Most of the knowledge available in the Semantic Web is context dependent. Examples of contextual information that is associated with knowledge are time, topic, provenance, reliability, etc. Recently, several paradigms, tools and languages have been proposed with the aim of adding context awareness into the Semantic Web. That is, enabling representation and reasoning not only with the knowledge alone, but also with the associated contextual information. Examples include RDF quadruples, named graphs, annotated RDF, and contextualized knowledge repositories. These new paradigms introduce a new dimension into knowledge engineering: in addition to individuals, concepts, properties and their relations, we also need to de ne the set of contexts, and we need to \split" the knowledge between these contexts. In this paper, we propose a modeling exercise with one of the tools, for which we choose the contextualized knowledge repository. The example is complex enough to highlight many issues connected with contextualized knowledge representation, and it could possibly become the rst benchmark for contextual knowledge representation tools.
The Wikipedia Infobox of the term \Italy" states that Italian President is \Giorgio Napolitano"; clearly, this fact holds only during the current legislature. Similarly, from Freebase one can see that Homer Simpson is a Nuclear Safety Inspector and that John McCarthy is a professor of Stanford University, these two facts hold under di erent circumstances, the former holds in the Simpsons ctional world while the latter holds in the current real world. Searching for Diego Maradona in the Sigma3 semantic search engine, one obtains that he is an attacking mid elder, and he coaches Argentina national team. These two facts cannot hold at the same time.
These are just simple examples showing that most of the knowledge
retrievable from the Semantic Web is context dependent. Nevertheless, the information
about the context is usually not speci ed in Semantic Web resources, and when it
is so, e.g., by adding attributes like rdfs:comment, owl:AnnotationProperty,
etc., this information is completely ignored in the reasoning process. The
importance of contextualized knowledge has been widely recognized and this has
3 http://sig.ma/
motivated proposals for extending Semantic Web languages with the possibility
of qualifying knowledge w.r.t. some speci c contextual dimension. For instance
[
Recently we have proposed a new architecture which accommodates
contextual knowledge within the current state-of-the-art semantic web technology [
In this paper, we show a practical modeling scenario on which the CKR architecture is applied. We demonstrate the modeling capabilities and main advantages of CKR. The proposed modeling scenario is from the FIFA World Cup domain which has been chosen for its inherent contextual nature and it is complex enough to highlight many issues connected with contextualized knowledge representation. We believe that this scenario can be possibly remodeled also in any other contextual Semantic Web framework thus constituting a modeling benchmark in this area. 2
As a case study for contextualized knowledge representation we propose the domain of football and in particular we focus on the FIFA World Cup 2010. The reasons for choosing this domain are the following: 1. it is a structured domain, and most of the information available, such as teams, matches, scores, etc., can be easily represented with the standard Semantic Web languages as RDF/OWL. 4 http://www.ontotext.com/owlim/ 2. large part of the knowledge about this event is context dependent. For instance, the players of a team can be di erent for each match. Two teams can play one against the other in two di erent matches obtaining di erent scores, a player can have a di erent role in di erent matches, etc. 3. the domain presents a high level of interconnection between knowledge contained in di erent contexts. For instance the players of a team are always the same along the entire competition, players do not change their shirt number, etc.
Already from the web site of the FIFA World Cup 20105, one can recognize a certain level of contextual representation of the information, and how contexts are used for a better presentation of the information. For instance, pages are organized by team, by player, by single match. The information contained in each single page focuses on a given topic, and it is supposed to hold within the contextual boundaries of the page. The contextual structure is mainly driven by the sake of e ective organization of the web site. We will analyze the page content in detail, starting from more speci c pages, proceeding to the more general, nally reaching the home page.
Among the most speci c pages, there are the pages associated to each single match. They contain information which holds only in that particular match. For instance the lineup formation, the yellow/red cards, the substitutions, the goals, etc. For instance the fact that \Gilardino was replaced by Di Natale" is contained in the page for Match 11 of Group F, and it is supposed to hold in this match (and not in other matches). In RDF, this information is represented by a triple of the form \hAlberto Gilardinoi:his substituted byi:hAntonio di Natalei". In this case, the triple is valid only in this particular context (i.e., that of the Match 11). However, not all of the information contained in a page is context dependent.
