Formalizing and validating Wikidata’s property constraints using SHACL and SPARQL

2.1.Data modeling in Wikidata

In this section, we describe how Wikidata’s data model – and specifically property constraints – are modeled in RDF and can be queried with SPARQL.99

To this end, let us start with the bare basics of RDF and SPARQL and then gradually dive into the specifics of Wikidata. When talking about RDF, as usual, we will refer to RDF graphs and their subgraphs as sets of triples

Fig. 1.

Simple RDF (sub-)graph example from Wikidata, showing two statements/triple, indicating that Lionel Messi (URL: wd:Q615) has two citizenships (property URL: wdt:P27): Spain (wd:Q29) and Argentina (wd:Q414).

Here, URIs are represented as namespace-prefixed identifiers, e.g. wd:Q615 which should be understood as a shortcut for a full URI, e.g. ⟨http://www.wikidata.org/entity/Q615⟩, according to the namespace prefixes defined in Table 1. Additionally – particularly in SHACL examples later on – we will also refer to RDF graphs using Turtle [10] syntax in the remainder of this paper. As an illustration, Gsimple can be written in Turtle concisely as follows:

For queries over RDF data, we will use SPARQL [32]: indeed the RDF representation of Wikidata can be fully queried by means of Wikidata’s SPARQL query service. Wikidata’s query service.,1010 which allows to formulate queries over RDF triples in terms of graph patterns, such as for instance:

    SELECT ?Citizenship WHERE { wd:Q615 wdt:P27 ?Citizenship }

Here, the triple pattern (wd:Q615, wdt:P27,?Citizenship) would match both countries, Argentina and Spain on the graph Gsimple.1111

Other methods, apart from Wikidata’s query service to access RDF from Wikidata include complete RDF dumps1212 or retrieving RDF triples per entity via Wikidata’s Web API directly.1313

Statement nodes: Wikidata’s internal data model heavily relies on meta-modeling, i.e., claims such as the ones represented by the triples in Gsimple can be annotated yet again with contextual meta-information, provenance and temporal information, etc. In order to map this meta-information to “flat” RDF triples, Wikidata’s RDF representation relies on the consistent usage of specific, authoritative [31,38]) namespaces,1414 the most important of which are listed in Table 1. We note that Wikidata’s meta-modeling in terms of specific namespaces can be seen as a custom reification mechanism: here, we mean “custom” in the sense of not following any “standard” reification scheme, such as the RDF reification vocabulary [34, Appendix D], named graphs [18], singleton reification [46], RDF-* [33], etc., for a detailed discussion, we refer the interested reader to [36].

Fig. 2.

Subgraph example from Wikidata. Direct claims can be stated (using wdt), while metadata is added through qualifiers (using pq). Statement ranks use the property Wikibase:rank.

In this reification model, Wikidata uses URIs that represent hashes for “anonymous” reified statement nodes and quantity value nodes as illustrated in our examples in the following: for instance, Fig. 2 shows a more complete graphical illustration of Wikidata’s RDF model including meta-information about Messi, adding such statement nodes, which yields the following set of triples G:

As a side note, let us emphasize that Wikidata’s use of such “hashed” statements nodes is a deliberate choice to avoid the use of blank nodes [39].1515

Entities: Items and properties, and lexemes In principle, any concept in Wikidata is an entity, such as real-world entities, but also properties, classes, or specific property constraint types; entities can be directly referred to as subjects or objects in statements via the namespace wd:. Entities are further subdivided into Properties, and Items which – rather than by prefix – can be distinguished by their numeric identifiers: Q-identifiers are used for Items, such as Q615, denoting the Item/Entity “Lionel Messi”, whereas P-identifiers are used for properties, such as P27 for the relation “country of citizenship”.

Besides Items and Properties, since a large part of Wikidata is also specialized in linguistics knowledge and multilinguality, another special kind of entities, so-called Lexemes, i.e., words with their senses and forms in particular different languages, are identified by separate L-identifiers, cf. Example 5 below.

Claims and statements: Claims made about entities are represented as “flat” RDF triples and use Properties in the predicate position with the namespace wdt:, such as the triples in Gsimple above. Note that, just like in the claim “Messi’s country of citizenship is Argentina”, which is represented by the RDF triple (wd:Q615,wdt:P27,wd:Q414), statements about Properties also use these different namespaces: that is, the wd: namespace is never used in a predicate position, whereas the wdt: namespace is never used in subject or object position. As an illustration, the claim that property country of citizenship (P27) is a subproperty of (P1647) country (P17) is denoted by the triple

    (wd:P27, wdt:P1647, wd:P17)

Such direct claims can be further described and annotated with meta-information. That is, for each claim, a separate, wds:-prefixed statement node is created in Wikidata’s RDF graph, which permits to refer to the claim itself in meta-statements, such as for instance declaring since when Messi has the Argentinean citizenship. These statement nodes are connected to the claim’s subject entity via the claim’s property using prefix p: instead of wdt:; additional meta-information about statement nodes uses specific so-called qualifier properties, denoted by the prefix pq:, and the statement node itself is connected back to the claim’s object via the claim’s property using prefix ps:.

Statement ranks and truthy statements: Note that not all statements in Wikidata are represented as directly queryable wdt: claims, the reason being that statements may be marked as normal (wikibase:NormalRank), preferred (wikibase:PreferredRank), or deprecated (wikibase:DeprecatedRank), via the special “statement-rank” (wikibase:rank) property. While in Fig. 2, both claims have rank wikibase:NormalRank, i.e. denoting equally valid – so-called “truthy” claims, let us provide another illustrating example to show a different setting.

    SELECT ?Capital WHERE { wd:Q30 wdt:P36 ?Capital }

    SELECT ?Capital WHERE { wd:Q30 p:P36/ps:P36 ?Capital }

Fig. 3.

A subgraph showing claims about two capitals (P36) of the USA (Q30) and their start and end times. According to a single-value constraint on P36, multiple values are allowed as long as they have different values for start time (P580) (and other so-called “separators”, not shown here).

Note that similarly, wikibase:DeprecatedRanked statements (which we do not illustrate at this point in a separate example, but which we will get back to later) do not have a wdt: claim in Wikidata’s RDF representation. Following the intuition that only preferred, non-deprecated, normal ranked statements without an “overriding” preferred statement are represented as wdt: triples, these wdt:statements are also called “truthy” statements in Wikidata terminology.

Quantity values: quantity values such as numbers, dates, etc. are represented in Wikidata – yet again different to RDFs typed literals – using a similar, specific reification mechanism, referring to properties using the separate namespace psv: to refer to quantity values, which can have an amount and unit, referred to by special wikibase: properties.

References: references can be given for any claims, where all such references are referred to with the prov:derivedFrom property. Similar to quantity values, reference nodes are represented by hash values in a separate namespace (wdref:), which can be further described with property-value pairs, using reference properties – identified by yet another separate namespace (pr:).

Fig. 4.

A subgraph containing a quantity claim about the height (P2048) of Messi, and a reference for this claim. According to an allowed-units constraint on P2048, centimetre (Q174728) is an allowed unit for this property.

Labels and descriptions: strings used to name or describe entities, i.e., Items, Properties, or also Lexemes, in different languages, are denoted in Wikidata’s RDF dump by language tagged literals, using the reserved properties rdfs:label and schema:description, respectively.

Fig. 5.

