Evaluation of Contextual Modelling in the FIFA World Cup Use Case

Technical ReportTR-FBK-DKM-2011-3

Loris Bozzato1, Francesco Corcoglioniti1,2, Martin Homola1,3, and Luciano Serafini1

1 Fondazione Bruno Kessler,Via Sommarive 18, 38123 Trento, Italy

2 DISI, University of Trento,Via Sommarive 14, 38123 Trento, Italy

3 FMFI, Comenius University,Mlynska dolina, 84248 Bratislava, Slovakia

{bozzato,corcoglio,homola,serafini}@fbk.eu

Abstract. This report presents and compares the modelling in the CKR framework and in the OWL 2 ontologylanguages of the FIFA World Cup domain. This modelling activity has been carried out as part of an evaluationactivity ongoing at FBK, DKM unit, of ontological frameworks based on the notion of context. The reportdescribes the goal, methodology, overall structure and single parts of the realized CKR and OWL 2 ontologies,and provides the rationale behind relevant modelling decisions.

Table of Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 CKR model: contextualized ontology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Metaknowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Knowledge inside the contexts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 Flat model: OWL 2 ontology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.1 Top Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.2 Sports Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.3 Football Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.4 FIFA World Cup Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1 Introduction

This report presents and compares two different ontologies for the representation of the FIFA WorldCup. These ontologies provide a detailed modelling of the World Cup tournaments and include theformalization of the necessary football and sport concepts.

The two ontologies have been realized with the goal to support the comparison of different onto-logical frameworks based on the notion of context, in particular for evaluating the effectiveness of theContextualized Knowledge Repository (CKR) framework presented in [3]. The comparison consists inevaluating the capabilities of those frameworks in modelling a complex domain such as the chosen one,with expressivity judged by analysing which features, constraints and queries existing in the domaincan be formalized in each framework. In this scenario, the two presented ontologies provide a com-parison between the CKR representation and an OWL 2 modelling of the domain. Being OWL 2 thestandard ontological language currently used in the Semantic Web community, the second ontology actsas the reference domain modelling against which the other, modelled with a notion of context, has to becompared.

The choice of using the FIFA World Cup as the domain for the comparison is dictacted by the factthat football knowledge is inherently contextual. Football competitions, competition stages and matchescan all be seen as contexts characterized by specific knowledge and rules which are local to them, suchas the ranking rules in a group of the FIFA World Cup or the constraint that a player can play only forone team, which holds in single competitions but not globally (consider e.g. a player that plays bothfor a club team and his national team). At the same time, individuals of the domain such as teams andplayers participate to different contexts, thus giving rise to cross-context relations and constraints suchas the qualification rules that specify how teams can progress from one competition stage (a context) tothe next stage (another context). The criteria for the decisions behind our modelling choices consist inthese three aspects:

1. The availability of data. We extended the comparison with a performance evaluation of knowledgebases built by populating the different ontologies modelling the domain (the OWL 2 ontology andthe contextual ontology) with significant amounts of ABox data [1]. Therefore, only aspects of thedomain for which ABox data is available have been considered.

2. The need to model the contextual aspects of the domain, as far as feasible, so to better supportevaluation of expressiveness. To this end, it has been decided to model the progressive refinementof concepts such as team, sportsman, competition and match in moving from the sport topic to thefootball topic and, finally, to the FIFA World Cup setting, thus modelling the different features ofthese concepts in each of these broad contexts. Another decision has been to model all the editionsof the FIFA World Cup and not just a specific edition, in order to cover also the temporal contextualdimension.

3. The need to support queries that span multiple contexts, as required by the performance evaluation.Examples of these queries are: ”which team Italy has played the largest number of matches againstin FIFA World Cup?” (need to consider multiple match contexts) and ”which players, in FIFA WorldCup, have played against team mates of their own football club?” (need to consider different teamsand competitions). To this end, it is important for the ontology to describe a large number of individ-uals participating to different contexts (such as a team or player playing in different competitions).This fact enables the formulation of queries that move from one context to another, by passingthrough the individuals shared in the two contexts.

The knowledge modelled in the ontology has been mainly retrieved from Wikipedia (see e.g.the following entries: http://en.wikipedia.org/wiki/Association football, http://en.wikipedia.org/wiki/FIFA World Cup and http://en.wikipedia.org/wiki/History of the FIFA World Cup) and the FIFAWeb site (www.fifa.com/). The list of concepts modelled in the contextualized ontology has been usedas a basis to bootstrap the modelling activity for the OWL 2 ontology. Due to the different ontologicallanguages, these concepts have been re-formalized from scratch in OWL 2, and new classes and roleshave been added to extend the modelling according to the criteria listed above and, in particular, to en-able the modelling of the different editions of the FIFA World Cup. Note that no existing ontology orvocabulary has been reused in the ontology, partly because of the lack of specialized ontologies for theFIFA World Cup or even the football domain, partly due to the aim of keeping the presented ontologyself contained, thus avoiding to complicate the comparison with unnecessary specificities of importedontologies. The ABox of the two knowledge bases was populated with data collected from publiclyavailable football Web sites, including soccerway.com4 and fifa.com5. The data covers the tour-nament phase of 4 editions of FIFA WC (1998 – 2010), with 256 matches, 61 national teams and 2014players.