For instance, the pages of matches contain more general information about the teams, the players, etc. which also holds in a broader context. The page related to the match also lists general information about players such as their height, the club where they currently play, etc. This information is \imported" and it is apparently listed here because it is considered to be relevant for the context. It is important to notice that, only a part of all information that is possibly available is \imported" in this context. For instance, the information about the club is relative only on the current year, and not all the clubs a player has ever played for.
There are other pages associated with di erent phases of the competition. For instance, the page entitled \group stage"6 summarizes the information of the initial phase of the competition, such as the composition of groups, and the matches taken within each group. Clearly, this information forms a broader context that encompasses all of the matches of the group stage. Some of the data listed cannot be associated with any of the particular matches, such as for instance the composition and the nal ranking of each group. 5 http://www. fa.com/ 6 http://www. fa.com/worldcup/matches/groupstage.html
The broadest context is the one associated with the whole competition. It contains information about the teams, the players, the stadiums, the schedule, etc. Such a context is not the broadest one can imagine, indeed one could consider all the di erent editions of the FIFA world cup, and the knowledge about all the football leagues in each country. As a consequence the context \FIFA world cup 2010" should be inserted in a larger contextual structure that involves all the other mentioned contexts. 3
According to the context as a box metaphor [
time(C; 2010-06-14); location(C; World); topic(C; FIFA WC Match 11) C =
TeamA(Team Italy) TeamB(Team Paraguay)
Referee(Benito Archundia)
Although contexts are possibly de ned on top of any logical language, we
focus on RDF and OWL and hence we will build contexts on top of description
logics (DL) [
De nition 1 (Context). A context is a triple hC; dim(C); K(C)i such that: 1. dim(C) is a set of assertions of the form A(C; v) where A is called dimensional attribute and v dimensional value; 2. K(C) is a DL knowledge base in SROIQ or some of its sublanguages.
The set of dimensional values dim(C) of a given context C determines its contextual boundaries. It is also called the dimensional vector of C. In a sense, it indicates the position of the context in the dimensional space, which is generated as the product of all dimensions. For instance the location dimension indicates the geographical location associated with the context. Similarly for dimensions such as time, topic and possibly others. A context is always speci ed with a total dimensional vector in which values for each dimension are given. Later on we will also employ partial dimensional vectors with some values missing (e.g., for querying in a CKR).
This determination may be precise, when all these values are constants. This is the case of the context above, in which location is set to World, time is set to 2010-06-14, and topic is set to FIFA WC Match 11. Such contexts are called primitive contexts. They contain information which is tightly bound with a particular set of dimensional values.
Besides for primitive contexts we will also make use of context classes. These are more generic contexts that allow us to specify some information which is valid for multiple sets of dimensional values. This is done by using a concept in place of one or more of the dimensional values. The semantics will then take care of that this information is associated with all primitive contexts whose dimensional vectors \instantiate" the dimensional vector of the class context. Let us take for example a generic context class representing a football match:
time( ; >); location( ; >); topic( ; Football Match) =
TeamA v Football Team TeamB v Football Team
TeamA v :TeamB
Provided that the value FIFA WC Match 11 is an instance of the concept Football Match, the semantics will associate this information with the context representing match 11 listed above, and similarly also with all other contexts representing particular FIFA matches that instantiate the context class.
In addition to context classes CKR o ers another more selective option to propagate knowledge across contexts. With quali ed concepts and roles, one can selectively query knowledge recorded in some other context. Syntactically this is done by adding the dimensional vector of the queried context into the subscript. For instance, if in the context of FIFA Match we wish to import information from the context FIFA WC representing the FIFA World Cup, we may write an axiom of the form: 9has NationalityFIFA WC :(Referee t Assistant Referee) u
9is National Team OfFIFA WC :(TeamA t TeamB) v ?