A subgraph illustrating additional RDF triples for representing (multi-lingual) labels and descriptions of Wikidata entities, leveraging RDF’s language-tagged literals.

Special statements about lexemes: linguistic knowledge about lexemes plays a key role in Wikidata, and uses a yet again dedicated representation; as a final example, we present a subgraph about the lexeme “football”, involving its senses (ontolex:sense) and lexical forms (ontolex:lexicalForm).

Fig. 6.

A subgraph about the English noun “football”, including normal claims, but also Wikidata-specific additional vocabulary to talk about languages.

As we can see in the example, lexemes can be involved in normal (wdt:) statements as discussed before, such as carrying external identifiers in particular dictionaries, but also involve lexeme-specific statements for identifying the language (dct:language), category (wikibase:lexicalCategory) and lexicographic forms and senses (prefix ontolex:). Note that these extra statements have no statement nodes nor qualifiers, somewhat deviating from the standard Wikidata statement model. Also observe, as opposed to language-tagged literals for labels and descriptions, these special statements about lexemes represent the language explicitly as an item (in our example Q1860 for English).

Figure 7(a) summarizes the modeling of regular statements and ranks, including the involved namespaces, in a more abstract manner. As shown in Fig. 7(b), the RDF model contains also triples to “navigate” between the differently prefixed URIs per property ID (PID); we will need to make use of these connections in our modeling of constraints in SHACL and SPARQL later on, but let us first turn to how these constraints themselves are actually represented within RDF model.

Fig. 7.

The Wikidata meta-model in RDF and its namespaces usage illustrated for (a) statements and claims, (b) properties, and (c) property constraint definitions. Dashed lines represent equivalent entities. Figures 2 and 3 illustrate concrete instantiations of the “Wikidata Statement” block (a), while Fig. 8(c) illustrates the block “property constraint definition” block (c). Abbreviations: QID = entity ID, PID = property ID.

2.2.Property constraints modeling by example

Wikidata property constraints make use of the described modeling to represent specific community-defined constraint types, where specific instantiations of a constraint type are defined as qualified statements on a particular property that should fulfill this constraint. To date, Wikidata represents 32 property constraint types as subclasses (P279) of property constraint (Q21502402). Table 2 gives an overview of all the constraint types.

Fig. 8.

Example of a Wikidata property constraint and data graphs with different behaviors (as of 2022-03-29).

Whereas each constraint type is modeled as an item – for instance, the item-requires-statement (IRS) constraint (Q21503247), such constraint types are instantiated and parameterized specifically per property. That is, each such instantiation is defined by a constraint-definition-statement linked to the respective constrained property P via the property constraint (P2302) property, as illustrated abstractly in Fig. 7(c).

In terms of parameters, constraint-type specific property qualifiers are used on the constraint-definition-statement: the overview in Table 2 list all property qualifiers that can be used per constraint type, as well as the number of different properties that use each constraint type (from February 2023).

For instance, the item-requires-statement (IRS) constraint type (Q21503247), is used to specify that each item with the constrained property P should also have another given property P′. The constraint is parameterized through the qualifiers

    (wd:P1469,p:P2302,wds:P1469-667F9488-5C36-4E3B-BEAA-6FD5834885ED)

    (wds:P1469-667F9488-5C36-4E3B-BEAA-6FD5834885ED,pq:P2306,wd:P106)

As a second example, let us look at another constraint type, the so-called single-value constraint (Q19474404), which imposes that property P is only allowed to have one single value unless there are different values for at least one separator, parameterizable by the separator (pq:P4155) qualifier.

Fig. 9.

Another example of a Wikidata property constraint and data graphs (as of 2022-08-20).

Exceptions to constraints Using the dedicated qualifier property exception to constraint (P2303), an instantiation of a constraint on a specific property can explicitly mention exceptions. These are items which, for various reasons may be valid, despite violating the constraint.

2.3.Constraint qualifiers

We hope that the previous subsection has sufficiently illustrated the most relevant aspects of modeling and parameterizing property constraints. Rather than in terms of fully elaborated examples, let us summarize all mentioned and remaining qualifiers used in the context of constraint modeling and parameterization in the following. To this end, Table 2 provides an overview of which qualifiers are used in current descriptions of constraints of different types. For each of the used qualifiers, we will provide a description of how they are used in the context of the different constraint types listed in Table 2, along with specific constrained properties P, also mentioning concrete usage examples. We present these qualifiers in three overall groups:

2.4.Additional challenges in understanding and verifying the semantics of constraints

The above summary of the used qualifier properties to parameterize constraints should have illustrated that the semantics of Wikidata’s vocabulary used to describe constraints are not always uniquely determined: indeed, the interpretation of constraint qualifiers depends on (i) in which context (ii) in which particular combination with other qualifiers, they are used (iii) in particular constraint types.

Before we continue in Section 3 with more details on how these qualifier properties are interpretable as parameters in SHACL-Core shapes for verifying different constraint types, let us discuss some additional challenges that potentially complicate these formalizations, and motivate our idea to design bespoke translations per constraint type.

The above description of Wikidata property constraints modeling in RDF defines how constraints are represented but not how they should be checked. To understand how to check constraints, a description property (schema:description) is provided along with the described at URL (P973) property, indicating a link to a page that describes the constraint. The vast majority of Wikidata constraint types (more precisely, 28 out of 32) have such a “Help”-page .2626 As these pages contain descriptions in natural language, they are often subject to ambiguity and different interpretations. Indeed, one of the main challenges when formalizing constraint types was the understanding of the semantics behind the constraint.

It is important to note here that the Wikidata community has defined all existing property constraint types in a manner where these types and their modeling have grown organically. In our formalizations of such constraints, we tried to stay as close as possible to the – partially heterogeneous – interpretations derivable from the natural language descriptions of constraint types. We could find and document several cases of textual ambiguity, leaving room for different interpretations and as a result, for different implementations of the respective constraint checks. We illustrate some of these issues.

    (wd:P524, wdt:P1647, wd:P582)

    SELECT * { ?s a wikibase:Property }

    SELECT * { ?s a wikibase:Item }

3.1.SHACL validation

The SHACL standard specifies constraints through so-called shapes, which are to be validated against an RDF graph. SHACL shapes themselves are represented as RDF Graphs, and may contain a wide variety of constraint components that allow the construction of possibly complex expressions to be checked over the input data. As usual in the majority of the SHACL works, in this paper, we focus on the core constraint components of SHACL and refer to it as SHACL-Core; an extension to this core language that allows the addition of full SPARQL queries for constraint checking will be introduced later, in Section 3.4.

A shapes graph contains shapes paired with targets specifying the focus nodes in the RDF graph that should be checked for validation. In a nutshell, an RDF data graph validates a shapes graph if these targets conform with the constraints specified in the corresponding shape. We illustrate these notions with a first example of a shapes graph implementing an item-requires-statement constraint type.

Overall, the shapes introduced in Example 9 define exactly the intended semantics of the item-requires-statement constraint represented in Fig. 8a, where we already give a hint, that even optional exception handling can be easily expressed in SHACL-Core.

Fig. 10.

SHACL shape item-requires-statement constraint for the (a) FIFA player ID (wdt:P1469) and (b) a variant with exceptions.