The remainder of this report presents the details of the two ontologies: in the following two sec-tions we describe the contextualized ontology (called CKR model) and the OWL 2 ontology (called Flat

4 http://www.soccerway.com/international/world/world-cup/5 http://www.fifa.com/worldcup/archive/index.html

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model). While in the presentation of the CKR model we mainly concentrate on the modelling method-ology we followed in its definition, in the description of the Flat model we principally present the actualmodelled aspects of the inspected domain. This presentation also allow us to highlight the difficulties inrepresenting contextualized knowledge without the support of a specific framework.

2 CKR model: contextualized ontology

In this section, we describe the contextualized ontology that we created for this comparison: we ex-plain our design decisions and point out the advantages of the contextualized representation. We willalso comment on the modeling methodology issues. In particular, the structure of this section followsintuitively the modelling process that we adopted: we first model the metaknowledge representing theorganization of contexts and then we detail their contents.

2.1 Metaknowledge

Definition of dimensions and dimensional values. First step in design of the metaknowledge is to decidewhich are the context dimensions. We required to organize knowledge on the base of time occurrence, lo-cation of interest and differences in subject. Thus, we decided to use three dimensions: topic, time and lo-cation.

Fig. 1. Cover hierarchy for topic

In order to come up with a suitable range of dimensional val-ues, we must consider the desired granularity of contexts. Inour use case the main focus is on various football tourna-ments, where the data is typically organized in units respec-tive to tournaments (editions), tournament stages, groupsand single matches. Therefore the most fine grained valueof the topic dimension will be a single match and we willhave one value for every match of every tournament of in-terest. We also use values for tournaments and their stages,and the most general values will include football and sports.The coverage between these values is based on the organi-zation of each tournament: an excerpt is shown in Fig. 1.

For the time dimension, the most granular value is a day:even if, for instance, we could represent concepts with amore fine grained temporal dimension (e.g. the score timeof a goal), since our aim is to represent facts concerningtournament matches, a day is the most reasonable value inour case, as very rarely the same teams play more than onematch in a single day. Other values such as year or seasonmay be also useful for querying and aggregating data. For lo-cation, we consider the countries in which the tournamentsare played, since we only deal with international competi-tions. Also in this case, more granular values can be intro-duced when needed. As a matter of fact, we note that in thismodel the dimension of location, while often useful in otherdomains, does not contribute to the structure of the coveragerelation: this actually depends by the fact that we assumethat each edition is held in a fixed location.

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Context classes definition. Following the idea of context class [3], the point of this step is to determinethe sets of contexts which share a large part of their axioms or that can be organized under similar de-scriptions. In our use case, we notice that a big part of knowledge related to a match is shared betweenall matches in the knowledge base: we thus introduced the context class Match, which defines the com-mon details of FIFA WC matches. Moreover, between such matches we can further recognize a subsetsharing similar properties in the set of matches of the knock-out stage: hence, we introduced a subclassof Match, called KOSMatch. Note that by this subclass relation, each context recognized as KOSMatchdirectly inherit the axioms stated by the class Match.

Methodology. In general a possible methodology to follow in the definition of metaknowledge is to startwith one dimension and then refine the dimensional structure with the other dimensions according totheir perceived priority. In our case we started with topic, then followed by time and consequently loca-tion. In other use cases, the relevance order of dimensions may be different, e.g., when modeling withingeographical domain, location will probably be the most relevant dimension to start with. In general,we expect the definition of the metaknowledge to be an iterative process, since it is often easier to startby recognizing some relevant values and then refine and organize them with respect to the structure oftheir dimension. Note that the criteria to choose a particular dimensional value are based on the valuerepresenting certain organizational entity along which the data in the domain is typically grouped butalso retrieved. In this sense, match is a well chosen value, but 1st period is not; similarly, 30 May 2010is well chosen while 30 May 2010 16.00 17.00 is not since rarely in fact we would query about thisperiod.

2.2 Knowledge inside the contexts

Once the dimensional structure and context classes are defined, we have to model the knowledge contentof each context class or single context. The structure of the dimensional hierarchy allows the modeller toproceed by directly following the covering relation. We now pass by the context hierarchy of our domainand explain how the TBoxes of the contexts were modeled.

Upper contexts. At the top of the context hierarchy there are four contexts that we call upper contexts:Ct (top), Cs (sports), Cfb (football), and Cpf (pro-football). They directly correspond to the top four levelsof the topic dimension and they have the most general values set for location and time. These contextsdescribe the general information which is universally valid in our domain. We split this information intofour contexts rather than having just one, in order to enable extensibility of the knowledge base with newsports (by introducing contexts under Cs) or even completely different topics, e.g., politics, or culture(by introducing new contexts under Ct).

