Context Representation for the Semantic Web
Jie Bao, Jiao Tao, Deborah L.
McGuinness
Tetherless World Constellation
Rensselaer Polytechnic Institue
Troy, NY 12180
fbaojie,taoj2,dlmg@cs.rpi.edu
Paul R. Smart
School of Electronics and Computer Science
University of Southampton
Southampton, SO17 1BJ, UK
ps02v@ecs.soton.ac.uk
ABSTRACT
Context modeling is critical for the unambiguous and ef-
fective delivery of data and knowledge on the Web, and in
particular, the Semantic Web. However, Contexts are of-
ten embedded in the application programs or are implied by
the application- or community-speci¯c agreements. In this
paper, we propose a framework for contexts modeling that
can provide formal and explicit representations for contexts
on the Semantic Web. The core component of the frame-
work is a new formalism of contexts based on the notion of
jurisdictions of knowledge statements. We also discuss the
semantic assumption (modeled as institutions) and prove-
nance aspects of contexts.
1. INTRODUCTION
The unambiguous and e®ective delivery of data and knowl-
edge on the Web relies heavily on the correct representation
and understanding of the associated contexts. However, the
current way of encoding contexts of data and knowledge on
the Web is largely ad hoc. Contexts are often embedded in
the application programs or are implied by the application-
or community-speci¯c agreements. This makes the linking
and reusing of data and knowledge, and thus the integration
of Web applications, a di±cult problem. Therefore, build-
ing the architectural support for contexts is one of the major
challenges for the Web, and in particular, for the Semantic
Web [31].
While the research of contexts has been extensively dis-
cussed in AI (see [2] for a survey), there are still no compre-
hensive studies on the generic and formal representation for
contexts on the Semantic Web. Notable exceptions include
C-OWL [12] and a context model for RDF [45]. However,
these work only cover speci¯c aspects of contexts, for exam-
ple, C-OWL addresses only contextual ontology mappings.
In this paper we present a formalism about representing
contexts on the Web by extending McCarthy's seminal work
on context formalization [37] (later extended by [38]). Our
main contributions are as following:
² McCarthy's context theory relates a proposition to its
context using the ist (\is true") relation. However,
this approach may cause problems when applied to an
open system like Web since the truth of a proposition
is often not applicable or unknown in a context. Our
framework, instead, uses a more generic jurisdiction
relation isin (\is in"). Thus, isin(c; p) means that a
proposition p should be interpreted in the context c
(while p is not necessarily true in c). A set of con-
text statements (as a generalized form of \lifting ax-
ioms" in [38]) can be used to state the relations be-
tween contexts, thus supporting automated reasoning
about contexts.
² While [38] does not consider semantic assumptions (e.g.,
the Open World Assumption) in contexts, our frame-
work allows such assumptions to be explicitly stated
as institutions [27], hence e®ectively avoids the risk
of reusing knowledge outside of situations with its in-
tended assumptions.
² In [38], a context is an object without a provenance
description (when, where, who, etc.). Utilizing recent
advances on provenance representation (e.g., PML [22,
39]), our framework allows associating a provenance
model to a context.
In summary, the proposed framework for contexts pro-
vides formal and explicit representations for the usually im-
plicit contextual assumptions of data and knowledge on the
Web. This is done by supporting the description of logic
institutions, relations of contexts, and provenance. Our
framework is able to tackle some critical issues for extending
Web as a \Social Machine" [31], such as, permitting di®er-
ent views on the same data, faithful knowledge integration
and situation awareness.
This paper is organized as follows: In Section 2 we intro-
duce the notion of jurisdiction-based contexts and relations
between contexts (e.g., compatibility and incompatibility).
In Section 3 we discuss how to represent provenance informa-
tion of a context and use it in inference with the context. In
Section 4 we present how to use the institution theory to for-
mally and explicitly capture semantic assumptions used in a
context, and practical approaches to make machine-readable
speci¯cations of institutions. Section 5 gives related work in
AI and Semantic Web research and Section 6 concludes the
paper with future work.
2. FORMALIZING CONTEXTS
In this section we introduce a formal representation of con-
texts, extending the McCarthy's context formalization [38]
(referred as McCarthy-style contexts thereafter).
2.1 Contexts as Jurisdictions
One key notion in [38] is that contexts are modeled as ¯rst
class objects. A basic relation between a proposition and a
1

context in [38] is
ist(c; p)
meaning that the proposition p is true in the context c.
Lifting axioms can be used to connect contexts. For exam-
ple, to transfer truth from one context c1 to a more general
outer context c2, we may use a lifting axiom:
ist(c1; p) ! ist(c2; p)
However, when applied to an open system such as the
Web, the McCarthy-style context modeling often can't rightly
capture the context of a proposition (often modeled as a
knowledge statement in an ontology on the Semantic Web)1.