The SHACL specification allows for shapes to refer to other shapes which may result even in cyclic references and recursive constraints. In this context, we note that the official specification only provides semantics for non-recursive constraints, therefore, in line with our goal, to create shapes with standard validators, we may consider it as a requirement to avoid such recursive shapes. Indeed, the shapes that we obtain in this paper are all non-recursive; the fact that current Wikidata property constraints apply locally (per Subject Item) and do not transitively or even recursively depend on the fulfillment of other constraints, plays in our favor: as our example shows, we can express an item-requires-statement, and as we will show most other constraint types, in single shapes.

The constructs defining a shapes graph can syntactically be viewed as concepts in expressive Description Logics [9], a well-known family of decidable fragments of first-order logic. That is, the shape components can be viewed as logical constructs, such as existential and universal quantifications, qualified number restrictions, constants, or regular path expressions. For instance, the shapes graph in Fig. 10a can be expressed as the tuple containing the target t=∃wdt:P1469.⊤ and DL concept: φ=∃wdt:P106.({wd:Q937857}∨{wd:Q18515558}∨{wd:Q21057452}∨{wd:Q628099}) defining the shape P1469_ItemRequiresStatementShape. The validation test can intuitively be viewed as the concept inclusion t⊑φ evaluated over the input data graph, that is checking whether the nodes obtained from the evaluation of the target expression t over the data graph are included in the evaluation of the shape expression φ over the data graph. For details on a formal logic-based representation of the syntax and semantics of SHACL-Core, we refer to [21]. The complete list of all SHACL constraint components and their semantics can be found in the W3C SHACL specification.3434 We will present and introduce further these components in Section 3.2 as needed.

3.2.Mapping Wikidata constraints to SHACL-Core

Let us proceed to describe more systematically now, how Wikidata property constraints can be translated to SHACL-Core shapes.

The targets of property constraints in Wikidata are always the subjects of the resp. constrained property P, i.e., we can use uniformly use SHACL-Core’s sh:targetSubjectsOf construct, to define target nodes across all our formalizations of various constraint types.

Constraint types requiring the existence of a specific statement, such as our running example’s item-requires-statement constraint (and, likewise required qualifier constraints, one-of constraints…), are naturally captured by SHACL-Core constraint components. Roughly speaking, these types of constraints can be represented by choosing a target node, verifying the existence of an sh:path, and, possibly, verifying the existence of a value using sh:minCount 1 or a qualified minimum count sh:qualifiedMinCount 1, as shown above.

On the contrary, constraints forbidding certain statements, such as conflicts-with, or likewise property scope constraints can modeled analogously with a combination of sh:path and sh:maxCount 0. As an example let us illustrate a simple conflicts-with (Q21502838) constraint for the property family name (P734); according to the constraint property, it should not be used together with the property P1560 (given name version for another gender), as expressible concisely in the following SHACL shape:

Further building upon and extending the discussion of Example 9, we discuss and illustrate translations to SHACL guided by the constraint qualifier properties to parameterize them in the following, where we go through the constraint qualifiers in the same order as in Section 2.3.

This concludes the discussion of the treatment of core constraint qualifiers (Section 2.3.1) in our translation: essentially, we have created templates for each constraint type using SHACL-Core expressible constraint qualifiers. I.e., these templates can be instantiated with the respective qualifiers used as parameters in an automated fashion. Before we present a prototype implementing this automatic translation in the next subsection (Section 3.3), let us also briefly elaborate on the treatment of constraint exception qualifiers (Section 2.3.2) and descriptive qualifiers (Section 2.3.3), which, as we will see, also partially can be cast into respective SHACL-Core constructs.

In summary, by “templating” the respective qualifier parameter translations from Wikidata’s constraint representation to SHACL shapes based on the illustrating above examples, we can cover most constraint types, and – additionally carry over also some useful descriptive information to dedicated SHACL-Core constructs, that are not strictly needed for validation as such, but can be used by validators to generate explaining output.

A prototype, reading constraint definitions in Wikidata’s representation and accordingly creating their shapes representation on-the-fly is presented in Section 3.3 below. Table 2 presents the entire set of analyzed constraint types, their Wikidata IDs, as well as a column to state whether it was possible to map the constraint type to SHACL (and SPARQL, respectively, see Section 4). The particular SHACL encodings, created by using the above-introduced “mappings” between Wikidata qualifiers and SHACL-Core components, can be found in an online GitHub repository accompanying our paper.3535

3.3.Tool to automatically convert Wikidata constraints to SHACL

In order to demonstrate the feasibility of an automated translation, we developed wd2shacl, a demo tool to automatically convert constraints from the Wikidata model to the corresponding SHACL shape (for those that could be represented). This allows for the creation of a large, real-world SHACL benchmark from Wikidata, thus also addressing the scarcity of respective benchmarks for SHACL-Core currently available. Wd2shacl allows testing Wikidata property constraints with SHACL validators and generates verifiable shapes for any Wikidata property, extracting its associated constraints.

In a nutshell, we first generalized the example SHACL shapes (such as the one in Fig. 10a to become templates for specific constraint types, e.g. by replacing the specific qualifier values assigned to a single property, illustrated by the following “template abstraction” for IRS constraints:

Our wd2shacl tool then populates these templates according to the actual qualifier values instantiated for a specific property P. The architecture of wd2shacl is shown in Fig. 11. As input, we provide the P=PID of the desired property. The controller (WdToShaclController) uses a data extractor to collect all constraint types from the property, as well as the respective qualifiers describing them. The data extractor (wikidataDataExtractor) directly queries the respective qualifier statements from a Wikibase instance via SPARQL, where our current implementation directly uses Wikidata’s endpoint (WikidataOnlineEndpointExtractor). Alternative inherited extractor classes can be created to consume data from an RDF dump in a predefined format if necessary (e.g. to query from HDT archived versions of Wikidata3636), or from another endpoint, for instance, to query alternative Wikibase instances. Indeed, other Wikibase instances, such as the EU Knowledge Graph3737 re-use the Wikidata property constraint mechanism and could be likewise checked using the tool via such alternative extractors.

Fig. 11.

Wikidata to SHACL architecture. Dashed lines represent abstract classes.

After collecting constraint types and qualifiers for the input property P, the controller instantiates the template to create respective SHACL constraints for the extracted applicable constraint types. A specific class (a concrete subclass of ConstraintType) is implemented for each SHACL-expressible constraint type to create the SHACL shape by combining the template with the given qualifiers. The controller returns the populated SHACL templates as SHACL Turtle files, containing the required prefixes and a list of SHACL shapes, written using SHACL-Core language, for all the translatable constraint types associated with the input PID. The tool is freely available online within our GitHub repository.3838

3.4.Limitations of SHACL-Core for checking Wikidata constraints

As shown in Table 2 the vast majority of Wikidata constraint types can be rewritten into SHACL-Core Shapes (26 out of 32); yet, three could only be partially translated, one cannot be expressed in a reasonable way, while for further two we did not find any way to express them in SHACL-Core at all. Let us discuss these, and the involved challenges in more detail:

Firstly, the difference-within-range (Q21510854) constraint requires the difference between two values to be calculated and compared to a predefined range. Despite SHACL-Core having components to check for equalities (sh:equals) and inequalities (sh:disjoint, and sh:lessThan), arithmetic operations for computing differences are not included, which yields SHACL-Core unusable for expressing this constraint.