By this axiom it is required in the context of a match that referees and assistant referees must not share nationality with any of the teams in the match. Since the information about the nationalities is part of the context FIFA WC we have used quali ed role names like has NationalityFIFA WC in order to access this information. The semantics will take care of that the interpretation of has NationalityFIFA WC is the same as the interpretation of has Nationality in the context FIFA WC.
This kind of knowledge transcendence is enabled by the fact that the topics of FIFA World Cup and the one of FIFA match are related (i.e., the latter is a subtopic of the former). Therefore the semantics of quali ed concepts and roles is closely related to the hierarchy of contexts, which in turn re ects the hierarchy of dimensions. Therefore a CKR consists of a collection of contexts C and of meta knowledge about the dimensions D, as we formally de ne below. De nition 2 (Contextualized Knowledge Repository). A contextualized knowledge repository (CKR) is a pair K = hD; Ci where C is a set of contexts, and D is a DL knowledge base such that: 1. D contains n distinct roles A = fA1; : : : ; Ang called dimensions (or dimensional attributes); 2. for every dimension A 2 A, D contains a nite set DA called the dimension values of A such that each v 2 DA is either a constant symbol or a concept in D; 3. for every dimension A 2 A, D contains a role coversA whose domain and range are the constants of DA; 4. the transitive closure of the relation fhd; d0i j D j= covers(d; d0)g, denoted by
A, is a partial order on DA.
Due to the hierarchy of dimensions, the organization of contexts in each CKR is hierarchical as well. Given a CKR K and two contexts C1 and C2 with dim(C1) = d and dim(C2) = e. We say that C1 is covered by C2 if dA A eA for each A 2 A. This is denoted by C1 C2 (also d e).
Context classes do not directly participate in the context hierarchy, as some of their dimensional values are not constants. This corresponds with our intuition that a context class is a special collection of knowledge that belongs into multiple contexts. These contexts are called instances of a given context class. A context C is an instance of a context class , if for each A 2 A either dim(C)A = dim( )A or D j= dim( )A(dim(C)A)7. This is denoted by (C) (also (dim(C))).
The semantics of a CKR is an extension of the model-theoretic semantics of
DL [
Entailment in a CKR is de ned with respect to a particular context.
Id j=
De nition 3. A formula (i.e., a subsumption X v Y or an assertion A(a))
is entailed by the CKR K in d, denoted by K j= d : , if for each model I of K,
8.
7 The somewhat clumsy notation D j= dim( )A(dim(C)A) refers to the standard
DLrelated reasoning task of instance checking, i.e., it is to be read: the knowledge base
D implies that the constant dim(C)A is an instance of the concept dim( )A [
All basic decision problems such as concept satis albility checking and
entailment with respect to a CKR knowledge base are decidable, and the complexity
of reasoning is not increased when compared to classical DL [
The advantages of explicit tracking of knowledge provenance by attaching contextual meta information are apparent. In addition, our system provides means for e cient manipulation of generic information that is valid in multiple contexts using the construct of context class. Also, knowledge propagation in the system is encoded in the semantics of quali ed concepts and roles and the complexity is hidden from the user which leads to practical and e cient modeling. We will demonstrate this in the next section. 4
In this section we describe how we model the domain of football, in particular the domain of FIFA Would Cup 2010, within a contextualized knowledge repository. The modeling is composed of three basic components. The rst component is the dimension hierarchies and the meta knowledge DFootball. In this knowledge base we represent the structure of the contexts in which we organize all the information about football. The structure of DFootball will be inspired by the structure of the FIFA World Cup 2010 web site. The second component of the modeling consists of the context classes which describe types of contexts that we will deal with, such as for instance matches, teams, groups, etc. Each context class contains all the axioms that should hold in all of its instance-contexts. Finally, the third component of the model are the contexts, with all the speci c knowledge. 4.1