Some typical scenarios include the following:
² The truth value of a statement cannot be meaningfully
determined in a context since it is not applicable in
that context. For example, the statement \Eric Cart-
man lives in South Park"2 is true in the context of the
television series \South Park", but it is meaningless to
assert whether this is true or false in other contexts,
for example, the context of \The Simpsons" or the
context of the real world.
² The truth value of a statement is unknown in the con-
text where it is stated or queried against. This may
be because determining the truth value of the state-
ment itself is an open problem (e.g., whether P=NP
in the theoretical computer science), or because of the
open nature of the system (e.g., even if there is no
real person named \Eric Cartman" currently listed on
Wikipedia, answer to the question whether such a per-
son exists is unknown in the context of Wikipedia since
Wikipedia does not have complete knowledge about
the world).
² The meaning of \true" itself may be di®erent in di®er-
ent contexts. For example, an description logic state-
ment is true against an ontology only if all models of
the ontology entails the statement, whereas a state-
ment is true against a logic programming knowledge
base if some selected set of models (e.g., minimal Her-
brand models) entail it. Thus, the meanings of truth
in a DL-based context (e.g., OWL) and a LP-based
context are not necessarily the same.
In this paper, we, instead, introducing a new context for-
malism based on the notion of \jurisdiction" based on the
following assumptions about contexts:
² When we say a statement is related to a context, we
do not necessarily mean the statement is true in the
context, rather, we mean the context has the juris-
diction to interpret the meaning of the statement. If a
context has no jurisdiction over a statement, the state-
ment shall not be interpreted in that context3.
1In this paper, instead of using \proposition", we use
\knowledge statement", or just \statement", as it is more
commonly used in the Semantic Web community.
2Here we use English statements for ease of understanding.
Equivalent statements can be easily made using an ontology
language such as OWL.
3An analogy to this in natural language is that an English
sentence should only be interpreted using the grammar of
English, but not the grammar of French, and that being un-
der the jurisdiction of English grammar does not necessarily
imply the truth of that sentence in English.
² A context may make explicit description of the seman-
tic assumptions it makes and the precise meaning of
truth in that context. We call such a description as
the institution of the context.
² A context maybe a rich object that has descriptions
about its properties (such as provenances) and rela-
tions to other contexts.
For these goals, we extend [38] by introducing a new rela-
tion \isin" (is in) to indicate the jurisdiction relation between
a statement and a context:
isin(c; ®)
where c is a context of the statement ®, i.e., ® can be inter-
preted using the semantic assumptions made in the institu-
tion of c (see more on institutions in Section 4). Note, in
general, we do not have
isin(c; ®) ! ist(c; ®)
However, since a statement is only true in an applicable
context, the reverse relation is always true:
ist(c; ®) ! isin(c; ®)
An \isin" relation can be negated or quanti¯ed same as
other statements. For example,
:isin(c; ®)
means that ® is not applicable in the context c, thus ist(c; ®)
is not a valid formula. When we see such a relation, either
explicitly stated or inferred using the context's properties
and axioms, we will be able to prevent using the statement
in a wrong context (\out of context").
The next statement, using universal quanti¯cation, says
that if the negation of a statement is a Propositional Logic
statement, then it is also a Propositional statement:
8®; isin(pl;:®) ! isin(pl; ®)
where pl stands for the context of Propositional Logic.
Note that in Propositional Logic of Context (PLC) [19], a
logic based on the framework of [38], consistency of contexts
requires that
8®; ist(c;:®) ! :ist(c; ®)
This shows a clear di®erence between the ist relation and
the isin relation.
2.2 Context Constructors and Axioms
Similar to lifting axioms in [38], there are many useful
relations between contexts that can be captured by context
constructors and axioms.
Union. A union constructors \_", e.g., in
isin(c1 _ c2; ®)
means that ® can be interpreted by either c1 or c2. For
example, an OWL DL ontology O can be interpreted either
by the OWL DL semantics (captured by a context sDL) or
the OWL Full Semantics (captured by a context sFull):
isin(sDL _ sFull; O)
Intersection. An intersection constructor, e.g., in
isin(c1 ^ c2; ®)
2

creates a new context that has properties from both c1 and
c2. For example, Bart Simpson is a child appeared in both
South Park (context \sp") and The Simpsons (context \ts"),
therefore we have:
isin(sp ^ ts; Child(BartSimpson))
Extension. A context c1 may extend another context
c2, denoted as c1 ) c2, such that it inherits institutional
properties of c2 (e.g., c2's semantic assumptions), possibly
with some additional properties of its own. c1 is said a
subcontext of c2 and c2 is a supercontext of c1. Therefore,
we have
(c1 ) c2 ^ isin(c1; ®)) ! isin(c2; ®)
(if ® is interpretable in c1 then it is interpretable in c2)
(c1 ) c2 ^ ist(c1; ®)) ! ist(c2; ®)
(if ® is true in c1 then it is also true in c2)
The reverse of the two context axioms are not necessarily
true.