Next, the allowed qualifiers (Q21510851) constraint is also not directly/reasonably expressible in SHACL-Core. This constraint type specifies that only the listed qualifiers should be used when a certain statement is made, meaning that the use of all other qualifiers is disallowed. The problem here lies in the fact that SHACL-Core does not have direct means to query non-allowed paths (e.g. by referring to a path/property via a specific type).3939 We present an admittedly “clumsy” workaround, i.e., listing all non-allowed qualifiers explicitly in our GitHub repository.4040 Apart from the ridiculous length of the resulting shape description, this approach seems impractical as it does not depend on the data graph and parameters describing the constraint itself, but on a complete list of qualifiers in Wikidata (reduced by those provided as parameters).

The allowed entity type (Q52004125) originally seemed easily expressible in SHACL-Core to us. However, as mentioned in Section 2.4.4, it needs a number of workarounds to be executable on Wikdata’s query service (and might not generalise to other Wikidata RDF serialisations). Figure 12 shows a respective translation of an allowed entity type constraint on the property object has role (P3831), restricting its subjects to the following entity types:

Fig. 12.

SHACL-Core shape for verifying an allowed entity type (Q52004125) constraint on property object has role (P3831) , incl. workarounds defined in Wikidata’s query service documentation to check entity types missing in the RDF serialization (cf. Section 2.4.4).

The last three constraint types in our problematic list (single-value (Q19474404)) distinct-values (Q21502410), and single-best-value (Q52060874)) are those using the separator (P4155) qualifier. We recall from Section 2.4.2 this qualifier is difficult to express in itself.

On the contrary, it is straightforward to verify the uniqueness or difference of a property value with respect to the claimed subject in the absence of separators: as such, both (single-value (Q19474404)) and distinct-values (Q21502410) constraints are easily expressible in SHACL-Core, as long as they do not specify separators. We illustrate this with a simple single-value “shape” in Fig. 13a.

Fig. 13.

SHACL shapes encoding: from simple SHACL-Core shapes to the SPARQL formalization.

The scenario changes though when a separator qualifier property is introduced. According to both possible interpretations I1 and I2 it is necessary to compare the values obtained through (shared) separators to assess uniqueness. However, it is not possible to compare the values of different paths that correspond to unique combinations of separators in SHACL-Core, i.e., it is not possible to distinguish different nodes matching the same regular path expression.

To illustrate this, consider again the instantiation of the separator qualifier for the single-value (Q19474404) constraint on the property capital (P36) from Fig. 9. In order to not have to distinguish between I1 and I2, it is sufficient to discuss the case with at most one separator here (i.e., a simplification of the actual constraint which (possibly) also involves other separator qualifiers). Intuitively speaking, a data graph validates this constraint if, for each node a of the graph, the following conditions hold: (i) node a has at most one capital-outgoing edge to a node that does not have separators defined, and (ii) if node a has capital-outgoing edges to two distinct nodes, then they must have start time edges and they must not have the same filler node for the start time edges… Clearly, (i) is easily representable in SHACL-Core by a combination of sh:maxCount 1 and negation sh:not:. E.g., in abstract syntax, the shape expression could be represented by the DL concept: ⩽1capital.(¬∃start time). However, to express condition (ii), we need mechanisms for identifying nodes along a path and for asserting identity properties on them, which are not supported in standard DLs. There has been significant research to extend DLs with identification constraints [17] or some sophisticated forms of path-based identification constraints [16]; the latter allows to consider complex paths with possibly inverse and non-functional properties, such as those in the Wikidata constraints. However, to the best of our knowledge, these DL extensions are not covered in SHACL-Core.

Therefore, the variants of all three, single-value (Q19474404)) distinct-values (Q21502410), and single-best-value (Q52060874) constraints which include separators cannot be represented in SHACL-Core. We additionally mention that, for analogous reasons, the single-best-value (Q52060874) constraint, used to specify that the property P shall only have a single value claim marked with wikibase:BestRank as wikibase:rank, is not expressible in SHACL-Core either, even without separators, due to a similar dependence on the rank.

We show in the next section how these remaining constraint types can be expressed with formalisms beyond SHACL-Core.

3.5.Beyond SHACL-Core: SHACL-SPARQL

Beyond its core language, SHACL provides a mechanism to refine constraints in terms of full SPARQL queries through a SPARQL-based constraint component (sh:sparql). In order to illustrate this feature, we refer to Figs 13a and 13b: both these SHACL shapes have the same semantics, while the shape in Fig. 13a uses only SHACL-Core language components, the one in Fig. 13b uses the sh:sparql extension to state that only one value is expected by means of a SPARQL query (starting at line 6): here, the reserved variable ?this refers to the target node, whereas the variables ?path and ?value denote the path and value pointing to a violation. We further demonstrate the versatility of this extension by gradually refining the query of Fig. 13b.

Figure 13c extends the SHACL-SPARQL shape the existence and – in case – equality of the start time (P580) qualifier, thereby implementing an extension towards handling a single separator.

However, as there may be several qualifiers, this shape is not sufficient. Figure 13d generalizes the SHACL shape to consider as violations entities that have qualifiers any with equal values, as such implementing interpretation I1 from Section 2.4.2. However, as we discussed there, this is again not the semantics used by Wikidata: finally, Fig. 13e implements the constraint according to interpretation I2 from Section 2.4.2. While we do not go into details to explain the relatively complex SPARQL query in the sh:sparql at this point (hang on until Section 4.2), we may ask the question first, whether SHACL with its limitations is at all the most adequate formalism for the kind of constraint checking we are looking for.

3.6.Towards SPARQL

In summary, we note the following limitations for the implementation of Wikidata property constraints via SHACL.

In summary, we observe that not all Wikidata constraints were possible to directly map as shapes in SHACL-Core.

As for the first item, clearly, the above-mentioned issues regarding the expressivity of Wikidata property constraints within SHACL-Core limit its applicability. Moreover, non-core features are unfortunately not mandatorily (and thus rarely) implemented by SHACL validators so far.

As for the second and third items, we argue that due to the limitations associated with the expressibility of the SHACL constraints and the lack of tools capable of efficiently validating large graphs, a direct SPARQL translation potentially presents itself as a more generic, flexible, and operationalizable approach for validating Wikidata Property constraints.

Let us demonstrate this idea with a straightforward SPARQL translation of a simple conflicts-with (Q21502838) constraint for the property family name (P734), which, according to the constraint property (P2306) qualifier should not be used together with the property given name version for another gender (P1560), as expressible relatively concisely in the following SHACL shape:

An even more direct and crisp, and also executable formulation of this constraint can be easily constructed by the following SPARQL query:

In fact, we claim that violations of this particular constraint type, i.e. the conflicts-with constraint, could be checked more generally on all properties in one go, with a single SPARQL query:4141

Indeed, this single query checks all violations of the conflicts-with constraint type and returns all violations of conflicts-with constraints at once. Intuitively, lines 2–3 lookup properties ?wdtprop and the corresponding entity ?wdprop (cf. the illustration in Fig. 7) having a conflict-with constraint (line 3) and retrieving the respective conflicting property ?conflicting_wdtprop (line 4). Finally, lines 5–6 check the existence of a statement using both conflicting properties for the target ?T. The query is executable directly on the Wikidata SPARQL endpoint, cf. Footnote 41, with the slight limitation that we need to LIMIT the results retrieved, as overall too many such violations exist to be retrieved via the UI at once; more details on that will be provided in our experiments section (Section 5). We stress that SHACL is not amenable to this approach: as a declarative constraint language, it does not have the querying capability to extract all constrained properties and their violations at once.