The most general context Ct contains the part of the knowledge which is universally valid. Forinstance, it contains the axioms:

Person v Agent Organization v Agent

Person v ¬Organization Team v Organization

This general knowledge is then refined and extended in three steps. First, knowledge related to sports isspecified in Cs. To keep the connection with the upper contexts, we often “import” concepts and furtherrefine them. For example, using the following axioms the concept Team is imported and refined in Cs:

Team v Teamtop Team v ∀hasMember.Sportsman

Sportsman v Persontop

This modeling is then further refined in Cfb:

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Cwc10 : fifa wc,2010, south africa

Cpf : pro football−,world

Cwc06 : fifa wc,2006, germany

Cwc98 : fifa wc,1998, france

Cwcq10 :

2010, south africafifa wc qualification,

Cwct10 :

2010, south africafifa wc tournament,

Cgs10 :

2010, south africafifa wc group stage,

Ckos10 :

2010, south africafifa wc knockout stage,

CgroupA10 :

2010, south africafifa wc group A,

CgroupH10 :

2010, south africafifa wc group H,

Cr1610 :

2010, south africafifa wc round of 16,

Cfm10 :

2010-07-11, south africafifa wc final match,

CgAm110 :

2010-06-11, south africafifa wc group A match 1,

CgAm610 :

2010-06-22, south africafifa wc group A match 6,

Cr16m110 :

2010-06-26, south africafifa wc round of 16 match 1,

Cr16m810 :

2010-06-29, south africafifa wc round of 16 match 8,

Fig. 2. Overview of FIFA WC contexts

Team v Teamsports hasPlayer v hasMembersports

Player v Sportsmansports Team v ∀hasPlayer.Player

Note that this gradual specialization of knowledge allows us to devise an appropriate description of thedomain at each level of specialization with minimum overhead of axioms, while reusing the genericknowledge from the upper context. For instance the fact that Person and Organization are declareddisjoint in Ct implies that Player and Team are disjoint in Cfb. Additional knowledge inside Cfb includesaxioms on player positions, coaches and referees, and basic types of teams (e.g., men, women andmixed teams). This knowledge is then further refined in Cpf with information specifically valid in theprofessional context, such as professional associations, player and team registrations, and additionaltypes of team based on age of players, club and national teams.

Tournaments and their organization. After modeling generic football and sports knowledge in the up-per contexts, we will now focus on FIFA World Cup tournament and its structure. An overview ofcontexts representing the FIFA WC editions (with details of WC 2010) is shown on Fig. 2. Three maincontexts are Cwc (FIFA WC, the whole competition), Cwcq (qualification) and Cwct (tournament). InCwc all data about participating teams and players is recorded. Generic concepts and roles represent-ing countries, teams, players and relations between them are imported from the upper contexts (e.g.,SeniorNationalTeam, MenTeam, hasCountry). Relations and constraints imposed in the upper contextspropagate to Cwc and thus we are able to reuse them in this context. An example is the concept Team,which is imported from the Cpf context and refined in Cwc as a subconcept of both MenTeam andSeniorNationalTeam:

Team v SeniorNationalTeam Team v MenTeam

The playing phases of the tournament are represented by sub-contexts of Cwc. The teams qualified to thefinal tournament are determined in the qualification phase Cwcq and its sub-contexts. The context Cwct

together with its sub-contexts represents the final tournament and its stages. We have separate contextsfor each of the 8 groups, for the group stage itself, and for each of the play-off stages up to the finalmatch. Individual matches are assigned contexts that are placed under the stage they belong to. In Cwct

teams are defined to be only the qualified teams imported from Cwcq and to be split into the 8 groups:

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Team ≡ QualifiedTeamqualification Teamgroup A v Team . . . Teamgroup H v Team

where Teamgroup A, . . . , Teamgroup H are also declared disjoint. In each group, the two successfulteams are recorded using the Winner and RunnerUp concepts. These are then aggregated under thePassedTeam concept in the Cgs context. Such modeling is then continued in the play-off contexts: theparticipating teams are here assured to be the passed teams from the previous stage. Rosters in the Cr16matches are determined based on the Winner and RunnerUp concepts from the groups. Finally, the finalranking is imported from the final stages into the super-contexts Cwct and Cwc.

Match context classes. One of the most specific parts of the TBox represents the details of a single matchof the FIFA WC. In other words, this TBox represents the axioms of the context class Match containingall of the matches in the FIFA WC competition: in particular, the class specifies the information toidentify the home and host team, to represent the key moments (goals, substitutions, referee calls etc.),periods (first half, second half, extra times) and initial line-ups of the represented match. For example,we find axioms of the form:

PlayerInMatch v Player ∃inLineUp.Team v PlayerInMatch

∃inSubstitutes.Team v PlayerInMatch

Substitution v KeyMoment Substitution v ∃hasSubstituteIn.Player

Substitution v ∃hasSubstituteOut.Player

Being a generic representation of a match, the class does not detail the form of specific WC matches. Onthe other hand, in the TBox for the context sub-class KOSMatch details specific for the kick-out stagematches are given: for example, we require that there exist a Winner and a RunnerUp and the match cannot be a tie.

KOSMatch v ∃hasParticipant.Winner KOSMatch v ¬TieMatch

KOSMatch v ∃hasParticipant.RunnerUp

Methodology. Our approach for modelling single ontologies has been to start by breaking down require-ments and decide what to represent in each context in the dimensional structure. A criterion for choosingin which context one axiom or requirement should be put is the specificity. i.e., the ”less specific” con-text. As it is exemplified by the Winner and PassedTeam concepts in the tournament part, axioms fromthe higher contexts can be imported and specialized, while on the other hand knowledge from lowercontexts can be abstracted and aggregated in the higher contexts.

3 Flat model: OWL 2 ontology

The OWL 2 ontology we present is organized in four modules. Figure 3 shows the modules, their importrelations and some examples of representative classes and roles defined by each module. Note that aunique namespace is assigned to each module, and QNames are used through the report to denote URIsof concepts, roles and individuals defined in the ontology.