The extension relation is transitive, thus
((c1 ) c2) ^ (c2 ) c3)) ! (c1 ) c3)
We always have that
c1 ^ c2 ) c1 and c1 ) c1 _ c2
Note that c1 may not necessarily inherits other properties
of c2, e.g., provenances.
Nesting. An isin assertion itself can be stated in another
\outer" context. For example, \Wikipedia says that in the
television series South Park, Eric Cartman lives in the place
South Park " can be represented as
isin(wikipedia; isin(sp; livesIn(EricCartman; SouthPark)))
where wikipedia is the context of Wikipedia, and sp is the
context of the television series South Park.
In general, we assume that there is a universal context c0
as the default outer context of all other contexts, and it can
be omitted whenever necessary.
Note that context nesting is di®erent from context exten-
sion: an extension transfers truth and jurisdiction of a state-
ment from a subcontext to a supercontext, whereas nesting
does not transfer these to the outer context. Therefore,
isin(wikipedia; livesIn(EricCartman; SouthPark))
does not follow from the previous assertion.
Incompatibility. Context incompatibility declarations
can prevent using a statement out of context. For a context
c, :c stands for the union of all contexts that are incompat-
ible with c. We have
isin(:c; ®) $ :isin(c; ®)
Therefore, we can express \c1 is incompatible with c2" as
isin(c1; ®) ! isin(:c2; ®)
or in short form as c1 ! :c2
We can easily see that if a context c1 has a supercontext
that is incompatible with c2, then c1 must be also incom-
patible with c2:
((c1 ) c0) ^ (c0 ! :c2)) ! c1 ! :c2
In the next section, we will show more examples on infer-
ring context incompatibility based its provenance properties.
Compatibility. Compatibility declarations transfer ju-
risdiction from one context to another context. \c1 is com-
patible with c2", denoted as c1 ! c2, means that
isin(c1; ®) ! isin(c2; ®)
Compatibility is weaker than extension since it only trans-
fers jurisdiction but not truth of statements.
The set of context constructors and axioms is not meant
to be complete. Other useful context description languages
may be designed.
2.3 Context IRIs and Dereferencing
On the Semantic Web, a context can be represented as
a Web resource and identi¯ed with an IRI (International-
ized Resource Identi¯er, a generalization form of URI and
URL). A context description document, either formally de-
scribed as a set of context axioms or informally stated as a
human-readable document, may be dereferenced at the IRI.
In addition, the dereferenced document may provide other
information about the context, such the provenance and in-
stitution descriptions of the context (as will be outlined later
in the paper).
3. PROVENANCES OF CONTEXTS
Contexts in our framework are rich objects such that they
may have properties. In particular, a set of common and
important properties are the provenance of a context, in-
cluding the aspects of temporal (when), spatial (where),
agent (who), casual (why) and other properties. Recent ad-
vances in provenance modeling (e.g., PML [22, 39]) allow
us to precisely describe provenances and conduct inference
with provenance knowledge4. The goal of this section is
not to propose or advocate a particular provenance model
for describing contexts { this decision is best left to domain
experts who model the contexts. Instead, we demonstrate
several typical scenarios when provenance information can
leverage inferences about contexts.
Quoting. Identifying a context using its provenance in-
formation can help us to realize quoting as supported by the
N3 Logic [7] and Named Graphs [20]. For example, in the
N3 Logic (the modeling using named graphs is similar), we
may use quoted formulae such as:
:wikipedia :says{
:sp :says {
:EricCartman :livesIn :SouthPark }}.
In our context model \wikipedia" and \sp" are repre-
sented as two contexts (as shown in the last section), and
we can attach provenance information to these contexts. For
example, we may add the following RDF statements about
\wikipedia" and \sp":
:wikipedia :sourcePage
"http://en.wikipedia.../Eric_Cartman"^^xsd:iri .
:wikipedia :date "2010-03-25"xsd:date .
4http://www.w3.org/2005/Incubator/prov/wiki/Provenance
Survey lists several survey papers on provenance.
3

:wikipedia :author user:JohnSmith .
:wikipedia :revision "352615356"^^xsd:intger .
......
:sp rdfs:comment "South Park context" .
:sp :author "Trey Parker" .
:sp :author "Matt Stone" .
:sp context:isIn :wikipedia .
......
Where \context:isIn" is a hypothetical property name to
represent the isin relation.
Note that there is an important di®erence between quot-
ing by graph ids as in [7, 20] and quoting using context
relations. A context of a statement does not need to be
the physical location where the statement is made, nor it
must be a graph, e.g., the \sp" context above refers to a
conceptual context with no corresponding graph. This sep-
aration of the conceptual context and the physical location
of a statement o®ers several advantages:
² It o®ers a °exible way to describe context. For exam-
ple, while the editors of Wikipedia's pages about South
Park may not be Trey Parker and Matt Stone them-
selves (thus, they are not the authors of the physical
location of the statement), we are still able to correctly
credit them as the creators of the South Park context.
