More details about ShEx and SHACL can be found in the book by Labra Gayo et al. A shapes graph is formed from a set of interrelated shapes. The shapes schema from Figure3.3 can be expressed as: For example, Event is a shape label (an element of \(S\)) that maps to a shape (an element of \(\phi\)). We formally define shapes following the conventions ofLabra Gayo et al. We may also consider, for example, that bus and flight are both sub-properties of a more general property connectsto. We use \(e\) to denote an arbitrary identifier representing the edge itself to which the context can be associated. Conversely, we may define the range of properties, indicating the class(es) of entities for nodes to which edges with that property extend; for example, we may define that the range of city is a class City, inferring that AricatypeCity. Another option is to place constraints on the number of nodes conforming to a particular shape that the conforming node can relate to with a property (thus generating edges between shapes); for example, Eventvenue1..*Venue denotes that conforming nodes for Event must relate to at least one node with the property venue that conforms to the Venue shape. Using this property, we could state the edge chile:Santiagoowl:sameAsgeo:SantiagoDeChile in our RDF graph, thus establishing an identity link between the corresponding nodes in both graphs. The first way to represent context is to consider it as data no different from other data. This mapping is defined by \(\lambda\). However, it can be inconvenient if a system is unable to definitely answer yes or no to questions such as is there a flight between Arica and Via del Mar?, especially when the organisation is certain that it has complete knowledge of the flights. Other datatypes commonly used in RDF data include xsd:string, xsd:integer, xsd:decimal, xsd:boolean, etc. One can verify, for example, that a path matches \(x\)city\(\cdot\)(flight|bus)*\(z\) in Figure2.1 if and only if there is a path matching \(X\)city\(\cdot\)(flight|bus)*\(Z\) in Figure3.5 such that \(x \in X\) and \(z \in Z\).
The shapes map \(\sigma\) is a way of labelling the nodes of \(G\) with the labels of shapes from \(S\). The natural way to define join is as the union of the sets of days, giving \(\color{blue}\{[123,125],[276,279]\}\). Henceforth, we refer to a data graph as a collection of data represented as nodes and edges using one of the models discussed in Chapter2. Since identifiers can be arbitrary, it is common to add edges that provide a human-interpretable label for nodes, such as wd:Q2887rdfs:labelSantiago, indicating how people may refer to the subject node linguistically. This gives rise to the notion of bisimilar quotient graphs. A quotient graph can merge multiple nodes into one node, keeping the edges of its constituent nodes.
We will return to such semantics later in Chapter4. In this chapter we describe extensions of the data graph relating to schema, identity and context that provide additional structures for accumulating knowledge. For example, the dates for the event EID15 in Figure2.1 can be seen as representing a form of temporal context, indicating the temporal scope within which edges such as EID15venueSantaLuca are held true. and types (e.g., string, dateTime, etc.)
Without further details, however, disambiguating nodes of this form may rely on heuristics prone to error in more difficult cases. We may further combine contexts, such as to indicate that Arica is a Chilean city (geographic) since 1883 (temporal) per the Treaty of Ancn (provenance). and two operators to combine domain values: meet and join.7note 7 The join operator for annotations is different from the join operator for relational algebra.
Taking again the edge SantiagoflightArica, Figure3.9 illustrates three higher-arity representations of temporal context. The presence of a semantic schema may, however, require adapting the validating schema. Existential nodes are supported in RDF as blank nodes[Cyganiak et al., 2014], which are also commonly used to support modelling complex elements in graphs, such as RDF lists[Cyganiak et al., 2014, Hogan et al., 2014]. The persistence of HTTP IRIs can then be improved by using namespaces defined through PURL services. An interesting property of bisimilarity is that it preserves forward-directed paths: given a path expression \(r\) without inverses and two bisimilar graphs, \(r\) will match a path in one graph if and only if it matches a corresponding path in the other bisimilar graph. \(\sigma(\)EID15, Event\() = 1\), \(\sigma(\)Santa Luca, Venue\() = 1\), \(\sigma(\)Santa Luca, Place\() = 1\), etc., but where \(\sigma(\)EID16, Event\() = 0\) (as it does not have the required values for start and end), etc., then we see that \(G\) is valid under \(\Sigma\) and \(T\). Thus while semantic schemata allow for inferring new graph data, validating schemata allow for validating a given data graph with respect to some constraints. More complex semantics for example, based on Kleenes three-valued logic[Corman et al., 2018, Labra Gayo et al., 2019] have been proposed that support partial shapes maps, where the satisfaction of some nodes for some shapes can be left as undefined. We now discuss various representations by which context can be made explicit at different levels. A second option is to use identity links to state that a local entity has the same identity as another coreferent entity found in an external source; an instantiation of this concept can be found in the OWL standard, which defines the owl:sameAs property relating coreferent entities. [2018].
However, a data graph will often exhibit latent structures that can be automatically extracted as an emergent schema[Pham et al., 2015] (aka graph summary[Liu et al., 2018, ebiri et al., 2019, Spahiu et al., 2016]). Taking the graph \(G\) from Figure2.1 and the shapes schema \(\Sigma\) from Figure3.3, first assume an empty shapes target \(T = \{\}\). The semantics of owl:sameAs defined by the OWL standard then allows us to combine the data for both nodes. We discuss three types of graph schemata: semantic, validating, and emergent. Second, we can use a property graph (Figure3.9b) where the temporal context is defined as a property on the edge. Most practical data models for graphs allow for defining nodes that are datatype values. Figure2.1 uses nodes like Santiago, but to which Santiago does this node refer? Such techniques aim to summarise the data graph into a higher-level topology.
There are many ways in which quotient graphs may be defined, depending on the equivalence relation that partitions nodes. We refer the reader to the respective papers for more details[Serafini and Homola, 2012, Schuetz et al., 2021]. However, shapes languages that freely combine recursion and negation may lead to semantic problems, depending on how their semantics are defined. If HTTP IRIs are used to identify the graphs entities, when the IRI is looked up (via HTTP), the web-server can return (or redirect to) a description of that entity in formats such as RDF. A notable example is that of contextual knowledge repositories[Serafini and Homola, 2012], which allow for assigning individual (sub-)graphs to their own context. This syntactic form is further recognisable by machine, meaning that with appropriate software, we could order such values in ascending or descending order, extract the year, etc. Assume we wished to compare tourism in Chile and Cuba, and we have acquired an appropriate knowledge graph for Cuba similar to the one we have for Chile. The least flexible option is RDF*, which, in the absence of an edge id, does not permit different groups of contextual values to be assigned to an edge; for example, if we add four contextual values to the edge ChilepresidentM.
[2012].
More generally, the semantics of terms used in a graph can be defined in much more depth than seen here, as is supported by the Web Ontology Language (OWL) standard[Hitzler et al., 2012] for RDF graphs. Consider the two date-times on the left of Figure2.1: how should we assign these nodes persistent/global identifiers? Considering our running example, it would be unreasonable to assume that the tourism organisation has complete knowledge of everything describable in its knowledge graph, and hence adopting the OWA appears more appropriate. Schuetz et al. if \((v'p,w') \in E'\) then there exists \(w\) such that \((v,p,w) \in E\) and \((w,w') \in R\). We refer to Hernndez et al. These edges denote that there exists a common venue for chile:EID42 and chile:EID42 without identifying it. Each dimension is associated with a partial order over its values e.g., 2020-03-22 \(\preceq\) 2020-03 \(\preceq\) 2020 enabling the selection and combination of sub-graphs that are valid within contexts at different granularities.
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