The knowledge base DFootball contains the meta knowledge and formalizes the structure of the contexts in the repository in a logical form. In the proposed implementation we consider the following three dimensions: time: values are time intervals of the form hstart-time; end-timei.9 Coverage relation is the standard containment relation between intervals. It does not require explicit representation because the containment relation between two intervals can be evaluated on the y; location: values determine the geographical region in which the set of statements in a context is true. This structure is represented by geographic ontology encoded in OWL and constructed from Geonames10, the resource of geographical places. The ontology de nes generic concepts, such as for instance Geographic Area or Country as well as speci c individuals for geographical places, such as World, Italy, or Florence. The concepts are then 9 For the sake of notation simplicity, to refer to the common temporal intervals, e.g., the whole year or day, we will just use the year or date instead of start-end tuple. 10 http://www.geonames.org/
Context description time location topic European Champions League 2010 2010 Europe Continental league FIFA World Cup 2010 2007{2010 World FIFA WC The nal tournaments of the FIFA 1990{2010 World World Cup of the last 20 years The group A of FIFA World Cup 2006 World FIFA WC group A 2006 TWhoerldnCalumpatch of the latest FIFA 2010 World
4.2
In the CKR architecture, context classes can be viewed as a tool which makes the representation of knowledge more e ective. Axioms that are valid in many contexts are asserted in a context class and they are automatically imported by the semantics into all contexts that instantiate the class. For example, in every context that describes a football match, certain general axioms should hold: e.g., there are two teams, one playing against the other, the number of players in the match is eleven or less per team, there is a goalkeeper in each team, etc. Instead of explicitly including all these axioms in each single context associated with a football match, one can create the context class Match containing the axioms and impose that all contexts that describe a particular match are instances of this context class.
Example 1. As an explanatory example we show the de nition of the context class Match associated to every match time(Match; Time Interval u 9start:( 1900)); location(Match; World); topic(Match; Football Match)
Team TeamA t TeamB Match = TeamA v :TeamB
Team v =11:in Lineup :> Team v 9has Captain:> has captain v in Lineup : : : The context class described above matches with all the contexts which describe any football match which is taken in any part of the world after 1900. When a context is declared to be an instance of this class it inherits the basic structure of a football match and as well as all the constraints de ned in the context class in terms of axioms.
Example 2. Another example is a context class that speci es the composition of a group during the FIFA World Cup and basic relations between the teams of the group, for instance, there are exactly four teams in the group, and in the end there is one winner and one runner-up winner who are among these four teams: topic(FIFA Group; FIFA Group)
Team Team1 t Team2 t Team3 t Team4 FIFA Group = Winner v Team
Runner-up v Team : : : The context class FIFA Group will match any of the eight contexts representing the actual groups of the FIFA World Cup, that is, groups A, B, C, D, E, F, G, H, and as a result it will de ne the notions of the winner and the runner-up in each of the groups. 4.3
The declaration of the actual contexts in the repository concludes the modeling process. It is important to stress that when a context is loaded into the CKR, rst all matching context classes are identi ed and then axioms contained in them are copied into the context. Let us now see some examples. Example 3. To represent the FIFA World Cup group A 2010, one gives the following de nitions: time(GA 2010; 2010); location(GA 2010; World); topic(GA 2010; FIFA WC group A)
Team1(Team Uruguay) GA 2010 = :T:e:am2(Team Mexico)
Winner(Team Uruguay)
Runner-up(Team Mexico)
Note that the axioms about the teams and the winners are imported due to the fact that the dimension value FIFA WC group A is an instance of the concept FIFA Group and hence the whole context is an instance of the eponymous context class.