Overall, we hope the illustrative examples in this section have sufficiently motivated that a direct translation of property constraints to SPARQL has advantages over SHACL for various reasons. That is, while in this section we in principle have made a case for using (a subset of) Wikidata’s property constraints as a “playground” to automatically generate a large testbed for SHACL(-Core) validators (and have also sketched how to extend this approach to SHACL-SPARQL), we also hope to have convinced the reader that this approach is not (yet) practically feasible, and in the end have made a case for direct generalizing our approach to fully operationalize Wikidata constraint validation via SPARQL.

4.1.Expressing and validating Wikidata constraints in SPARQL

In this section, we describe the overall structure of our Wikidata constraint validation approach using SPARQL queries. We again illustrate it via our running example from Fig. 8.

Figure 15a presents a generic structure followed by each SPARQL query proposed in this paper. We generalize queries into different “blocks”, such that each block can contain multiple triple patterns as exemplified in Fig. 15b, which fulfill different functions. Figure 15b represents the concrete query for the item-requires-statement constraint: for this constraint type a required property and its required value(s) need to be checked. Each block of the query structure of Fig. 15b is detailed as follows.

Block #1, i.e., the SELECT clause, represents the information to be returned by the query describing the violation; usually it is composed of the claim containing the property that is violating the constraint (Fig. 15b line 2), plus extra information about the triple or about the constraint – in our case, the property missing for the subject – (line 3), and finally, we also return the constraint status or reason for deprecation (line 4), if given.

Block #2 i.e., the beginning of WHERE clause, matches the properties (and associated statements) that use the particular constraint type (lines 6 and 7) – in our case for the item-requires-statement (Q21503247). To retrieve properties using another specific property constraint type, one obviously only needs to adapt the constraint id in line 7.

Block #3: statements from Block #2 are then used to retrieve the required constraint qualifiers for the specific constraint type (lines 9 and 10), i.e., in our case the required property (line 9) and value (line 10), as explained in Section 3 above, plus optional qualifiers such as the constraint status or information about constraint deprecation (lines 12 and 13). We note that these additional OPTIONAL parts may affect query performance, and could be potentially left out, but we suggest retrieving them if present for additional detailed information about actual violations.

Block #4 matches the actual statements that must be checked for constraint verification (line 15). As we can see in this example, we need to navigate between the different property namespaces described in Fig. 7 above before matching the subject and object (line 16).

Block #5 combines the statement qualifiers values from Block #3 and the triples from Block #4 to check the actual violation. For the item-requires-statement constraint, the goal is to check the non-existence of the required property along with the required value (lines 19 and 20) while removing the explicit exceptions (P2303) to the constraint (line 22).

Block #6 is optional with the intention to parameterize the query. The FILTER restricts the query to retrieve violations for one specific property, in our case, “FIFA player ID” (line 24). Although our queries are designed to retrieve violations for all properties of a single constraint type, we recommend execution for a specific property at a time due to Wikidata’s size and the limitation of resources available on the online endpoint.

We have encoded all 32 constraint types (some of which are in separate queries for different variations) in SPARQL queries, following similar patterns corresponding to Block#1–Block#6 in our example. These queries are designed to retrieve information about any violations (somewhat orthogonal to the SHACL encodings that model conformance instead). The full list of these SPARQL queries can be found in Table 2 – as shortcut links to our GitHub repository (cf. Footnote 35), and executable on Wikidata’s query service. The list contains examples for checking particular properties per constraint type. For instance, our query https://short.wu.ac.at/72ng implementing the FIFA Player ID’s item-requires-statement constraint returned 190 violations, as opposed to the 192 on Wikidata’s database report page (cf. Footnote 43) at the time of writing. In our formalization, we divide the item-requires statement constraint checking into two queries, one including required properties and another including required properties and values. The second query https://short.wu.ac.at/rmba retrieves the remaining 2 violations. Although both checks could be combined in one UNION query, we prefer this design with multiple queries in case of different possible constraint variations, cf. the respective lines of Table 2 pointing to multiple queries.

Again, we note that apart from Wikidata itself, there are an increasing number of other Wikibase instances listed in the Wikibase Registry4444 that partially re-use Wikidata’s property constraints. Obviously, for Wikibase instances that declare constraints using the Wikidata property constraints model, it should likewise be possible to check constraint violations on Wikibase instances using our SPARQL templates. For instance, The EU Knowledge Graph4545 is a Wikibase knowledge graph containing information about institutions of the European Union, countries, projects financed by the EU and their beneficiaries [23], which imports Wikidata’s property constraints. As an example, we used our SPARQL template to search for format constraint violations on this KG, with our query https://short.wu.ac.at/xmsm returning 472 violations at the time of writing.

4.2.Formalizing constraint types not captured with SHACL-Core in SPARQL

We now show how to formally express the constraint types that could not be directly represented with SHACL-Core in SPARQL.

Single-value Used to specify that one property generally contains a single value per concept, we already discussed the partial representability within SHACL-Core, when there are no separators defined. The following SPARQL query for the property capital (P36) shows how to capture violations in two scenarios: either there are multiple different values with no separators or there are separators with equal values. Block 4 binds multiple statements that are further tested in block 5. In block 5, it is tested if the values are different (line 14), if there are no separators (lines 16–19), or if it does not exist a separator (line 23) where the separator values (lines 24 and 25) for two different statements are different (line 26). Overall, this captures the intended semantics I2, described in Section 2.4.2. The same principle also applies for distinct-values and single-best-value, the two other constraint types that make use of separator qualifiers and can be expressed in SPARQL similarly, for details we refer to the links in Table 2.

Allowed qualifiers This constraint type specifies that only the listed qualifiers should be used when a certain statement is made, meaning that the use of all other qualifiers needs to be restricted. Since there is no way to list non-allowed paths implicitly (e.g. by referring to a path/property via a specific type), this constraint could not be expressed with SHACL-Core. However, when using SPARQL, it is possible to test all the predicates where the statement node is a subject. The following query presents the SPARQL formalization for property party chief representative (P210), where Block 4 binds all the statements about P210 (line 6) and their respective qualifiers (lines 7 and 8). Next, Block 5 creates the violation pattern, where the statement of Block 4 is considered a violation if at least one found qualifier is not part of the set of expected ones.

Difference-within-range The constraint requires the difference between two values to be calculated and compared to a predefined range. SHACL-Core provides functionalities for checking equalities and inequalities, but it does not encompass arithmetic operations as part of its components. Below we present a simplified version of the query to check difference-within-range violations for date of burial or cremation (P4602). Block 3 binds all the necessary qualifiers, such as the minimum and maximum value (lines 10 and 11) and the property necessary to create a valid range (line 12), which in this case is date of death (P570). Block 4 binds the values for P4602 and P570. Finally, the interval is compared with the expected period (block 5).

6.1.One-of constraint

The first results concern the One-of constraint, and they are available in Table 3. Three properties were skipped for this constraint type due to timeout issues on the Wikidata SPARQL endpoint.

