Denotation as a Two-Step Mapping
in Semantic Web Architecture
David Booth
Cleveland Clinic (contractor)
david@dbooth.org
Preprint from Twenty-first
International Joint Conference on Artificial Intelligence (IJCAI-09),
11-Jul-2009
Latest version: http://dbooth.org/2009/denotation/
Views
expressed herein are those of the author and do not necessarily
reflect those of Cleveland Clinic.
Abstract.
In RDF, URIs are used to denote resources -- things in the universe of
discourse. According to RDF semantics, an interpretation defines
the mapping
from a URI to a resource. Many interpretations may be consistent
with a given RDF graph, and RDF semantics does not specify how to
select a suitable interpretation from among the possible
candidates. In other writings the author has advocated that
in semantic web architecture, such denotation should be viewed as a
two-step mapping: from the URI to a
set of core assertions specified in a URI
declaration, and thence to the resource. The reason for
this view is that it permits a consistent resource identity to be
associated with a URI: the constraints expressed in the URI declaration
represent a common identity for that URI. This paper shows how
this view of denotation corresponds to established RDF semantics.
Key words: Semantic Web, RDF,
identity, URI declaration, URI definition, denotation, RDF semantics
1
Introduction
In RDF[Klyne 2004] URI
references (hereinafter called URIs)
are used to denote
resources
--
things in the
universe of discourse. In some cases, these resources are web
pages -- what the Architecture of the World Wide Web[Jacobs 2004] calls
information
resources
-- but in
many cases they are not: they are things like people, proteins and
cars. This discussion will focus on non-information
resources, but the reasoning can be extended to cover information
resources.
In other
writings,
Booth[Booth 2007][Booth 2008]
has advocated the view that in RDF
assertions, the use of a URI to denote a resource involves a two-step
mapping: from the URI to a set of assertions, and to thence to the
resource, as illustrated in Figure 1.
This view is
based on the idea that each URI is associated with a
particular set of core assertions, specified in a URI
declaration, that should be
used both by statement authors writing RDF and by applications
consuming and interpreting that RDF. The purpose of this view is
to establish a more stable notion of resource identity by constraining
the interpretations of that URI in a consistent, well-defined way.
At first
glance, this view of denotation as a two-step mapping may
appear to deviate from established RDF semantics [Hayes 2004] (and classic logic
theory). To dispel any such misunderstanding, this paper explains
the correspondence between this view and RDF semantics.
1.1
RDF semantics
in
the context of a semantic web application
Consider a
semantic web application that applies RDF semantics to draw
conclusions about the resources denoted by URIs in a set of RDF
assertions. In the RDF semantics, an interpretation
specifies a
mapping from URIs to a set of resources and
properties.
However, RDF semantics is intentionally silent about two questions that
are critically important to the application:
- Given that many sets of RDF
assertions may be available from many
sources, how should the application decide which assertions to
use? For
example, if Abby, Bob and Carol all offer RDF documents that may be
relevant to Sam's application, which ones should Sam use? Clearly
this question involves complicated issues of trust, provenance and
relevance, and for this reason it is typically left to human judgement.
- Once a set of assertions has
been selected for a particular
application, how should a suitable interpretation be selected? In
other words, how should the application decide which mapping of URIs to
resources should be used? The RDF semantics limits the set of
possible interpretations, but typically it does not completely
constrain them to a unique interpretation. For example, the RDF
semantics of Sam's chosen assertions may constrain the interpretation
of URI http://example#apple to denote some kind of apple, but which
kind? One interpretation may map http://example/apple to a red
apple, and another may map it to a green apple. Which one should
Sam use?
These questions
correspond to steps 1 and 3 in Figure 2, which
illustrates the broad process by which the application makes use of RDF
assertions. In step 1, assertions are selected that are deemed
relevant to the
application. This is often an iterative or recursive process, as
illustrated by the additional step 1.a: when an RDF document is
selected for use, it may refer to ontologies that are defined in other
documents, using mechanisms such as owl:imports[Dean 2004], and
hence the
assertions in those documents may also be merged with the set of
assertions that have already been selected for use by the
application.
After a set of
RDF assertions has been selected, the selected
assertions are often used in three ways:
- The formal
assertions
form the RDF graph whose entailments will be determined in step 2, by
applying RDF semantics (and any extension semantics).
- Particular URIs -- typically
namespaces -- may be recognized and
trigger the inclusion of particular semantic
extensions [Hayes
2004, section 6]
in step 2. For example, the
namespace URI http://www.w3.org/2002/07/owl# signals that the semantic
extensions defined by OWL [Dean 2004]
should be used. Although such
semantic
extensions are often associated with well known vocabularies such as
OWL, any URI may signal the use of semantic extensions. For
example,
http://example#FruitOnt might signal that some special entailment rules
related to fruits should be used.
- Embedded informal assertions,
such as prose contained in rdfs:comment [Brickley 2004]
statements, may be used
later in step 3 to help the user select the most appropriate
interpretation corresponding to a particular URI.