Each module models the domain at a different abstraction level, with the modelling of more generalmodules imported and progressively refined in more specific modules. Moving from the most general tothe most specific, the four modules of the ontology are:

– Top Module. It models common, domain-independent knowledge not specific to sport or football.To a certain extent, it covers the role of an upper ontology, laying the foundations of the ontologyon top of which other modules build. The choice of not using an upper ontology is motivated by thegoal to keep the presented ontology self-contained, and thus avoid to complicate the comparison ofcontextual frameworks with unnecessary upper ontology details.

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Top Module

top: http://dkm.fbk.eu/fkb#

Sport Module

sport: http://dkm.fbk.eu/fkb/sport#

Football Module

fb: http://dkm.fbk.eu/fkb/sport/football#

FIFA World Cup Module

wc: http://dkm.fbk.eu/fkb/sport/football/fifa-wc#

Representative classes: top:Country, top:Organization, top:Person, top:Event

Representative roles: top:hasCountry, top:hasMemberOrganization, top:hasParticipant, top:hasOrganizer, top:hasChildEvent, top:hasParentEvent

Representative classes: sport:Sport, sport:GoverningBody, sport:Team, sport:Coach, sport:Referee, sport:Sportsman, sport:Competition, sport:Match, sport:PlayerTeamMembership (ternary relation)

Representative roles: sport:hasSport, sport:administratesIn, sport:hasWinner, sport:hasQualifiedParticipant, sport:hasOfficial

Representative classes: fb:NationalTeam, fb:ClubTeam, fb:Coach, fb:Referee, fb:Player, fb:PlayerPosition, fb:Competition, fb:Match, fb:Period, fb:KeyMoment, fb:Goal, fb:Substitution, fb:RedCard

Representative roles: fb:hasPosition, fb:hasReferee, fb:hasHomeTeam, fb:hasHostTeam

Representative classes: wc:Team, wc:Match, wc:WorldCup, wc:QualificationPhase, wc:Tournament, wc:GroupStage, wc:KnockoutStage

imports

imports

imports

Fig. 3. Overview of the ontology modules.

– Sport Module. The module refines the concepts of the Top Module to model knowledge commonto different sports, such as the notions of sportsman, team, competition and match. The importantternary relation sport:TeamMembership is introduced to link these entities together, representing ina context-dependent manner the membership of sportsmen to teams in certain matches or competi-tions.

– Football Module. The module refines the concepts of the Sport Module in the scope of football. Alarge part of the module deals with the modelling of matches, with the notions of fb:Period andfb:KeyMoment introduced, the latter permitting, through its specializations, to model match-relatedevents such as goals, substitutions and referee calls. Football player positions are also introducedand different types of football teams are defined.

– FIFA World Cup Module. This is the most specific module and provides both a general, edition-independent characterization of the FIFA World Cup, and the modelling of edition-specific con-straints. The structure of the FIFA World Cup is modelled by defining classes for the differentcompetition stages. Differences in format between editions are formalized with concept inclusionaxioms that specify which stages are included in the World Cup and how many teams participate orqualify to each stage. It is worth noting that the FIFA World Cup module does not introduce newproperties or individuals; instead, it essentially consists in the specialization of football classes withthe addition of axioms to constrain them. This confirms that all the concepts necessary to model afootball competition are already defined in the Football Module, and that the modelling of specificcompetitions can be simply obtained by subclassing and adding axioms to constrain the use of theseconcepts.

In the following sections we describe in details the contents of the four modules of the OWL 2 ontology,in particular highlighting the choices that have been adopted in the separation and refinements for themodelled concepts among the modules.

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3.1 Top Module

The Top Module defines general concepts representing common knowledge not specific of the sport andfootball domains. These concepts provide a shared conceptualization which is inherited and refined bydomain-specific modules and can be exploited to align different modules, in case other domain-specificmodules are added to the ontology beyond the Sport Module.

Three main disjoint concepts are introduced, together with their subsumption hierarchies: top:Agent,top:Event and top:Place.

Places Class top:Place represents a generic region of space and is at the root of a class hierarchy definingthe types of places required in the sport domain, e.g. in order to model locations of events and countriesof teams. At the topmost level, places are differentiated among the disjoint top:Country, top:City andtop:Locality. Class top:Venue is introduced to model the place where a sport event is held, such as astadium or an analogous facility.

Geo-polical entities are related to the rest of the ontology via three general-purpose object proper-ties: top:locatedIn, top:hasCountry and top:hasNationality. These properties model, respectively, thegeographical containment among places, the belonging of something to a country and (as a special caseof the latter) the nationality of a person. The use of top:locatedIn is restricted by the following twoaxioms, that prevent a top:Country or top:City to be located inside a top:City or top:Locality:

top:Country v ¬∃ top:locatedIn .( top:City t top:Locality )

top:City v ¬∃ top:locatedIn .( top:City t top:Locality )

Agents Agents are defined in the context of this ontology as entities capable of intentionality. Two rele-vant types of agents are top:Organization and top:Person. As agents, these disjoint concepts share com-mon properties expressing contact information, e.g. top:hasPhoneNumber and top:hasHomePage. Per-sons are further characterized by gender (modelled through disjoint sub-classes top:Male and top:Female),first and last names, nationality and, since mainly dealing with athletes, by height and weight (by proper-ties top:hasPersonHeight and top:hasPersonWeight, expressed respectively in meters and kilograms).Organizations are further characterized by the foundation year and by the possibility to organize them inhierarchies via object property top:hasMemberOrganization, which encodes a direct (i.e. non transitive)membership relation between organizations.