² It leverages data integration. Knowledge statements
from di®erent graphs may share the same context, then
we will immediately know that they can be combined
context-safely.
² It allows us to associate multiple contexts to a state-
ment whereas in N3 Logic or named graphs a state-
ment can only reside in one graph. For example, we
may associate to the statement livesIn(EricCartman,
SouthPark), in addition to sp, also contexts \us" (United
States) and \fol" (First Order Logic).
Inferring (In)compatibility. Provenance information
may be used in determining whether a statement is applica-
ble in a context, or a context is (in)compatible with another
context. For example, we may have the following statements
saying that news from CNN should not be interpreted in the
contexts that are from the Fox News:
8c1; c2; hasSource(c1; CNN) ^ hasSource(c2; FoxNews)
! (c1 ! :c2)
where hasSource relates a contexts to its source.
The next example shows that annual reports of mutual
funds can be put together for comparison only if they are
from the same year
8c1; c2; 9y; hasYear(c1; y) ^ hasYear(c2; y)^
AnnualReport(c1) ^ AnnualReport(c2)
! (c1 ! c2) ^ (c2 ! c1)
Selective Importing. The current importing mecha-
nism in OWL has the implicit assumption that all ontologies
in the importing transitive closure are compatible to other
each such that a union of them can be made and the im-
porter ontology is interpreted under this union. However,
this is not always desired as importing is often used as ci-
tation whereas the \cited" content is not necessarily always
true in the importer's context (e.g., in the case of citing for
critique). Also, since importing can be transitive but the
trust of content is not always transitive, using an indirectly
imported ontology may result in unintended consequences.
Using the context mechanism, we will be able to realize
selective importing such that only trusted ontologies in the
importing transitive closure is taken into account. For ex-
ample, the next strategy says that only ontologies published
by an educational organization (with domain name \.edu")
should be used. We assume, if an ontology does not declare
a context where it is in, it uses a default context with a
property iri which is the ontology's iri; imports+ is the
importing transitive closure relation; topDomain is a func-
tion that parses the top-level domain of an iri.
isin(c;O) ^ imports+(O;O0) ^ isin(c0; O0)^
iri(c0; x) ^ (topDomain(x) == "edu") ! isin(c;O0)
4. INSTITUTIONS OF CONTEXTS
4.1 Modeling Semantic Assumptions Using In-
stitutions
The isin relation does not specify whether a statement is
true in a context. This is left to be validated using the insti-
tution of the context, i.e., the set of semantic assumptions
made in the context. The term \institution" is adopted un-
der the in°uence of the institution theory [27] which speci¯es
a framework for abstract description of a logic system. Note
that a description of an institution does not necessarily be a
formal or machine-readable description (while this is desired
and more details are discussed in the next subsection). For
example, N3 Logic [7] currently does not have a formal se-
mantics; the OWL syntax and semantic document [41] gives
a formal yet only human-readable description for OWL [40]
and is currently implicitly used as the default institution
document for OWL ontologies. In particular, if a context is
not logic-dependent, it may have no associated institution.
Basically, an institution description speci¯es the following
common aspects of a logic system:
² A signature, i.e., some vocabulary that can be used to
construct sentences;
² A sentence generation grammar using the signature;
² A mapping from the signature to the models of the
institution;
² A satisfaction relation between sentences and models.
These can be formally describe based on the category the-
ory as given in Def. 1 (for basic notions in the category
theory, cf. [5]):
Definition 1.: ([27] De¯nition 1) An institution I con-
sists of
1. a category Sign, whose objects are called signatures,
2. a functor SEN : Sign ! Set, giving for each signature
§ 2 jSignj a set of sentences of the signature,
3. a functor MOD : Sign ! Catop, giving for each signa-
ture § 2 jSignj a category whose objects are called §-
models, and whose arrows are called §-(model) mor-
phisms,
4. a relation ²§µ jMOD(§)j £ SEN(§) for each § 2
jSignj, called §-satisfaction.
4

such that for each morphism Á : § ! §0 in Sign, the Sat-
isfaction Condition holds:
m0 ²§0 SEN(Á)(e) i® MOD(Á)(m0) ²§ e
For example, OWL DL is an institution where the signa-
ture is the set of all named classes, properties and individu-
als; sentences are constructed following the grammar given
in [41]; its models are the set of all ¯rst-order models; the
satisfaction relation is given in [41] under the open world
assumption and non-unique name assumption. This institu-
tion can be used as the default institution of an \OWL DL"
context which handles all syntactically valid OWL DL on-
tologies. Similarly, we may have the RDFS institution and
the OWL Full institution.
