It may seem as though “$red$” is a reasonable property to ascribe to things in the world. You may do this because you want to tell the delivery robot to go and get the red parcel. In the world, there are surfaces absorbing some frequencies and reflecting other frequencies of light. Some user may have decided that, for some application, some particular set of reflectance properties should be called $red$. Some other modeler might decide on another mapping of the spectrum and use the terms $pink$, $scarlet$, $ruby$, and $crimson$, and yet another modeler may divide the spectrum into regions that do not correspond to words in any language but are those regions most useful to distinguish different categories of individuals.

Suppose you decide that “red” is an appropriate category for classifying individuals. You could treat the name $red$ as a unary relation and write that parcel $a$ is red:

If you represent the color information in this way, then you can easily ask what is red:

The $X$ returned are the red individuals.

With this representation, it is hard to ask the question “What color is parcel $a$?” In the syntax of definite clauses, you cannot ask

because, in languages based on first-order logic, predicate names cannot be variables. In second-order or higher-order logic, this may return any property of $a$, not just its color.

There are alternative representations that allow you to ask about the color of parcel $a$. There is nothing in the world that forces you to make $red$ a predicate. You could just as easily say that colors are individuals too, and you could use the constant $red$ to denote the color red. Given that $red$ is a constant, you can use the predicate $color$ where $color(Ind,Val)$ means that physical individual $Ind$ has color $Val$. “Parcel $a$ is red” can now be written as

What you have done is reconceive the world: the world now consists of colors as individuals that you can name. There is now a new binary relation $color$ between physical individuals and colors. Under this new representation you can ask “What has color red?” with the query

and ask “What color is block $a$?” with the query

It seems as though there is no disadvantage to the new representation of colors in the previous example. Everything that could be done before can be done now. It is not much more difficult to write $color(X,red)$ than $red(X)$, but you can now ask about the color of things. So the question arises of whether you can do this to every relation, and what do you end up with?

You can do a similar analysis for the $color$ predicate as for the $red$ predicate in Example 16.2. The representation with $color$ as a predicate does not allow you to ask the question “Which property of parcel $a$ has value $red$?” where the appropriate answer is “color.” Carrying out a similar transformation to that of Example 16.2, you can reify properties such as $color$ as individuals, and invent a relation $prop$ and write “individual $a$ has the $color$ $red$” as

This representation allows for all of the queries of this and the previous example. You do not have to do this again, because you can write all relations in terms of the $prop$ relation.

Consider $parcel(a)$, which means that $a$ is a parcel; there are two ways to represent it using triples.

The first is to reify the concept parcel to say that $a$ is a parcel:

where $type$ is a property that relates an individual to a class. The constant $parcel$ denotes the class of all, real or potential, things that are parcels. This triple specifies that the individual $a$ is in the class $parcel$. The property $type$ is sometimes written as is_a, in which case the triple represents “a is_a parcel”.

The second is to make parcel a property and write “$a$ is a parcel” as

In this representation, $parcel$ is a Boolean property which is true of things that are parcels. The property corresponds to an indicator variable used in CSPs and in machine learning.

The verb “give” requires three participants: an agent giving, a recipient, and a patient (the item being given). The sentence “Alex gave Chris a book” loses information if only two of the entities involved are specified in a relation. It could be represented by $gave(alex,chris,book)$. It can be represented using triples by inventing a giving act, say $ga3545$, with the triples:

Here, $ga3545$ is a reified entity denoting the action, and $b342$ is the book given. The $agent$ is the one carrying out the action, the $patient$ is the object the action is carried out on, and the $recipient$ is the one receiving the patient. The properties $agent$, $patient$, and $recipient$ are thematic relations or semantic roles used for giving meaning to sentences. The reification allows for other properties of the giving act, such as the date or perhaps the price paid.

Christine Sinclair is a Canadian association football (soccer) player, who has scored more goals than any other player in international play. In Wikidata [2021], Christine Sinclair is represented using the identifier “http://www.wikidata.org/entity/Q262802”, which we shorten to “Q262802”. Wikidata uses this to disambiguate the footballer from any other person called Christine Sinclair. The identifier “http://www.wikidata.org/entity/Q262802” denotes the footballer, not the web page (which doesn’t play football).

Wikidata uses unique identifiers for properties. For example, it uses the identifier “http://schema.org/name” for the property that gives the name of the subject. We use “name”, but remember that it is an abbreviation for the property defined by schema.org. If you don’t want that meaning, you should use another identifier. The value of a triple with “name” as the property is the pair of a string and a language, such as (“Christine Sinclair”,en).

Wikidata uses “http://www.wikidata.org/prop/direct/P27” for the property “country of citizenship”, where the subject is a person and the object is a country they are a citizen of. Canada is “http://www.wikidata.org/entity/Q16”, so “Christine Sinclair is a citizen of Canada” is represented using the triple

/entity/Q262802   /prop/direct/P27   /entity/Q16

but using the full IRIs (including “http://www.wikidata.org”).

Figure 16.1 shows part of the Wikidata knowledge graph about Christine Sinclair (Q262802). Wikidata provides over 3400 triples about her, including her name in 47 languages (as of August 2022); her name in English and Korean is shown.

Christine Sinclair is a citizen of Canada. Instead of the Wikidata name, “http://www.wikidata.org/prop/direct/P27”, $country\mathrm{\_}of\mathrm{\_}citizenship$ is shown.

She has played 319 games since 2000 for the Canada women’s national soccer team (identifier Q499946), scoring 190 goals. The relationship between her and the team is reified using the identifier Q262802-9c5c267f (the actual identifier is longer than this), connected to her with the property “http://www.wikidata.org/prop/P54” (member of sports team). The property between the reified entity and Q499946 is “http://www.wikidata.org/prop/statement/P54”, also shown as member_of_sports_team.

She has played 161 games for Portland Thorns (identifier Q1446672) since 2013, scoring 65 goals.