Denotation as a Two-Step Mapping
in Semantic Web Architecture

David Booth
Cleveland Clinic (contractor)

Preprint from Twenty-first International Joint Conference on Artificial Intelligence (IJCAI-09), 11-Jul-2009
Latest version:

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.

Figure 1: Denotation as a two-step mapping from URI to resource

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:
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. 
Figure 2: RDF semantics for an application

After a set of RDF assertions has been selected, the selected assertions are often used in three ways:
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.
Figure 2a: Interpretations of a 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:
Figure 3: Selecting interpretations in two stepsFigure 4: Getting URI declarations as ontologies

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:
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.


Thanks to Jonathan Rees for his description of ambiguity from classic logic theory [Rees 2009], which inspired this document.


[Booth 2007] David Booth.  URI Declaration in Semantic Web Architecture.  25-Jul-2007.

[Booth 2008] David Booth.  Why URI Declarations?  A comparison of architectural approaches.  ESWC-08 workshop on Identity and Reference on the Semantic Web 2008, 2-Jun-2008.

[Booth 2009] David Booth.  Splitting Identities in Semantic Web Architecture, 26-Feb-2009,

[Bouquet 2008] Paulo Bouquet, Heiko Stoermer and Claudia Niederee.  Entity Name System: The Backbone of an Open and Scalable Web of Data.  Proceedings of the IEEE International Conference on Semantic Computing, ICSC 2008, number CSS-ICSC 2008-4-28-25, pages 554-561, IEEE Computer Society, August 2008.

[Brickley 2004] Dan Brickley, R. V. Guha.  RDF Vocabulary Description Language 1.0: RDF Schema.  W3C Recommendation 10-Feb-2004.

[Dean 2004] Mike Dean, Guus Schreiber, editors.  OWL Web Ontology Language Reference.  W3C Recommendation 10-Feb-2004.

[Hayes 2004] Patrick Hayes, editor.  RDF Semantics.  W3C Recommendation 10-Feb-2004.

[Jacobs 2004] Ian Jacobs, Norman Walsh, editors.  Architecture of the World Wide Web, Volume One.  W3C Recommendation 15-Dec-2004.

[Klyne 2004] Graham Klyne, Jeremy J. Carroll and Brian McBride, editors.  Resource Description Framework (RDF): Concepts and Abstract Syntax.  W3C Recommendation 10-Feb-2004.

[Rees 2009] Jonathan Rees. Learning from other disciplines.  W3C public email archive, 26-Feb-2009.

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.