relaxation scores using multiple distance functions. These scores range from 0 to 1, where 1 indicates no interchangeability, and 0 indicates perfect interchangeability. For instance, distance(:blue, :navy) might be 0.2, suggesting :navy as a good relaxation for generic :blue. The choice of the distance functions depends on attribute types, such as normalized distances for numeric attributes or Levenshtein distance for string attributes. Background knowledge, including similarity tables, can also be used. This approach positions the original query as the reference point and maps entities into an n-dimensional space. The closest entity value to the query is chosen. An overall relaxation score is computed for each entity based on its distance from the original query, facilitating result ranking. Users can assign vagueness scores to attribute-value pairs to control relaxation by property. It also proposes a concurrence measure that matches RDF resources based on the cardinality of property-value pairs in the dataset.

Considering our running example, a query that searches students enrolled in a “very easy” course, will give no answer as in our dataset there are no courses described as very easy (only easy and hard). But, if we use the Levenshtein distance, “easy” can replace “very easy” because “easy” is closer to “very easy” than “hard”.

Experimental setup The proposed relaxation framework was tested against the vehicles dataset of the EADS project (European Aeronautic Defence and Space Company) which is considered a small dataset. The effectiveness of this framework was also evaluated over three small queries. These queries were defined from their expression in natural language. Then, handmade, the expressions were transformed into SPARQL queries with vagueness scores. Transforming natural language phrases automatically into queries is out of the scope of this paper.

Evaluation Top 5 approximate answers of each query were collected and evaluated using scores based on root-mean-square deviation. From these observations, it was deduced that this approach has a weakness due to the functions declared in the framework. This weakness states that different functions may produce very similar values. Therefore, it becomes challenging to compare these values and determine the most suitable relaxation, making it difficult to distinguish the most relevant answers.

4.2.3.Partitioning-based relaxation

Ferré [8] proposes a strategy for finding approximate answers and optimizing the evaluation of relaxed queries. This work allows query relaxation to be applied effectively on large queries and not only on queries with few triple patterns. The usage of ontology in relaxing queries is not mandatory. Thus, this strategy is considered instance-based relaxation but it can also behave like an ontology-based relaxation approach. The foundation of this strategy is Formal Concept Analysis [13], a mathematical theory for deriving implicit relations between objects based on common attributes. In the context of semantic web queries, objects refer to RDF nodes, and attributes are the properties or characteristics associated with these nodes. When we formulate a query in the semantic web, it essentially acts as a description of RDF nodes. The query specifies certain conditions or properties that we are interested in when searching for information in a knowledge graph. Consider two classes in a knowledge graph, such as Course and Talk. These classes may have common properties, like duration, topic, and audience. Instances of these classes are the specific nodes in the graph, and when these instances share similar properties, they can be grouped together as part of a broader concept. For instance, if there are instances of both classes Course and Talk with same duration, topic, and audience, these instances could be identified as part of a broader concept – let’s call it EducationalEvent. In this context, the query represents a description of RDF nodes, and relaxed queries symbolically describe similar nodes. This work relies on symbolic similarity rather than numeric measures and utilizes relaxation distance to establish a partial ordering instead of a total ordering.

This paper proposes two algorithms: Answers partitioning and Lazy join.

This approach starts initially with a single partition defined by the fully relaxed query, i.e., the query with an empty body and the set of all possible answers. In addition, a set of candidate triple patterns is identified, containing all the triple patterns from the initial query that failed to produce enough results. Then each partition will be split in two parts by using a triple pattern as discriminating criteria generating a binary tree. As the choice of triple patterns is free, in our running example, the triple pattern (?student rdf:type ex:Student) could be chosen first. Based on this, the initial partition is split into two partitions. The first partition consists of a relaxed query that contains only this triple pattern and a set of answers that validate this query (ex:John, ex:Maria, and ex:Maya). While the second partition will remove this triple pattern and the results will be the complement of the results of the first partition. The algorithm stops when no partition can be split further. This algorithm is anytime because a partition is defined at all time so it can be stopped at any level. The partitions can be split in any sequence, enabling the adoption of either depth-first or breadth-first strategies, or the application of heuristics. The selection of the splitting triple pattern is also unrestricted and remains independent from one partition to another.

Experimental setup This approach was implemented in OCaml.2424^,2525 The experimental evaluation involved multiple datasets, including MONDIAL,2626 LUBM10, and LUBM100, with varying query sizes. Both datasets are interesting in this work since they are both rich in multi-valued properties. LUBM was used in the evaluation experiments to study the performance of this work in terms of ontology. While the MONDIAL dataset had a good role in studying the efficiency of similarity search using the rich node descriptions of this dataset. For every dataset, sets of small and large queries were both considered.

Evaluation The experimental results showed the efficiency of these algorithms in query relaxation over the small queries. In addition, it was proved that these algortihms are capable of exploring the search space in the absence of ontological definitions for queries having up to 1500 triple patterns. But still some strategies must be considered for choosing the proper cluster to split and the splitting element that allow to retrieve good results at earlier levels of relaxations.