Events The basic modelling of events in the Top Module serves as a basis for the different types of eventintroduced in other modules, such as matches and competitions. A top:Event is something that happensat a certain point in time and space, represented respectively by functional properties top:hasDate andtop:hasVenue. Events may be further characterized by their organizers (property top:hasOrganizer) andparticipants (property top:hasParticipant and inverse top:participateTo), which are both top:Agents.

Four object properties permit to organize events in a containment hierarchy, where containment isintended both from a temporal and organizational point of view. Direct containment is expressed by theirreflexive properties top:hasParentEvent and the inverse top:hasChildEvent. Their transitive closureconsists of properties top:occoursIn and top:containsEvent.

3.2 Sports Module

The Sport Module refines the concepts of the Top Module to model knowledge common to differentsports. Sports are modelled as individuals of class sport:Sport and its sub-classes. They are differentiatedbetween sport:IndividualSport and sport:TeamSport (disjoint), the first being sports played by singleindividuals (e.g. tennis) while the latter being played by teams (e.g. football). Property sport:hasSportis used to link instances of other sport concepts – such as teams, sportsman, sport events – to the sport(s)they play or refer to.

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Two kinds of organizations are introduced: sport:Team and sport:GoverningBody. Teams are or-ganizations that participate to sport events and retain their identity even if their composition may varyin time. Governing bodies are organizations such as FIFA which supervise the professional playing ofa sport; they can be organized in hierarchies through the inherited top:hasMemberOrganization prop-erty (e.g. the Italian FIGC is member of UEFA which is member of FIFA) and operate in a certaingeo-political scope, encoded by the mandatory property sport:administratesIn:

sport:GoverningBody v ∃ sport:administratesIn . top:Place

The module models the different roles a person may play in a sport: sport:Sportsman (the actual player),sport:Coach and sport:Referee. Note that these classes are not disjoint for the sake of generality (e.g.,a player can be also a coach). Sportsmen are further divided between sport:AmateurSportsman andsport:ProSportsman (in the ontology, pro generally stands for professional).

The last main concept introduced by the module is sport:Event, which stands for a generic sport-related event. Some sport events may consist in sportsmen or teams playing one against the others, sothat a final ranking can be formed: for this kind of events, the functional properties sport:hasWinner,sport:hasRunnerUp, sport:hasThirdPlace and sport:hasFourthPlace are introduced to model the firstand usually most relevant positions of the ranking.

Two relevant and disjoint types of sport events are sport:Match and sport:Competition. A match is asport event where two (or rarely more) competitors (teams or individual sportsmen) play one against theother according to the specific rules of the sport, producing some result (e.g. scores). A competition, onthe other hand, is a more articulated event that involves a larger set of competitors, may comprise sev-eral matches and may include the assignment of prizes at the end. Another orthogonal distinction amongsport events is between professional and non professional events; sport:ProEvents are disputed by pro-fessional teams or sportsman, and are formalized by requiring that child events, if any, are professionalevents themselves:

sport:ProEvent v ∀ top:hasChildEvent . sport:ProEvent

The detailed modelling of competitions, matches and teams are presented in the following sections: inthe last section we also describe the use of a reified ternary relation to model the composition of teamswith respect to specific sport events.

Competitions As top:Events, competitions may be organized hierarchically via propertiestop:hasChildEvent and top:hasParentEvent. Competitions which are child events of another compe-tition are termed sport:CompetitionStages; for consistency, they are required to be child of exactly onesport competition:

sport:CompetitionStage ≡ sport:Competitionu∃ top:hasParentEvent . sport:Competition

sport:CompetitionStage v (≤ 1) top:hasParentEvent . sport:Competition

For competitions organized in stages, qualification to the next stages is represented via propertysport:hasQualifiedParticipant, that refines top:hasParticipant.

A first classification of competitions is based on the geo-political scope and consists in the disjointsport:InternationalCompetition, sport:NationalCompetition and sport:RegionalCompetition. A partic-ular kind of international competition is the sport:CountryHostedCompetition, which is any interna-tional competition hosted in one or more countries, identified by property sport:hasHostCountry:

sport:CountryHostedCompetition ≡ sport:InternationalCompetitionu∃ sport:hasHostCountry . top:Country

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Another classification criterion is the competition format. From this point of view, a relevant type ofcompetition is the sport:MatchCompetition, which is any competition whose final result is based onthe outcomes of one or more matches among its participants. Two special types of match competitionsare sport:Groups and sport:KnockoutRounds (and their specializations), which can be used as “buildingblocks” when modelling the stages of a complex competition.

Note that the classification by competition format, the classification by geographical scope and thenotion of competition stage are all orthogonal and can be combined together, this fact being exploited inthe modelling of the FIFA World Cup competition.