The institution theory also allows us to formally describe
syntactical and semantic relations between two di®erent in-
stitutions using institution morphisms:
Definition 2.: ([27] De¯nition 32) Let I1 = hSign1;
SEN1;MOD1;²1i and I2 = hSign2; SEN2;MOD2;²2i be two
institutions. An institution morphism © : I1 ! I2 con-
sists of
1. A functor f : Sign1 ! Sign2
2. A natural transformation ® : f ± SEN2 ) SEN1
3. A natural transformation ¯ : MOD1 ) fop ±MOD2
such that the following Satisfaction Condition holds:
m ²1§ ®§(e) i® ¯§(m) ²2f(§) e
for any §-model m from I1 and any f(§)-sentence e from
I2.
For readers who are not familiar with the category the-
ory, the above de¯nition can be understood as a systematic
mapping of the vocabularies, the sentence grammars and
the models between the two institutions under some satis-
faction preservation conditions. For example, the RIF RDF
and OWL Compatibility document [23] describes an embed-
ding of RDF in RIF, while it does not directly use institution
theory notions, covers the above aspects of institution map-
ping using a formal, human-readable description.
Associating an explicitly stated institution to a context
brings several bene¯ts:
² It separates of the making of a statement and that as-
serting the statement is true, which is useful to enable
quoting, citing without supporting and expressing un-
certainty, just for a few examples.
² It enables us to connect knowledge bases stated in dif-
ferent logics or using di®erent semantic assumptions.
² It may better guide tools to process the ontology in an
intended way. For example, one may publish an syn-
tactically valid OWL-DL ontology but wish tools to
use it as an OWL Full ontology (e.g., instead of per-
forming tableau-based inference, perform a rule-based
inference for the ontology); this can be realized by as-
sociating the OWL Full institution to the context of
the ontology5.
5For a discussion of intended semantics of an OWL docu-
ment, cf. http://www.w3.org/2007/OWL/tracker/issues/
111
² It facilitates extending an existing institutions in a
modular and explicit way. For example, one may want
to use OWL-DL but also use the unique name assump-
tion (UNA); this may be realized by de¯ning an UNA
context and institution, and then declare that the on-
tology uses an intersection context of the OWL-DL
context and the UNA context.
4.2 Machine-readable Institution Specifications
While most of institution descriptions on the Semantic
Web is formal, few of them is machine-readable. A machine-
readable de¯nition of the syntax and semantics of an insti-
tution will greatly facilitate the automatic validation and
processing of contexts that use the institution. A notable
exception is RIF-BLD (Basic Logic Dialect) [8], which, as
a specialization of RIF-FLD (The Framework for Logic Di-
alects) [9], is provided with a formal syntactic, semantic and
XML serialization framework. In fact, RIF-FLD o®ers a
comprehensive framework to specify \both syntax and se-
mantics...through a number of mechanisms that are com-
monly used for various logic languages" [9]. RIF-FLD has
the following main components:
² Syntactic framework, which de¯nes the formal presen-
tation syntax of the logic, e.g., alphabet, symbol space
and well-formed formulas;
² Semantic framework, which speci¯es a model-theoretical
semantics of the logic and relates the syntax to models;
² XML serialization framework, which de¯nes the gen-
eral principles for specifying concrete XML-based syn-
taxes of the logic.
We believe that the generic nature of RIF-FLD makes
it an ideal candidate for creating machine-readable institu-
tion speci¯cations. This has been evidenced by that various
non-o±cial dialects have de¯ned using this framework, e.g.,
RIF-URD (Uncertainty Rule Dialect) [48] and RIF-CASPD
(Core Answer Set Programming Dialect) [32].
Another potential approach to design an institution speci-
¯cation language is to extend Common Logic6 with a machine-
readable syntax. CL also allows the de¯nition of a variety
of di®erent dialects, including FOL and even higher-order
logics.
5. RELATED WORK
Contexts have been extensively studied in AI and other
¯elds. We can only discuss the most relevant work here due
to page limits. For surveys on contexts in AI, cf. [14, 15,
1, 35] and for a survey on context representation for the
Semantic Web pre-2004 cf. [10]. The Context Conference7
is also a good source about context research.
5.1 Contexts in AI
McCarthy-style Contexts: Our work extends McCarthy's
work on context modeling [37, 38] by separating the notions
of truth-based contexts and jurisdiction-based contexts. We
have shown that such a separation is useful for Semantic
Web applications where truth of a statement is often un-
known or meaningless when it is applied in a wrong context.
6http://www.common-logic.org
7http://www.informatik.uni-trier.de/~ley/db/conf/context/index.html
5

Guha [28] has extended McCarthy's notion of context and
applied it in building the CYC system [34]. Knowledge
statements in CYC is divided into microtheories which serve
as the contexts of the statements. A microtheory, similar to
contexts in [38], is an object that has a name and can be or-
ganized in a microtheory hierarchy. Guha's approach shares
the same limitations as McCarthy's to be used for Semantic
Web.
