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interpretation map the URI to an individual. Then unlike standard first-order logic,
this individual then maps to different extensions depending on the role the URI
is playing as a property or class in the triple. A simple example should suffice
to give a flavour of the formal semantics, where a relation is just another kind
of individual. What is the formal semantics of
ex:EiffelTower ex:architect
ex:Gustave Eiffel
? To simplify slightly, Hayes defines the formal semantics in
terms of set theory, where there is a set of resources that compose the model of
the language, a set of properties, and a set of URIs that can refer to resources. The
interpretation of any RDF statement is then given as an extensional mapping from
the set of properties to the powerset of resources, to the set of pairs of resources.
So, given a set-theoretic model consisting of elements (given by italics)
Gustave
Eiffel
and
the Eiffel Tower
and
being the architect of
,then
ex:EiffelTower
|
=
the
Eiffel Tower
,
ex:Gustave Eiffel
|
=
being
the architect of
, so that the entire triple maps to a set of pairs:
ex:EiffelTower
ex:architect ex:Gustave Eiffel
Gustave Eiffel
and
ex:architect
|
=
(..., (the Eiffel Tower, Gustave Eiffel),
...)
. Common-sense human intuitions will likely have this interpretation map
to
ex:EiffelTower ex:architect ex:Gustave EiffelTower
, and using the
axioms defined in the RDF formal semantics a few new triples can be inferred,
such as
ex:architect rdf:type rdf:Property
,i.e.
being an architect of
is a
property of something.
However, the inherent pluralism of the Tarski approach to models also means
that another equally valid interpretation would be the inverse, i.e. the mapping of
ex:EiffelTower
to
Gustave Eiffel
and
ex:Gustave Eiffel
to
the Eiffel Tower
.
In other words,
ex:architect
|
=
|
=
being the architect of
, so that the entire triple
maps to a set of pairs
ex:EiffelTower ex:architect ex:Gustave Eiffel
|
=
(..., (Gustave Eiffel, Eiffel Tower), ...)
. Due to the unconstrained nature of RDF,
ex:architect
has no 'natural' relationship to anything in particular, but could
easily be assigned either
the Eiffel Tower
or
Gustave Eiffel
just as easily as
being
the architect of
. Furthermore, the model could just as easily be given by something
as abstract as the integers
1
and
2
, and an equally valid mapping would be for
ex:EiffelTower
2
,sothat
ex:architect
|
=
being the architect of
, so that the entire triple maps to a set of pairs
ex:EiffelTower
ex:architect ex:Gustave Eiffel
|
=
1
and
ex:Gustave Eiffel
|
=
(..., (1,2), ...)
. Indeed, the extreme plu-
ralism of a Tarski-style semantics shows that, at least if all one has is a single lone
triple statement, that triple can be satisfied by any model. This is no mere oddity
of formal languages, this would also hold for any lone sentence in a language
like English - such as “Gustave Eiffel is the architect of the Eiffel Tower” - as
long as one subscribed to a Tarski-style semantics for natural language. As the
number of triples increased, the amount of possible things that satisfy the model
is thought to decrease, but in such a loose language as RDF, Hayes notes that it
is “usually impossible to assert enough in any language to completely constrain
the interpretations to a single possible world, so there is no such thing as 'the'
unique interpretation” (Hayes 2004). This descriptivist theory of reference, where
descriptions are logical statements in RDF, is illustrated in Fig.
4.2
.
|
=
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