Matches Several types of match are modelled: a first distinction is between played and yet to be playedmatches. A sport:PlayedMatch has an outcome, but the only possible distinction at this level of abstrac-tion is between matches ended in a tie (sport:TieMatch) or not ended in a tie (sport:NotTieMatch). Thisis a total classification of played matches, with sport:NotTieMatches required to have a winner. Thesetwo facts are formalized as follows:

sport:PlayedMatch ≡ sport:NotTieMatch t sport:TieMatch

sport:NotTieMatch v ∃ sport:hasWinner . sport:Team

Among competitive matches, a further and useful distinction is between sport:OneLegTieMatch andsport:TwoLegTieMatch, respectively played in the scope of a one- or two- leg knockout round. The firstkind of match cannot end in a draw, hence it is disjoint with sport:TieMatch. The definition of these twoclasses is formalized as follows:

sport:OneLegTieMatch ≡ sport:CompetitiveMatchu∃ top:hasParentEvent . sport:OneLegKnockoutRound

sport:TwoLegTieMatch ≡ sport:CompetitiveMatchu∃ top:hasParentEvent . sport:TwoLegKnockoutRound

Dis( sport:OneLegTieMatch , sport:TieMatch )

Teams Classification of teams is performed based on the gender and professional / amateur status oftheir members. In the first case, the distinction is between sport:MenTeam, sport:WomenTeam andsport:MixedTeam, all disjoint. In the second case, members of a sport:ProTeam are required to be allsport:ProSportsman. Professional teams are further classified in sport:ClubTeam and sport:NationalTeam,with the latter required to represent exactly one country and to participate only to international compe-titions.

In order to formalize the different sub-classes of sport:Team, the membership relation defining thecomposition of a team must be introduced. Composition of a team may vary with time; moreover, dif-ferent types of composition should be considered, including: (1) the membership to a team line-up orsubstitues in a particular match, (2) the membership to the list of team players registered to a partic-ular competition and (3) the contractual employment in a team not depending on a particular matchor competition. To simplify, this complex dependency on time and scope is approximated as a sim-pler dependency on the sport event, leading to the reified, ternary sport:TeamMembership relationdepicted in figure 4. Instances of this class represents instances of the relation, whose participatingteam, person and event are respectively identified by properties sport:hasMember, sport:hasPerson andsport:hasParticipatingTeamMember (the directions of these properties have been chosen in order tofacilitate the definition of axioms). This solution permits to explicitly and concisely model the first twocases of compositions, plus additional cases where, for instance, membership w.r.t. a competition stageshould be considered; on the other hand, the third case of contractual employment is left out and it hasnot been modelled in the module so far6.

6 This case can be modelled through another ternary relation between team, person and time period, or it can be approximatedby restating the membership to a team for each different competition the member participated to while employed in the team.

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sport:Event

sport:Team

Membershipsport:hasParticipatingTeamMember

(inv.func.)

sport:Teamsport:hasMember

(inv.func.)

top:Person

sport:Sportsman

sport:Coach

sport:hasPerson (func.)

sport:CoachTeamMembership sport:hasCoach

(⊑sport:hasPerson)

sport:PlayerTeamMembership

sport:hasPlayerNumber: xsd:positiveInteger (func.)

sport:hasPlayer (⊑sport:hasPerson)

disjoint

Fig. 4. Modelling of membership of persons to teams in the scope of sport events.

The role of a team member is modelled by specializing the membership relation. Therefore, the twoclasses sport:PlayerTeamMembership and sport:CoachTeamMembership are introduced as a total clas-sification of sport:TeamMembership.

Although the refinement of sport:TeamMembership in two sub-classes is sufficient to model roles,it is convenient to also specialize property sport:hasPerson in sport:hasPlayer and sport:hasCoach, re-spectively for classes sport:PlayerTeamMembership and sport:CoachTeamMembership, so to facilitatethe definition of constraints on team members (more details below). These two sub-properties are de-clared as disjoint and are related to the two sub-classes of sport:TeamMembership.

Based on the defined sport:PlayerTeamMembership relation and property sport:hasPlayer, the foursub-classes sport:MenTeam, sport:WomenTeam, sport:MixedTeam and sport:ProTeam are formalizedas follows:

sport:ProTeam v ∀ sport:hasMember .(∀ sport:hasPlayer . sport:ProSportsman )

sport:MenTeam v ∀ sport:hasMember .(∀ sport:hasPlayer . top:Male )

sport:WomenTeam v ∀ sport:hasMember .(∀ sport:hasPlayer . top:Female )

sport:MixedTeam v ∃ sport:hasMember .(∃ sport:hasPlayer . top:Male )u∃ sport:hasMember .(∃ sport:hasPlayer . top:Female )

3.3 Football Module

The Football Module models common knowledge in the football domain, abstracting from specific foot-ball competitions and building on the definitions of upper modules.

Since sports are modelled as individual in the Sport Module, a fb:football individual is introducedto identify the football sport. The use of this individual permits to denote football events, teams, play-ers, . . . by using property sport:hasSport together with concepts defined in the Sport Module. For in-stance, a football player can be denoted with the concept expression:

sport:Sportsman u ∃ sport:hasSport .{ fb:football }

Refinements for sub-classes of concepts from upper modules are defined as follows:

fb:Match ≡ sport:Match u fb:Event

fb:Competition ≡ sport:MatchCompetition u fb:Event

fb:PlayedMatch ≡ sport:PlayedMatch u fb:Match

fb:ProMatch ≡ sport:ProEvent u fb:Match . . .

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A detailed characterization of these specialized concepts is provided in the Football Module. In addi-tion, the central concepts of fb:Period, fb:KeyMoment and fb:PlayerPosition are introduced to modelrespectively the phases and key moments (e.g. a goal) of a football match and the different positions thatfootball players can play in.