Buvac and others8 applied McCarthy's framework in var-
ious logics, leading to the study of Propositional Logic of
Context (PLC) [19, 17] and Quanti¯cational Logic of Con-
text [16, 36]. Buvac showed that the \ist" relation is essen-
tially a modal operator, and a formal semantics and calculus
in the modal logic fashion can be given for McCarthy-style
contexts in propositional logics and quanti¯cational (predi-
cate) logics. In fact, Buvac and Mason [18] have shown PLC
can be reduced to propositional multi-modal logic. Buvac's
approach requires all contexts to be in the same institution
whereas this is not required in our approach.
MultiContext Logics. Multicontext logics9 [26] is a
family of logics based on two principles:
² Locality - In inference, only partial knowledge is avail-
able and this part is call the context for the inference
process.
² Compatibility - There is compatibility among the rea-
soning performed in di®erent contexts.
A multi-context system (MCS) is formally described using
the Local Models Semantics [25] and its proof theory (a
generalization of natural deduction) is composed of inter-
nal rules (for intra-context inference and bridge rules (for
inter-context inference). Multicontext logics in°uenced Dis-
tributed First Order Logics [24] and Distributed Description
Logics (DDL) [11], with the latter has a close relation to Se-
mantic Web applications.
Bouquet and Sera¯ni [13, 42] have compared multicontext
logics and McCarthy-style contexts and have shown that
lifting axioms are special forms of bridge rules in MCS, and
in general, McCarthy-style contexts are less expressive than
the multicontext logics.
Applying the multicontext logics in the Semantic Web,
while is conceptually straightforward, has some practical is-
sues in specifying compatibility relations between contexts.
Two well-known problems are that knowledge can not be
transitively reused in DDL and bridge rules o®er only lim-
ited expressivities to relate ontologies since they require dis-
joint vocabularies in di®erent ontologies [4].
Contexts based on Situation Theory. Akman and
Surav [3] used Situation Theory [6] to model contexts. A
situation is a limited viewpoint of the world from an agent.
A context is a situation that contains a set of ground knowl-
edge assertions (called \infons" in the theory) and constraints
for deriving new facts. McCarthy-style context assertions
can be represented as infons such as:
ist(c; p(x)) ) ¿ pc; x; 1 À
where pc is a new predicate (context c's version of p), and
\1" means pc(x) is true in the situation.
8http://www-formal.stanford.edu/buvac/
9http://www.dit.unitn.it/~context/
The situation theory based approach may face an explo-
sion blow-up of newly introduced predicates when there are
many predicates and contexts. In addition, the lack of a
natural deduction system in [3] is a critical limitation for its
practical use.
5.2 Context Modeling in Semantic Web
Guha and others [29] applied McCarthy-style contexts for
Semantic Web use, targeting aggregation of independently
published data. This proposal shares some common prop-
erties with our framework, such that each document has a
context which can be identi¯ed by an IRI/URL. It provides
a small ontology to describe contexts, and an alternative
approach to provide an extended RDF model theory for in-
troducing contexts.
Stoermer[44, 45] also applied McCarthy-style contexts for
RDF context management. For this purpose, this work
introduces a Context Relations Ontology (CRO) without
adding new language features to RDF (which is di®erent
from [29])
Since both [29] and [44, 45] are based on the ist rela-
tion, inherent limitations of the McCarthy-style contexts
also present in these proposals.
C-OWL [12] is an extension of OWL based on Distributed
Description Logics. The expressivity of C-OWL is limited to
be used largely as an ontology mapping language. For exam-
ple, an \into" bridge rule can be used to establish subclass-
like relationship between classes in two ontologies. In ad-
dition, since a context is not an object in C-OWL, one can
not assert provenance or other properties about a context.
Several other researchers have applied context modeling
in semantic desktops [30], information sharing and privacy
protection [21], data integration [46] and semantic wikis [33,
47]. These works' goals are not providing a generic context
modeling framework, which is the focus of our paper.
6. CONCLUSIONS
We investigated extending McCarthy's context framework
to address context modeling on the Semantic Web. We show
that by introducing the notion of context jurisdiction, we
can model many scenarios that are no expressible using the
McCarthy's original framework, e.g., citation without sup-
porting, asserting statements with unknown truth values,
and preventing interpreting statements in wrong contexts.
We showed that by using provenance information of a con-
text we are able to realize quoting, incompatibility inference
and selective importing. We also discussed making (usually
implicit) semantic assumptions used in an ontology explicit
as logic institutions and presented practical approaches to
specify an institution.
This paper is only the ¯rst step towards an expressive
context modeling framework. Many details of the framework
are to be investigated in the future, including the following:
² A formal semantics to specify the precise meaning of
the isin relation and to derive a natural deduction sys-
tem for the framework.
² A concrete syntax for expressing contexts that can
work with RDF and OWL.
² An investigation into how to use policy languages to
manage multiple applicable contexts of an ontology
and to realize situation-aware context selection.