Another powerful modeling mechanism proposed in the CKR is the notion of quali ed concepts and roles. This mechanism allows to refer from one context to concepts and roles of another context. For example, according to the format of the FIFA World Cup, after the group stage matches only the winner and the runner-up team from each group pass into the next tournament stage, called \round of sixteen", here, group A is one context and a match in the round of sixteen is another. With help of quali ed concepts and roles we are able to express complex axioms in the latter context reusing knowledge of the former. Example 4. To represent the constraint that during the match 46 in the round of sixteen the teams Uruguay and Republic Korea are actually the winner and the runner-up of the groups A and B accordingly, we insert the following axioms in the context of the match:
time(Match 49; 2010); location(Match 49; World); topic(Match 49; FIFA WC Match 49) Match 49 = TTeeaammAA(vTeWaminUnerru2g0u10a;yW)orld;FIFA WC group A
: : : The semantics of quali ed symbols will take care that the quali ed concept Winner2010;World;FIFA WC group A actually refers to Winner in the context with the dimensions h2010; World; FIFA WC group Ai, that is, the one that we above named GA 2010.
Example 5. To represent the context of the nal match of the FIFA World Cup 2010, the following declarations can be used: time(Final 2010; 2010); location(Final 2010; World); topic(Final 2010; FIFA WC nal match) TeamA(Team Spain)
TeamB(Team Netherlands) Final 2010 = in Lineup(Team Netherlands; Maarten Stekelenburg) in Lineup(Team Netherlands; Giovanni van Bronckhorst ) has Captain(Team Netherlands; Giovanni van Bronckhorst ) : : : We also assert in the meta-knowledge that FIFA WC nal match is an instance of the concept Football Match and hence this context will inherit all the axioms from the context class Match. In addition, please note the role of each player and the shirt number of the player do not change between the matches in one tournament, thus this information is not speci ed here but it can be imported from the more general context of the FIFA World Cup 2010 whenever needed. This approach is also re ected at the actual web site of the FIFA tournament. 5
In this section we will take a look on conjunctive query answering in a CKR. We show how the notion of conjunctive query has to be generalized in order to be useful in a situation involving multiple contexts and we will explain how answers for the conjunctive queries are de ned. We will then show several examples of conjunctive queries and the answers building on our FIFA World Cup scenario introduced above.
In the classical setting a conjunctive query (CQ) is an expression of the form
Q(x) 9y Vin=1 i(x; y) where x and y are tuples of variables, and each i(x; y)
is either an unary or a binary predicate taking variables from x and y [
query (CCQ) over a CKR is an expression of the form Q(x) 9y Vin=1 di : i(x; y) where for each i, di is a possibly partial dimensional vector, and i(x; y) is a conjunction of unary and binary predicates taking variables from x and y. If x is empty then the query is called boolean. If for each i, di is a total dimensional vector then the query is said to be fully contextualized.
In CKR, queries can span over multiple contexts with di erent conceptualizations and hence the result can be seen as a mash-up of knowledge from di erent contexts. We will make use of substitution and completion. By [x=a] we will understand the expression derived from in which each element of x is replaced by the respective element of a. Given two dimensional vectors d and e, by d + e we will understand a completed vector which contains all elements of d plus the elements of e for those dimensions which d is missing. The semantics of CCQ is de ned as follows.
De nition 5. A fully contextualized boolean CCQ Q() 9y Vin=1 di : i(y) is said to be entailed by a CKR K, if for each model I of K there is a substitution u such that Idi j= (y)[y=u]. This is denoted by K j= Q().
The expression e : a formed by a dimensional tuple e and a tuple of constants a is an answer for a CCQ Q(x) 9y Vik=1 di : i(x; y) with respect to a CKR K, if K j= Vik=1 di + e : i(x; y)[x=a].
Let us now see some practical examples of CCQ.