Player positions Player positions are modelled as instances of class fb:PlayerPosition and are used intwo ways: (1) to denote the positions a football player is capable of playing in, by means of propertyfb:canPlayInPosition, and (2) to denote the actual position(s) of a player in a particular football event,such as a match, by means of property fb:hasPosition that further characterizes the ternary relationsport:PlayerTeamMebership between sportsmen, teams and events.

Player Positions are organized in a broader / narrower hierarchy by means of the transitive prop-erty fb:isPositionTypeOf. The choice of modelling positions as individuals stems from the fact that aplayer may change position with time, from one match or competition to another, and therefore classassignment cannot be used if that dynamic is to be modelled. Modelling of the broader / narrower rela-tion with an object property has been preferred over the alternative solution of introducing sub-classesof fb:PlayerPosition, since it avoids the needless (in this case) “one class per individual” redundancyintroduced by the latter.

Teams Being a specialization of sport:Team, football teams inherit the modelling of teams in the SportModule, included the ternary relation sport:TeamMembership used to specify the composition of ateam in a specific event. The sport:PlayerTeamMembership specialization of the relation is extendedwith property fb:hasPosition, which specifies the position covered by a player in the football event. Thefollowing two axioms are necessary to constrain the use of the ternary relation in the football domain:

fb:Event v ∀ sport:hasParticipatingTeamMember .(∀ sport:hasCoach . fb:Coachu∀ sport:hasPlayer . fb:Playeru∀ sport:hasMember −. fb:Team )

fb:Team v ∀ sport:hasMember .(∀ sport:hasCoach . fb:Coachu∀ sport:hasPlayer . fb:Player )

The first axiom requires a football event to be participated only by football teams composed of footballplayers and coaches, thus disallowing e.g. a volley team to play a football match. The second axiomrequires a football team to be composed only of football players and coaches, but does not preventa football team to participate to events not related to football. Each of these axioms can be seen asconstraining the participation to the ternary relation of one of its participant classes.

Different types of football teams are defined in this module. The first three levels of the team hi-erarchy (up to fb:ClubTeam and fb:NationalTeam) mirror the corresponding concepts defined in theSport Module, while National football teams are further differentiated based on the age on players (e.g.fb:SeniorNationalTeam, fb:U21NationalTeam).

Professional football teams are composed of professional players, with player numbers assigned foreach football event the team participates in and have a coach. Using the ternary fb:TeamMembershiprelation, this corresponds to requiring each team to include a coach in each event it participates in,but this constraint cannot be modelled since it applies to team / event pairs. Professional teams mayregister with football governing bodies, such as the Italian FIGC or UEFA. Football governing bod-ies may have other football governing bodies as members (by the top:hasMemberOrganization prop-erty). A fb:ContinentalConfederation is a particular type of football governing body administrating in afb:ContinentalZone (e.g. Europe, South America, . . . ) and consisting in the confederation of the nationalfootball associations of that zone. Each national football team is required to register with the continentalconfederation administrating in the continental zone the team’s country is located in. This is partiallyformalized as follows, with the constraint on the confederation jurisidiction not formalizable in OWL 2:

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fb:NationalTeam v ∃ fb:registeredWith . fb:ContinentalConfederation

Matches Also matches in the Football Module, similarly to teams, inherit from the modelling of matchesin the Sport Module. Football matches are compound events: a fb:Match consists of one or morefb:Period and a fb:Period contains fb:KeyMoments, which represent relevant events occurring in a foot-ball match. The containment relation is specified using the top:hasChildEvent and top:hasParentEventproperties of top:Event, inherited from the Top Module and restricted as follows:

fb:Match v ∃ top:hasChildEvent . fb:Period

fb:Period v (≤ 1) top:hasParentEvent

fb:Period v ∀ top:hasParentEvent . fb:Match

fb:Period v ∃ top:hasParentEvent .>fb:KeyMoment v (≤ 1) top:hasParentEvent

fb:KeyMoment v ∀ top:hasParentEvent . fb:Period

fb:KeyMoment v ∃ top:hasParentEvent .>

Standard match periods (e.g. fb:NormalTime and fb:ExtraTime ) are modelled as sub-classes of fb:Period:both normal and extra times are organized in a first and second half, with an additional penalty shootoutperiod possibly occourring in case of draw.

A football match has at least a referee and exactly two participating teams: a home team, speci-fied by fb:hasHomeTeam, and a host team, specified by fb:hasHostTeam, the two properties extend-ing top:hasParticipant and being functional and disjoint. Two datatype properties, fb:hasScoreHomeand fb:hasScoreHost, are introduced to express the score of the home and host teams at the end of afb:Period or fb:Match, hence their domain is the union of the two classes. Scores are known for playedmatches; more precisely, knowing the final scores of a match is a sufficient condition for knowing thatthe match has been played. Football match officials may include assistant referees and a fourth official,specified by means of properties fb:hasAssistantReferee and fb:hasFourthOfficial. These roles cannotoverlap, hence corresponding properties are disjoint; in addition, assistant referees are mandatory forprofessional matches.