For genre (P136), 11 violations were not found by our approach because the SPARQL queries (cf. explanation of Block#4 above) are checking constraints on the exported truthy statements in the Wikidata RDF dump,4949 i.e., the non-deprecated statements in the wdt: namespace, which include the PreferredRank values (when there is one) when there are multiple values and the NormalRank values when there is no PreferredRank. Due to this, 8 out of 11 subjects were found by our approach but associated with different values. For instance, we found Baroque music (Q8361) as the PreferredRank and a violation for the entity Johann Sebastian Bach (Q1339), while for the Wikidata Reports western classical music (Q9730), a NormalRank object is a violation. In applies to part (P518), the 147 violations identified by both approaches contain the property P518 used as the main property (wdt: prefix), and these violations are also highlighted by the Wikidata page of each entity in the UI,5050 e.g. elder abuse (Q427883) has three different values for P518; all of their violations to the constraint. Notably, the remaining reported violations not identified by the SPARQL query are also not considered violations in the Wikidata pages in the UI, because the property P518 is used as a qualifier in these cases. For instance, Catalan Countries (Q234963) has Italy (Q38) as country (P17), but this applies to part (P518) Alghero (Q166282). Currently, this is not displayed as a violation by the Wikidata pages, but the Database reports are testing the constraint also for qualifiers. In our case, it would be necessary to adapt the triple pattern “?s wdt:P518?o” to alternatively also test the qualifier namespace (pq:) if one wants to test the query also for qualifiers.

The four violations not captured by our approach for the property distribution format (P437) are due to the same reason highlighted for P136. We identified these four subjects but since the property has multiple values and there is one PreferredRank value, the SPARQL query computes the violation for the value in the PreferredRank. For instance, The Simpsons (Q886) has video on demand (Q723685) and terrestrial television (Q175122) as distribution format (P437) but terrestrial television (Q175122) is marked as the PreferredRank. While the SPARQL query captures a violation for terrestrial television (Q175122), Wikidata Reports captures a violation for video on demand (Q723685). Again, for sport (P641), the four violations are regarding multiple values with different Ranks. For instance, Tove Alexandersson (Q113200) has sport (P641) orienteering (Q29358), ski orienteering (Q428242), skyrunning (Q3962667), and ski mountaineering (Q1075998). In addition, orienteering (Q29358) is the PreferredRank. While the SPARQL query captures orienteering (Q29358) as the violation, the Wikidata reports capture the other values. The analysis of the one-of constraint for the property P641 reveals that an improvement option would be: instead of listing every possible sports type, the constraint could refer to a superclass of sports and include hierarchical class inference when testing the constraint. Therefore, all the orienteering types would be under the same subclass of sport and it would not be necessary to add a new type of sport to the constraint once this type is connected to a superclass.

Lastly, in academic degree (P512), the 10 missing violations stem again from the lack of existence of the triple pattern “?s wdt:P512?o” between the tested subject and object (checking only preferred or truthy statements, as discussed above). A simple adaptation of the query to also check non-preferred statements could be achieved by replacing “?s wdt:PID?o” with “?s p:PID/ps:PID?o”. This allows for consideration of all possible statement nodes as demonstrated in query https://w.wiki/6HKA. This query shows that the proposed adaptation is able to find all the four violating values described for Tove Alexandersson (Q113200) and sport (P641).

6.2.Item-requires-statement constraint

For Item requires statement constraints (IRS), which are very common, ten properties were skipped due to the timeout in the Wikidata SPARQL endpoint. The values displayed in the VA column of Table 4 can exceed the value 5001 for this constraint type because the same property can have multiple IRS instances. Moreover, such instances can request the existence of only one property or a pair ⟨property, value⟩. Therefore, the Wikidata database reports present a list of violations for each instance of IRS, which we summed up in tables to report the respective VA numbers.

In Table 4, note that for the top 3 properties (P1559, P1976, and P2539), our approach found all the available violations and some extra violations that unfortunately cannot be compared because the results available in the Wikidata database reports are incomplete. For ResearcherID (P1053), five statements were not captured by our queries due to deprecated values, i.e., again, Wikidata does not match the pattern “?s wdt:P1053?o” when?o is deprecated (i.e., non-truthy). Further, on property P1053, Wikidata database reports point to four violations on the IRS with the required property instance of (P31) and value human (Q5). Our approach identified these four violations and two more not reported by the database reports: Milieu Intérieur Consortium (Q86498220) and Wolfgang Wagner (Q73833983). The first one is an instance of project (Q170584), and the second one has conflation (Q14946528) as the PreferredRank value. In this case, we can also notice a bad usage of the constraint, because the IRS constraint was used to restrict the type of the subject, simulating the behavior of what should actually be a subject type constraint.

The 90 violations not found by our SPARQL query for IUCN protected areas category (P814) are because the objects are empty values. Therefore, as the Wikidata RDF dump does not contain “?s wdt:P814 ⟨empty⟩” for empty objects we can not retrieve them. For instance, Sandgrube Seligenthal (Q2220711) has an empty value for IUCN protected areas category (P814). We demonstrate, using query https://short.wu.ac.at/5be5, that again our approach could be easily adapted to include empty objects by replacing the “?s wdt:PID []” pattern by “?s p:PID []”. Yet again, whether empty values should be reported as violations here or not is in our opinion a matter of interpretation.

6.3.Single-value constraint

The statistic table of the Wikidata database reports points to Single-value constraint as the third most violated constraint type. We notice that this statistic takes into account Single-value (Q19474404) and Single-Best-value (Q52060874) constraints. Therefore, it was necessary to use the queries designed for these two types of constraints to perform the experiment. Eleven properties were skipped for presenting timeout in the SPARQL endpoint for at least one of the query types. The results are presented in Table 5, where, unlike the previous tables, we include in columns VA and OV the total number of unique entities found, i.e., the total number without repeated entities.

In type of variable star (P881), V Sagittae (Q56303735) is pointed as a violation by the database reports but not by the Wikidata entity page and not by our query. V Sagittae (Q56303735) has indeed two values for type of variable star (P881): nova-like star (Q9283100) and eclipsing binary star (Q1457376). However, nova-like star (Q9283100) is marked as the PreferredRank value, therefore we do not take this as a violation. According to the definition of single-best-value, the property generally contains a single “best” value per item, though other values may be included as long as the “best” value is marked with PreferredRank. For surface gravity (P7015), SDSS J1539+0239 (Q4048714) is pointed as a violation by the database reports but, interestingly neither by the Wikidata entity page UI nor by our query. SDSS J1539+0239 (Q4048714) has indeed two values for surface gravity (P7015): “1,450 centimeter per square second” and “3±0.15”. However, “3±0.15” is marked as the PreferredRank value, therefore we do not consider this a violation because it is in accordance with the definition.

The analysis of male population (P1540) reveals that there are 5073 unique entities reported by Wikidata database reports as violations and not reported by our approach. 4841 of them have a PreferredRank defined, therefore we do not consider them violations. The other 232 we captured with our query. The same is also the case for female population (P1539), where 5076 unique entities were reported by the Wikidata database as violations and not reported by our approach. 4832 of them have a PreferredRank and the other 244 we identified. Finally, for the property metallicity (P2227), the two entities that database reports consider violations are HD 1461 (Q523743) and SDSS J1539+0239 (Q4048714). Again, our approach does not consider them as violations because, although they have multiple values, in both cases there is a value marked with PreferredRank. In fact, the respective pages in the Wikidata UI also do not highlight violations for these statements.

The occurrence of properties from the astronomy domain, such as type of variable star (P881) and surface gravity (P7015), was expected, since the astronomy community in Wikidata uses deprecation and different rankings to represent historical data, as also observed in [55]. Therefore, it is common to find statements with multiple values, where the higher-ranked ones represent more accurate or currently accepted data by the community.