Step 2 is the only step governed by RDF semantics. In step 2,
entailment rules defined by the RDF semantics and any
semantic extensions are applied to the formal assertions selected in
step 1 to produce entailments that constrain the set of possible
interpretations for the given graph. RDF semantics does not
require entailment rules defined by semantic
extensions to be used, but if the application wishes to extract the
most benefit from the selected assertions, typically they will be
desired. Note that according to the RDF semantics, semantic
extensions must be monotonic, such that any entailments that hold
without the use of the semantic extensions must also hold if the
semantic extensions are used.
In step 3, an
interpretation is selected from the set of possible
interpretations, perhaps with the aid of informal assertions. The
selected interpretation maps a URI used in the RDF selected in step 1,
such as http://example#apple, to a resource, such as a particular green
apple.
Interpretations
for a URI. The RDF semantics document
speaks of an interpretation of a vocabulary,
which includes the URIs and literals used in an RDF graph whose
semantics are being examined, and the RDF semantics constrains the set
of possible interpretations for a given RDF graph. Each
interpretation maps each URI to a resource. Thus, for a given URI
in a given graph, the possible interpretations map that URI to a set of
resources, as illustrated in Figure 2a. For convenience, we refer
to this as the set of possible interpretations
for the URI.
1.2 Denotation as
a
two-step mapping in RDF semantics
There are two
ways that the two-step mapping of Figure 1 can be
described in terms of RDF semantics as illustrated in Figure 2.
The first is that the act of selecting an
interpretation (i.e., step 3 of Figure 2) can be decomposed into two
sub-steps corresponding to a two-step mapping, as shown in Figure 3:
- In step 3.a the set of possible
interpretations determined by
step 2 is further constrained by the core assertions from the URI
declarations of the URIs used in the RDF selected in step 1, thus
resulting in a (presumably) smaller set of possible
interpretations.
- In step 3.b an interpretation
is selected from this smaller set
of possible interpretations, perhaps with the aid of informal
assertions, as previously described.
Although this
is
the simplest way to conceptualize the correspondence, in practice the
additional assertions introduced by the URI declarations are likely to
be processed in a manner that is very similar to the way ontologies are
processed. In Figure 4, step 1.a is expanded to perform the
iterative or
recursive inclusion of both ontologies and URI declarations: when an
RDF document is selected for use, both ontologies and URI declarations
that it uses are obtained and merged with the set of selected
assertions.
The ontological
closure
is
obtained if all such referenced ontologies (and URI declarations) are
recursively merged.
However, RDF semantics does not require an application to obtain the
ontological closure: it is free to stop chasing references at any point
it chooses. However, if the application does not obtain the
ontological closure:
- the application may forego some entailments that it otherwise
could have been obtained; and
- the application runs the risk that it may fail to detect a
logical
inconsistency that otherwise would have been exposed.
From the
perspective of semantic web
architecture, this means that, although the application is free to make
this choice, the quality
of
the application may suffer if it fails to obtain the ontological
closure.
1.3 Relationships between URIs, URI declarations and
resources
Normally an RDF assertion would relate two resources that are denoted
by URIs. But relationships between URIs themselves, and between
URI declarations, are also relevant. For example, one might wish
to indicate that one URI deprecates another URI, even though they might
have equivalent URI declarations and might denote the same
resource. Or one might wish to indicate that one URI declaration
is broader or narrower than another URI
declaration, as described in Splitting
Identities in Semantic Web Architecture [Booth 2009]. This
is not the same as saying that the resource denoted by a URI is broader
or narrower than the resource denoted by another URI: if URI
declaration for URI u1 is
broader than the URI declaration for URI u2, then the possible
intepretations, defined by the RDF semantics [Hayes 2004], for u1 are a superset of the possible
interpretations for u2.
2
Related Work
Okkam [Bouquet
et al., 2008] is an ambitious project that seeks to establish
common URI identity by providing a service for mapping from a resource
description to a URI, such that multiple users who wish to refer to
that resource can determine what URI to use. In principle the
Okkam approach seems orthogonal (and compatible) with the two-step
mapping described here, since its purpose is to map in the opposite
direction: given a description of an entity, what URI should be used to
denote that entity?
3
Conclusions
This view of
denotation as a two-step mapping from URIs to
resources is entirely consistent with established RDF semantics (and
classic logic theory). It merely seeks to partially specify the
step of selecting a suitable interpretation for a URI -- a step that is
unspecified in RDF semantics. In partially specifying this step,
the range of possible interpretations for a URI is constrained by the
core assertions contained in its URI declaration. This approach
enables the URI to have a stable resource identity across applications:
the resource identity is always constrained to a set of interpretations
that is delimited by the URI declaration.
Acknowledgements
Thanks to
Jonathan Rees for his description of ambiguity from classic
logic
theory [Rees
2009],
which inspired this document.
References
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Change
log
27-May-2010: Added figure 2a and definition of "interpretations for a
URI" from slides.
19-May-2009: Added section on relationships between URIs, URI
declarations and resources, and made minor editorial fixes.
14-May-2009:
Editorial fixes and added section on related work.
16-Mar-2009:
Initial
version.