Example 6. As a simple example, consider the following query which retrieves the list of all goalkeepers and the teams they play for in the current World Cup: Q(x; y)
h2010; World; FIFA WCi : Goalkeeper(x) ^ in Squad(x; y) The answer set will look like:
x y Gianluigi Bu on Team Italy Federico Marchetti Team Italy
Tim Howard Team USA Example 7. The previous query is concerned with a sole context of the 2010 World Cup, which is fully speci ed in the query. We may of course query over multiple contexts. The next query retrieves the list of goalkeepers who played for the team Italy in any FIFA World Cup:
Q(x)
hWorld; FIFA WCi : Goalkeeper(x) ^ in Squad(x; Team Italy) As we can see, by omitting one of the dimensions in the dimensional vector within the query, this query is evaluated by substituting all possible dimensional values for this dimension and querying in every resulting context. This yields the answer set:
Context time location 2010 World 2010 World 2006 World 2006 World
World
topic x FIFA WC Gianluigi Bu on FIFA WC Federico Marchetti FIFA WC Gianluigi Bu on FIFA WC Angelo Peruzzi
FIFA WC Note that the answer set is contextualized, that is, for each answer we get also the context in which it answers the query. We can also see that some individuals are listed more than once, each time in a di erent context.
Example 8. Of course, we have the possibility to explicitly address more than one context. In the following query, we ask about the list of players who did in fact play in some match. For this we have to consider the context FIFA WC, which contains the list of players and then the contexts of particular matches. Q(x; y)
9zh2010; World; FIFA WCi : in Squad(x; y) ^h2010; Worldi : in Lineup(z; x) The rst context we have speci ed fully and for the second one we again use the same feature as above: we omit the value for the topic dimension, thus all possible values are substituted here. Due to the fact that the predicate in Lineup is inherent to the contexts that represent matches, the query is evaluated once per each match. The answer set will look as follows: We can see that same goalkeepers played in several matches, but in addition there are also matches in which more than one goalkeeper played.
From the examples, we conclude that CCQ are a natural and particularly versatile extension of CQ that provides a exible mechanism for data retrieval over a CKR that allows us to retrieve and combine data from multiple contexts and in addition it allows predicating over contextual meta data in order to re ne the query. 6
In this section we outline some notable approaches and systems for modeling contextualized knowledge with semantic web technologies, particularly focusing on the football domain selected for the use case in the present work. Though the football domain is characterized by well structuredness of the available information (e.g., tournaments, teams, players, matches, etc.), which simpli es its representation with RDF/OWL semantic web standards, the challenging problem is to re ect and consistently represent context dependency of the most of knowledge with RDF/OWL (e.g., lineups within a certain match, authors of goal shots, etc.).
The 2006 FIFA World Cup was one of the main application scenarios
investigated within the SmartWeb11 research project. The corresponding knowledge
on the world cup has been encoded in the SWIntO Sport Event RDFS ontology
[
Another notable example extensively modeling football domain is Freebase. Freebase12 is a massive collaboratively-edited RDF-exportable knowledge base of facts about people, organizations, events, etc. The knowledge base is organized into domains (e.g., sport disciplines, politics, etc.), grouping relevant types (e.g., sport championships, clubs and players, politicians and parties, etc.). 11 http://smartweb.dfki.de/ 12 http://www.freebase.com/ Types have properties (e.g., Date of birth for type Person), and can be organized in inheritance hierarchies (e.g., Football Player type extends generic type Person) allowing for property inheritance. For example, for representation of facts about 2010 FIFA World Cup Freebase contains a dedicated type FIFA World Cup 201013. One of the distinguishing characteristics of Freebase is extensive use of rei cation in order to support compound multi-dimensional properties, allowing to assign contextually bounded values. An example of such a compound property is Football Player Match Participation allowing to assert for a given match a player and a team he plays. 7
Contextualized Knowledge Repository (CKR) constitutes a novel architecture
for the Semantic Web that has been lately proposed and implemented [
In this paper, we describe a modeling scenario from the domain of football, by which we demonstrate the features of the CKR architecture, we show how to model with it in practise, and highlight its particular advantages. The choice of this particular domain is due to its inherent contextual nature and su cient complexity. Although equivalent modeling can surely be done in any ontology language such as OWL that does not provide any context aware features, it is apparent from our demonstration that with CKR an increased e ciency of the representation and more intuitive modeling are achieved. We believe that the scenario can be remodeled also in any other contextualized Semantic Web framework and thus it may serve in future as a modeling benchmark in this area. 13 http://www.freebase.com/view/en/2010 fa world cup