6.4.Required qualifier constraint

The required qualifier constraint has the same principle described for IRS: the same property can have multiple instances of the required qualifier constraint, each one of them requiring a different property to be used as a qualifier for a given statement. For this constraint type, which again is very common, three properties were skipped due to timeout on the Wikidata SPARQL endpoint, where the properties with the next highest violation rates were selected. The results are available in Table 6, showing that the whole set of available violations (VA) was found by our SPARQL approach (OV).

6.5.Value-requires-statement constraint

Finally, Value-requires statement constraints (VRS) are similar to IRS, but instead of requiring the existence of a statement in the subject, these quite common constraints require a statement in the object. Ten overly common properties were skipped due to timeouts in the SPARQL endpoint. Two different queries were used for each property, one checking required properties and another checking pairs of required properties and values. The main results are available in Table 7.

For molecular function (P680) and associated cadastral district (P10254), the intersection is equal to the number of violations published by the Wikidata database reports. The eight statements not found for has edition or translation (P747) and the 18 for consecrator (P1598) are due to the existence of one PreferredRank value among multiple values. Lastly, for the most violated property, heritage designation (P1435), the 13 statements claimed as violations by database reports and not reported by our approach fall into the same category. There are multiple values and one of them is marked as PreferredRank value, therefore the pattern “?s wdt:P1435?o” does not capture the remaining values. For instance, Vatican City (Q237) has as heritage designation (P1435) the values UNESCO World Heritage Site (Q9259) and Cultural property under special protection (Q26086651), however UNESCO World Heritage Site (Q9259) is marked as the PreferredRank. Our query can be easily adapted to focus on the statement nodes instead of the direct value, as illustrated in query https://short.wu.ac.at/xasn. It is only necessary to replace “?s wdt:P1435?o” by “?s p:P1435/ps:P1435?o”.

In summary, common reasons for mismatches include – as a matter of interpretation – whether only truthy statements or also non-preferred and deprecated statements should be checked for constraint violations. Also, other deviations could arguably be identified as a matter of interpretation. As we also discussed, our constraints could be adapted to the respective different interpretations relatively easily with minor modifications of our query patterns. Overall, while we only conducted these analyses on a sample, we argue that the experiment has confirmed our opinion that a declarative and adaptable formulation of Wikidata property constraints in terms of SPARQL queries is both feasible and could add to the clarification of the constraints’ actual semantics. The deviations between the Wikidata UI pages and the Wikidata database reports confirm our opinion that such clarification is dearly needed.

Regarding the practical feasibility of the proposed approach, it is important to acknowledge the generic nature of the SPARQL queries proposed in this study. The absence of hard-coded parameters ensures adaptability to diverse constraint parameters, with queries exclusively relying on the Wikidata data model to match the triple patterns that generate specific constraint violations. This flexibility enables the applicability of generic queries checking violations across all properties instantiating a specific constraint type. On the downside, as we have discussed, such generic queries potentially lead to scalability problems for current SPARQL engines. As a practical workaround, constraints can also be checked by instantiating our generic queries per property, mitigating scalability challenges to a certain extent: in the context of the Wikidata ecosystem, the envisaged solution is therefore promising for deployment as a background process capable of processing batches of properties. By doing so, the system can systematically uncover candidate inconsistencies, according to the available resources and relevance of properties.

7.1.Constraint languages for graph data

RDF has long served as the W3C-recommended graph-based data model for presenting information in the Semantic Web, whereas a standardized language to express and validate data graphs has only recently been introduced. Ontology languages like RDFS, OWL, and its sublanguages, which have been standardized along with RDF, have been widely used for modeling the data through axiomatic structures. For instance, DBpedia, like other open knowledge graphs (e.g. YAGO, GeoNames), makes use of ontologies to model the data, which have been employed also for detecting (some) inconsistencies (e.g., [11,48]). However, ontologies have been particularly criticized for their limited use when checking the conformance of data graphs. Indeed, the primary utility of ontologies lies in facilitating deductive reasoning tasks, such as node classification or evaluating overall satisfiability, and not in describing constraints on KGs. With the growing emphasis on data accuracy for graph-based applications, the absence of constraint languages similar to those found in relational [3] and semi-structured data [2] contexts became noticeable. To address this gap, multiple strategies have emerged. Hogan [38] used rule-based fragments of OWL/RDFS for scalable inconsistency identification and repair suggestions. The idea to use scalable variants of bespoke Datalog-based reasoning for constraint checking and verification originally imposed in Hogan’s thesis may be argued to be not unlike our approach: SPARQL has been shown to be equally expressive as non-recursive Datalog with negation [8], where features like property paths only mildly add harmless, linear recursion [51]. Another line of research regards extending ontology languages to treat axioms as integrity constraints under the closed-world assumption [45,58].

In particular, to address the lack of dedicated constraint languages for graph data, novel schema formalisms for RDF graph validation like the Shape Expressions language (ShEx) [13,29,56,57] were proposed before SHACL became a W3C recommendation. ShEx is a formal modeling and validation language for RDF data, which allows for the declaration of expected properties, cardinalities, and the type and structure of their objects. ShEx is closely related to SHACL, and in some cases, it is possible to translate SHACL shapes into ShEx shape expressions since their expressiveness is similar for common cases [29]. For instance, the shapes graph presented in Fig. 10 can be respectively represented in ShEx as follows:

Yet, we leave a full discussion about whether our approach, and therefore all existing constraint types transfer over to ShEx as an open question to future work. Additionally, validation languages based on ShEx supporting the Wikibase data model have been recently proposed in the literature [28], however, they still lack support for many Wikibase constructs and there is no operational validator yet.

Furthermore, SPARQL-based approaches to validate knowledge graphs can also be found in the literature [42,59], including the SPARQL Inferencing Notation (SPIN) 5151 framework. SPARQL can also be used to validate numerical and statistical computations [29]. While in [42] the authors use SPARQL queries to validate and compute index data for linked data applications, in [59] SPARQL is used to specifically validate epidemiological data on Wikidata. Corman et al. proposed in cf. [20,22] a SPARQL-based method for validating possibly recursive SHACL shapes by translating them to SPARQL queries; non-recursive shapes are translated into single SPARQL queries. These queries are then directly evaluated on a SPARQL endpoint. They present a prototype implementation of their approach, called SHACL2SPARQL. Since in this work we translate the Wikidata constraints to SHACL shapes, a natural approach would have been to employ SHACL2SPARQL to generate the corresponding SPARQL queries. However, the primary focus of their algorithm is to handle fragments of recursive shapes, which makes validation significantly more involved. As a result, for the – in principle simple – non-recursive shapes we obtain in the present work, which however use a variety of SHACL-Core constructs not covered in SHACL2SPARQL, the prototype yields, in general, infeasible translations. More specifically, their approach generates SPARQL queries reporting violations by NOT EXISTS sub-queries expressing the conditions to be verified by the respective targets specified by the shapes graph. The construction of these subqueries is modularly defined via the SHACL grammar. For instance, consider a simple conflicts-with (Q21502838) constraint on the property family name (P734). According to the constraint property, it should not be used together with the property P1560 (given name version for another gender), as expressible concisely in the following SHACL shape:

According to Corman et al.’s translation, sh:maxCount 0 is again translatable to a NOT EXISTS query, yielding overall a query like the following with nested NOT EXISTS operators:

Unfortunately, this query currently times out on Wikidata’s SPARQL endpoint, mainly due to the nested negation yielding from a modular translation. The NOT EXISTS operator is particularly hard to evaluate for SPARQL engines. Also note that our SPARQL formulation, to be executable at all, needs to “copy” the target definition within the verification part (line 3), due to the broken recursive correlation semantics of the (NOT) EXISTS operator in SPARQL, cf. [35,47]. A more direct and crisp, and also executable formulation of this query can be easily constructed:

In addition, not all Wikidata constraints could be directly represented in SHACL-Core. We therefore had to devise specific SPARQL queries for each of the 32 Wikidata constraint types to generate viable and functional solutions.