6

² An investigation into use of the context framework to
address some common modeling problems. One such
problem is modeling integrity constraints [43] which
may be modeled as an extension of the standard RDF/OWL
context with some variations of the Closed World As-
sumption. We are also interested in studying the ap-
plication of contexts in modeling modular ontologies
[4].
Acknowledgments: This work is supported in part by
NSF #0524481, DARPA #FA8650-06-C-7605, #FA8750-
07-D-0185, #55-002001, #F30602-00-2-0579, and ITA project
W911NF-06-3-0001.
7. REFERENCES
[1] Varol Akman. Context in Arti¯cial Intelligence: A
Fleeting Overview. McGraw-Hill, Milano, 2002.
[2] Varol Akman and Mehmet Surav. Steps toward
formalizing context. AI Magazine, 17(3):55{72, 1996.
[3] Varol Akman and Mehmet Surav. The use of situation
theory in context modeling. Computational
Intelligence, 13(3):427{438, 1997.
[4] Jie Bao, Doina Caragea, and Vasant Honavar. On the
semantics of linking and importing in modular
ontologies. In International Semantic Web Conference
(ISWC), pages 72{86, 2006.
[5] Michael Barr and Charles Wells, editors. Category
theory for computing science, 2nd ed. Prentice Hall
International (UK) Ltd., Hertfordshire, UK, UK, 1995.
[6] J Barwise. Situations and small worlds. In In The
Situation in Logic, number 17 in CSLI Lecture Notes,
pages 79{92, 1987.
[7] Tim Berners-Lee, Dan Connolly, Lalana Kagal, Yosi
Scharf, and Jim Hendler. N3logic: A logical framework
for the world wide web. TPLP, 8(3):249{269, 2008.
[8] Harold Boley and Michael Kifer. RIF Basic Logic
Dialect. Candidate Recommendation
CR-rif-bld-20091001, World Wide Web Consortium,
Oct 2009.
[9] Harold Boley and Michael Kifer. RIF Framework for
Logic Dialects. Candidate Recommendation
CR-rif-°d-20091001, World Wide Web Consortium,
Oct 2009.
[10] Elena Paslaru Bontas. Context representation and
usage for the semantic web: A state of the art.
Technical Report B-04-30, Freie UniversitÄat Berlin,
http://www.inf.fu-berlin.de/inst/pubs/
tr-b-04-30.abstract.html, 2004.
[11] Alexander Borgida and Luciano Sera¯ni. Distributed
description logics: Assimilating information from peer
sources. Journal of Data Semantics, 1:153{184, 2003.
[12] Paolo Bouquet, Fausto Giunchiglia, Frank van
Harmelen, Luciano Sera¯ni, and Heiner
Stuckenschmidt. C-OWL: Contextualizing ontologies.
In Dieter Fensel, Katia P. Sycara, and John
Mylopoulos, editors, International Semantic Web
Conference, volume 2870 of Lecture Notes in
Computer Science, pages 164{179. Springer, 2003.
[13] Paolo Bouquet and Luciano Sera¯ni. On the di®erence
between bridge rules and lifting axioms. In Patrick
Blackburn, Chiara Ghidini, Roy M. Turner, and
Fausto Giunchiglia, editors, CONTEXT, volume 2680
of Lecture Notes in Computer Science, pages 80{93.
Springer, 2003.
[14] Patrick Br¶ezillon. Context in arti¯cial intelligence: I. a
survey of the literature. Computers and Arti¯cial
Intelligence, 18(4), 1999.
[15] Patrick Br¶ezillon. Context in arti¯cial intelligence ii.
key elements of contexts. Computers and Arti¯cial
Intelligence, 18(5), 1999.
[16] Sasa Buvac. Quanti¯cational logic of context. In
AAAI/IAAI, Vol. 1, pages 600{606, 1996.
[17] Sasa Buvac, Vanja Buvac, and Ian A. Mason. The
semantics of propositional contexts. In ISMIS, pages
468{477, 1994.
[18] Sasa Buvac, Vanja Buvac, and Ian A. Mason.
Metamathematics of contexts. Fundam. Inform.,
23(2/3/4):263{301, 1995.
[19] Sasa Buvac and Ian A. Mason. Propositional logic of
context. In AAAI, pages 412{419, 1993.
[20] Jeremy J. Carroll, Christian Bizer, Patrick J. Hayes,
and Patrick Stickler. Named graphs, provenance and
trust. In WWW, pages 613{622, 2005.
[21] Harry Chen, Timothy W. Finin, and Anupam Joshi.
Semantic web in the context broker architecture. In
PerCom, pages 277{286, 2004.
[22] Paulo Pinheiro da Silva, Deborah L. McGuinness, and
Richard Fikes. A proof markup language for Semantic
Web services. Inf. Syst., 31(4-5):381{395, 2006.
[23] Jos de Bruijn. RIF RDF and OWL Compatibility.
