Applications in many industry sectors rely on quantity values with units of measures, for sensor observations, actuation, design calculations/simulations, quantitative general knowledge, etc. A typical way to convey the value of a quantity in RDF consists in using a structure with one triple providing a numerical value as a literal in standard datatypes (xsd:float,xsd:double,xsd:decimal), and a triple with an IRI identifying the unit. A dedicated ontology can define the properties that connect the quantity value to the numerical value and the unit. An alternative approach relies on custom datatypes [5].

In this paper, we introduce an RDF datatype,cdt:ucum, that transposes to RDF the full expressive power of the Unified Code for Units of Measure (UCUM [8]), enabling lightweight descriptions and querying of physical quantities using a single datatype. We currently provide 32 more specific datatypes such ascdt:speed andcdt:length to further specify the quantity kind of quantity values, but more datatypes may be introduced in the future.

We first show in Sect. 2 how quantity values are typically described in RDF with existing ontologies or custom datatypes. Then, in Sect. 3, we introduce thecdt:ucum datatype, highlighting the conciseness of the representation with many examples. Finally, in Sect. 4, we describe our implementation as an extension of Apache Jena with support forcdt:ucum in SPARQL queries, with an online testing tool.

We identify two approaches to represent physical quantities in RDF: using ontologies, or using custom datatypes.

Using ontologies of units of measurements. The classical approach consists in using an ontology to describe units, their relations, and measurements. A recent survey [4] compares and evaluates eight well known ontologies for units of measurements, among which MUO [6], QUDV [1], OM [7], QUDT [3]. This survey also report on the Wikidata corpus^Footnote1 that currently contains over 4.4 k measurement units and 4.1 k non-prefixed units. Using such ontologies, quantity values are usually represented as OWL individuals linked to some numeric value and to some individual representing a unit of measure. For example, Listing 1.1 represents the quantity value\(29 \ ^\circ \text {C}\) using QUDT 1.1.

Not all possible units of measurement are (or will be) defined in these ontologies, for example QUDT 1.1 defines a unit for kilowatt hour, but not megawatt hour. Application developers in the energy domain can force themselves to use units they are not used to, or they can define missing units using the definition mechanism provided by QUDT. This extension mechanism uses concepts such as base units, conversion offsets and multipliers, numerator and denominator. For example, Listing 1.2 illustrates how the unit megawatt hour may be defined. Even then, two energy operators may define the same unit using different URIs, leading to potential interoperability issues.

Datasets using quantity values defined with such ontologies require 4 triples every time a quantity needs to be linked to a quantity value, and complex mechanisms are needed to canonicalize quantity values so as to query them uniformly. We are not aware of any existing support of QUDT or OM custom units in any RDF or SPARQL engine.

Using datatypes. DBpedia has many datatypes^Footnote2, which are hard-coded inOntologyDatatypes.scala and listed in the DBpedia Mappings Wiki for reference. Dbpedia defines datatypes for physical dimensions (http://dbpedia.org/datatype/Area) along with datatypes for specific units of measures (http://dbpedia.org/datatype/cubicInch). Yet, these datatypes do not dereference, so one cannot understand if Inch here is in the international customary units, U.S. survey lengths, British Imperial lengths, for example. Again, not all possible units of measurement are (or will be) defined in the Dbpedia ontology, and complex mechanisms are needed to canonicalize quantity values so as to query them uniformly.

We previously proposed an approach for RDF and SPARQL engines to support arbitrarily complex custom datatypes on-the-fly by dereferencing their URIs and retrieving specifications in JavaScript [5]. In this paper we are exclusively interested in datatypes for quantity values, and do not consider on-the-fly support capabilities.

The Unified Code for Units of Measure (UCUM) [8] is a code system intended to includeall units of measures being contemporarily used in international science, engineering, and business.

We define a RDF datatype UCUM identified by IRIhttp://w3id.org/lindt/custom_datatypes#ucum, abbreviated ascdt:ucum. Its lexical space is the concatenation of anxsd:decimal, optionally followed by or and the lexical form of anxsd:integer, at least one space, and a unit chosen in the case sensitive version of the UCUM code system. The value space corresponds to the set of measures, or quantity values as defined by the International Systems of Quantities. The lexical-to-value mapping maps lexical forms with a UCUM unit to their corresponding measures according to the International Systems of Quantities.

We also define a set of additional datatypes such ascdt:length andcdt:speed that further specify the quantity kind of quantity values. Their lexical spaces, value spaces, and lexical-to-value mappings are subsets of those ofcdt:ucum. More such datatypes may be defined in the future. Table 1 lists examples of validcdt:ucum literals, and their equivalent using more specific datatypes.

The UCUM specification has implementations in different languages. We used the latest version ofsystems-ucum-java8^Footnote3, an implementation leveraging the recent Java units of measurement API 2.0 (JSR 385), to add support of the 33 datatypes specified above on top of Apache Jena. Our extension, namedjena-ucum, is open-source and available online^Footnote4. It overloads native SPARQL operators (=,<, etc.) to compare UCUM literals, and arithmetic functions (+, −, *, /) to manipulate quantity value literals: 1. Add two commensurable quantity value literals; 2. Subtract a quantity value literals to a commensurable one; 3. Multiply two quantity value literals, or a quantity value literal and a scalar (xsd:int,xsd:decimal,xsd:float,xsd:double); 4. Divide a quantity value literal by a quantity value literal, a quantity value literal by a scalar, or a scalar by a quantity value literal. We additionally define a custom SPARQL function with IRI:http://w3id.org/lindt/custom_datatypes#sameDimension which takes two parameters and returns true if they are commensurable quantity values.

Screenshot of the UCUM datatypes playgroundhttps://w3id.org/lindt/playground.html.

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We demonstrate the UCUM datatypes using a playground illustrated on Fig. 1 and accessible online.^Footnote5 The user can enter a SPARQL Construct or Select query and the default graph of the RDF Dataset on which it is evaluated. The result is computed in real-time and returned to the user using the WebSocket protocol.

Queries are predefined to progressively introduce the use of SPARQL comparison operators, arithmetic functions, solution sequence modifiers (ORDER BY). Other predefined queries are predefined to illustrate each of the 33 currently defined UCUM datatypes. We will also showcase how the UCUM datatypes may be used in combination with other vocabularies such as SOSA/SSN [2].

Using the UCUM datatypes, one only requires 1 triple to link a quantity to a fully qualified value, and one does not require custom mechanisms to canonicalize literals based on external descriptions of units of measurements. Using UCUM Datatypes, datasets are therefore drastically lightened, and queries are also simpler. The UCUM datatype can inherently represent an infinite set of custom units, and is therefore suitable for an open set of application domains.

A similar datatype could be defined to support amounts of money, potentially with any type of currencies and a timestamp for this currency.