7.2.Constraints in Wikidata

Data restrictions within Wikidata are also discussed by the community and implemented through further projects using other pre-established technologies. For instance, the Wikidata Schemas project5252 relies on ShEx. As opposed to property constraints, the Schemas Project is focused on defining entity (Wikidata concepts) restrictions. At the time of writing, Wikidata has more than 200k classes5353 and the Schemas project counts with 375 ShEx schemas.5454 This is a ratio of approximately only 0.2% of all classes having a defined ShEx schema. On the other hand, 99% of properties (107885555 out of 108125656) are restricted by at least one property constraint type. These numbers illustrate that the impact of understanding the semantics of property constraints is – at the moment – more significant than ShEx schemas. A separate analysis would be required for analyzing the Schemas project in more detail: taking, for instance, the entity schema E105757 for the class human as an example, using ShEx as rather descriptive than prescriptive constraint language [14], some properties are highlighted as “desired” properties only in the schema. For instance, in the mentioned schema E10, the property mother (P25) is defined with a Kleene star

  wdt:P25 @<human> *;

meaning that the absence of a “mother” does not lead to inconsistencies, which indicates that the objective of such schema is rather to assist in the “design” of classes than constraint checking in the strict sense. Also, although there are some ShEx to SHACL conversion tools,5858 additional challenges related to recursion impose further limitations on the process [29], as a lot of the theoretical work on SHACL either restricts or excludes recursive shapes (e.g. [20,22]. The mentioned entity schema E10, for instance, restricts fathers, mothers, siblings, etc. also (recursively) to be humans. The SHACL shapes we obtain from the translation of Wikidata constraints are all non-recursive and make use of also SHACL-Core features that have not been yet universally implemented in validators.

Erxleben et al. [24] exploit properties describing taxonomic relations in Wikidata to extract an OWL ontology from Wikidata. The authors also propose the extraction of schematic information from property constraints and discuss their expressibility in terms of OWL axioms. However, whereas we focus herein concretely on covering all property constraints as a means to find possible violations in the data, Erxleben and colleagues rather stress the value of their corresponding OWL ontology as a (declarative) high-level description of the data, without claiming complete coverage of all Wikidata property constraints.

Martin and Patel-Schneider [44] discuss the representation of Wikidata property constraints through multi-attributed relational structures (MARS), as a logical framework for Wikidata. Constraints are represented in MARS using extended multi-attributed predicate logic (eMAPL), providing a logical characterization for constraints. Despite covering 26 different constraint types, to the best of our knowledge, the authors have not performed experiments to evaluate the accuracy of the proposed formalization, nor its efficiency, and do not discuss implementability. In fact, the theoretical framework partially skips over the subtleties of checking certain constraints in practice. As an example, the translation of allowed entity types constraints in the extended version of [44] assumes that entity types in Wikidata can be checked via simple instance-of type checking. Our SPARQL query shows that this is not the case in practice for all entity types as they are differently represented in the actual Wikidata RDF dump.5959 Our work – focusing on the practical implementability of property constraints in SPARQL – complements such theoretical approaches.

Abián et al. [1] propose a definition of contemporary constraint that was indeed later adopted by Wikidata property constraints. Shenoy et al. [55] present a quality analysis of Wikidata focusing on correctness, checking for weak statements under three main indicators: constraint violation, community agreement, and deprecation. The premise is that a statement receives a low-quality score when it violates some constraint, highlighting the importance of constraints for KG refinement. Boneva et al. [12] present a tool for designing/editing shape constraints in SHACL and ShEx suggesting Wikidata as a potential use case, but – to the best of our knowledge – without exhaustively covering or discussing the existing Wikidata property constraints.

Apart from works specifically on constraint for Wikidata, in [48] the authors systematically identify errors in DBpedia, using the DOLCE ontology as background knowledge to find inconsistencies in the assertional axioms. They feed target information extracted from DBpedia and linked to the DOLCE ontology into a reasoner checking for inconsistencies. Before, Bischof et al. [11] already highlighted logical inconsistencies in DBpedia which can be detected using OWL QL, rewritten to SPARQL 1.1 property paths – not unlike our general approach.

7.3.SHACL and SPARQL benchmarks

Despite the partially negative result that some of our SPARQL queries time out, and also – as we discussed above – we did not find SHACL validators that would allow us to check our constraint violations at the scale of Wikidata, we believe, besides our primary goal of clarifying Wikidata property constraint semantics, our results should be considered as a real-world challenge benchmark for both SPARQL engines and SHACL validators.

As for SHACL, real-world performance benchmarks still seem to be rare. Schaffenrath et al. [53] have presented a benchmark consisting of 58 SHACL shapes over a graph with 1M N-quads sample from a tourism knowledge graph, evaluated with different graph databases, emphasizing that “larger data exceeded […] available resources”. The shapes we present are on the one hand targeting an (orders of magnitude) larger dataset, but on the other hand can also be evaluated locally on a per entity level, thus providing a benchmark of quite different nature. Also, the evolving nature of Wikidata makes a dynamic/evolving benchmark that can be evaluated/scaled along the natural evolution and growth of Wikidata itself. Next, [27] presents a synthetic SHACL benchmark derived from the famous LUBM ontology benchmark, while also emphasizing the current lack of real-world benchmarks for SHACL.

Closest but also orthogonal in focus to our own work is a recent paper by Rabbani et al. [52], which focuses on the orthogonal problem of automatically extracting shapes (representable as SHACL) from large KGs such as Wikidata in a data-driven manner, rather than on the formalization of community-driven constraints as we do.

Finally, apart from serving as a basis for novel benchmarks for SHACL, our SPARQL formalization particularly extends, and in our opinion complements, the existing landscape of real-world SPARQL benchmarks. Indeed, the – to the best of our knowledge – only benchmark for Wikidata, WDbench [6] covers a significantly different kind of Wikidata queries than we do. WDbench is a benchmark extracted from Wikidata query logs, focusing on queries that time out on the regular Wikidata query endpoint, but it is restricted to queries on truthy statements only, that is for instance not covering queries on qualifiers. Our queries on the contrary, by definition all relate to querying qualifiers and, as such they require the whole Wikidata graph and cannot be answered on the truthy statements alone. Yet, similar to the WDbench queries, many of the queries we present, particularly on very common properties, suffer from timeouts, as our experiments confirm. Thus, while the approach we present shows in principle feasible, it calls for novel more scalable approaches to efficiently solve such SPARQL queries that currently time out. We hope, as the queries we focus on typically only affect local contexts of entities and properties, they could hopefully be solved, e.g., by clever modularisation and partitioning techniques.