Candidate Recommendation CR-rif-rdf-owl-20091001,
World Wide Web Consortium, Oct 2009.
[24] C. Ghidini and L. Sera¯ni. Frontiers Of Combining
Systems 2, Studies in Logic and Computation, chapter
Distributed First Order Logics, pages 121{140.
Research Studies Press, 1998.
[25] Chiara Ghidini and Fausto Giunchiglia. Local models
semantics, or contextual
reasoning=locality+compatibility. Arti¯cial
Intelligence, 127(2):221{259, 2001.
[26] Fausto Giunchiglia and Fausto Giunchiglia.
Contextual reasoning. Epistemologia, special issue on
I Linguaggi e le Macchine, 345:345{364, 1992.
[27] Joseph A. Goguen and Rod M. Burstall. Institutions:
Abstract model theory for speci¯cation and
programming. J. ACM, 39(1):95{146, 1992.
[28] Ramanathan V. Guha. Contexts: a formalization and
some applications. PhD thesis, Stanford University,
1991.
[29] Ramanathan V. Guha, Rob McCool, and Richard
Fikes. Contexts for the semantic web. In Sheila A.
McIlraith, Dimitris Plexousakis, and Frank van
Harmelen, editors, International Semantic Web
Conference, volume 3298 of Lecture Notes in
Computer Science, pages 32{46. Springer, 2004.
[30] Tom Heath, Enrico Motta, and Martin Dzbor.
Context as a foundation for a semantic desktop. In
Semantic Desktop Workshop, 2005.
[31] Jim Hendler and Tim Berners-Lee. From the Semantic
Web to social machines: A research challenge for AI
on the World Wide Web. Arti¯cial Intelligence,
174(2):156 { 161, 2010. Special Review Issue.
[32] Stijn Heymans and Michael Kifer. RIF Core Answer
7

Set Programming Dialect. Editor's Draft
RIF-CASPD, World Wide Web Consortium and The
Rule Markup Initiative, Dec 2009.
[33] Malte Kiesel, Sven Schwarz, Ludger van Elst, and
Georg Buscher. Mymory: Enhancing a semantic wiki
with context annotations. In ESWC, pages 817{821,
2008.
[34] Douglas B. Lenat. Cyc: A large-scale investment in
knowledge infrastructure. Commun. ACM,
38(11):32{38, 1995.
[35] William Loyola. Comparison of approaches toward
formalizing context: Implementation characteristics
and capacities. Electronic Journal of Knowledge
Management, 5(2):203{214, 2007.
[36] Selene Makarios. A model theory for a quanti¯ed
generalized logic of contexts. Technical Report
KSL-06-08, Knowledge Systems, AI Laboratory, 2006.
[37] John McCarthy. Notes on formalizing context. In
IJCAI, pages 555{562, 1993.
[38] John McCarthy and Sasa Buvac. Formalizing context
(expanded notes). Technical report, Stanford, CA,
USA, 1994.
[39] Deborah L. McGuinness, Li Ding, Paulo Pinheiro
da Silva, and Cynthia Chang. PML 2: A Modular
Explanation Interlingua. In ExaCt, pages 49{55, 2007.
[40] Deborah L. McGuinness and Frank van Harmelen.
OWL Web Ontology Language Overview. Technical
Report REC-owl-features-20040210, W3C, 2004.
[41] P.F. Patel-Schneider, P.Hayes, and I. Horrocks. Web
Ontlogy Language (OWL) Abstract Syntax and
Semantics. http://www.w3.org/TR/owl-semantics/,
February 2004.
[42] Luciano Sera¯ni and Paolo Bouquet. Comparing
formal theories of context in ai. Artif. Intell.,
155(1-2):41{67, 2004.
[43] Evren Sirin and Jiao Tao. Towards integrity
constraints in owl. In OWLED, 2009.
[44] Heiko Stoermer. Introducing Context into Semantic
Web Knowledge Bases. In Proceedings of the
CAISE*06 Doctoral Consortium, June 2006.
http://dme.uma.pt/caise06dc/papers/Stoermer.pdf.
[45] Heiko Stoermer, Paolo Bouquet, Ignazio Palmisano,
and Domenico Redavid. A context-based architecture
for rdf knowledge bases: Approach, implementation
and preliminary results. In RR, pages 209{218, 2007.
[46] Philip Tan, Stuart E. Madnick, and Kian-Lee Tan.
Context mediation in the semantic web: Handling owl
ontology and data disparity through context
interchange. In SWDB, pages 140{154, 2004.
[47] Ludger van Elst, Malte Kiesel, Sven Schwarz, Georg
Buscher, Andreas Lauer, and Andreas Dengel.
Contextualized knowledge acquisition in a personal
semantic wiki. In EKAW, pages 172{187, 2008.
[48] Jidi Zhao and Harold Boley. Uncertainty treatment in
the rule interchange format: From encoding to
extension. In URSW, 2008.
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