Home and host teams of a match participate each with 11 line-up players and (possibly) witha limited number of substitutes. Team line-up and substitutes are modelled by specializing propertysport:hasParticipatingTeamMember of the ternary membership relation, so to specify the role (homevs host, line-up vs substitute) a player covers in a football match. Therefore, the following four sub-properties are defined: fb:hasHomeTeamLineUp, fb:hasHostTeamLineUp, fb:hasHomeTeamSubstituteand fb:hasHostTeamSubstitute. These properties are declared as disjoint, so to avoid a player to be si-multaneously in the home and host teams or in the line-up and substitutes of the same team.

Moving to key moments, a fb:KeyMoment is associated to one or more players via propertyfb:hasKeyMomentPlayer and its specializations, and occours in a match period at a certain minute, iden-tified via the mandatory functional property fb:hasMinute. Class fb:KeyMoment and propertyfb:hasKeyMomentPlayer are specialized for the most relevant types of key moments. Sub-class fb:Injurymodels player injuries with the injured player(s) identified by mandatory property fb:hasInjuredPlayer.Substitutions are modelled by fb:Substitution, with the two players entering and leaving the field iden-tified respectively by the disjoint properties fb:hasSubstituteIn and fb:hasSubstituteOut. The classfb:AwardedKick and its sub-classes model the different types of kicks that can be awarded by the ref-eree to a team, that is fb:CornerKicks, fb:PenaltyKicks and fb:FreeKicks, the latter further divided by atotal classification in fb:DirectFreeKick and fb:IndirectFreeKick based on whether the kick is allowedto directly result in a goal. The functional and mandatory property fb:hasExecutorPlayer applies to allthe fb:AwardedKick classes and denotes the player executing the awarded kick. Referee calls are mod-elled by fb:RefereeCall and its sub-classes fb:YellowCard and fb:RedCard: they are characterized by

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at least one called player, identified by property fb:hasCalledPlayer: A fb:Goal is characterized by thescoring team and player, identified respectively via fb:hasScorerTeam and fb:hasScorerPlayer, and byan optional assistant player, identified by fb:hasAssistantPlayer and different from the scorer player:

fb:Goal v ∃ fb:hasScorerPlayer .>fb:Goal v ∃ fb:hasScorerTeam .>Dis( fb:hasScorerPlayer , fb:hasAssistantPlayer )

Auto-goals are distinguished by having the scorer player not playing for the scorer team. However, thisdefinition cannot be formalized, so fb:AutoGoal is simply declared as a sub-class of fb:Goal.

3.4 FIFA World Cup Module

The FIFA World Cup Module completes the ontology by extending previous modules to model thedomain of the FIFA World Cup football competition. The module provides a general modelling of theFIFA World Cup and then specializes it by formalizing the differences between specific editions of theWorld Cup, which mainly affect the competition format (e.g. number of participants and structure of thecompetition). We first present the general, edition-independent modelling for FIFA World Cup and thenwe describe the details of specific editions. We conclude the discussion of this module by presentingadditional constraints not modelled in the ontology, because not formalizable in OWL 2.

General modelling The module starts by introducing the three main concepts of wc:Team, wc:Matchand wc:Competition, as refinements of the concepts introduced in the upper modules. FIFA World Cupteams are national senior football teams composed only by men, while wc:Matches are professional,competitive football matches for which a fourth official is mandatory. Class wc:Competition models boththe FIFA World Cup overall competition and its stages and represents their commonalities, included thefact they are all international competitions. In order to control their nesting along the top:hasChildEvent /top:hasParentEvent dimension, the following axiom prevents a wc:Competition to include stages whichare not related to the FIFA World Cup:

wc:Competition v ∀ top:hasChildEvent .(¬ sport:Competition t wc:Competition )

The links among FIFA World Cup competitions, matches and teams are governed by the followingaxioms, which constrain participants to wc:Matches and wc:Competitions to be wc:Team and requirewc:Matches and wc:Competitions to occour together:

wc:Competition v ∀ top:hasParticipant .wc:Team

wc:Match v ∀ top:hasParticipant .wc:Team

wc:Match v ∀ top:hasParentEvent .wc:Competition

wc:Competition v ∀ top:hasChildEvent .(¬ sport:Match t wc:Match )

The module defines the different types of competition stages the FIFA World Cup is composed of, bothcurrently or in the past. Abstracting from the details of specific editions, it is possible to organize theFIFA World Cup in an optional wc:QualificationPhase, consisting of six wc:QualificationTournamentsone for each fb:ContinentalZone the World is divided in, and in a mandatory conclusive wc:Tournament.Although the format of the tournament changes in time, it has always been composed of one, two or threeof the following consecutive stages: wc:FirstGroupStage, wc:SecondGroupStage and wc:KnockoutStage.For ease of modelling, the two group stages descend from the common wc:GroupStage ancestor in the

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ontology. Each of them consists of one or more wc:Groups, which may include two, three or four teams(respectively, classes wc:TwoTeamsGroup, wc:ThreeTeamsGroup and wc:FourTeamsGroup). The knock-out stage, instead, consists of one or more wc:KnockoutRounds, represented by the optionalwc:RoundOf16, wc:QuarterFinals, wc:SemiFinals, wc:ThirdPlacePlayoff and by the mandatory wc:Final.

The different editions of the FIFA World Cup (1930 – 2010) may be represented by properly ar-ranging instances of competition stage classes via properties top:hasChildEvent / top:hasParentEvent.In order to form meaningful structures, nesting along these properties is constrained by axioms assuringthat cardinality and type of child stages respects the intended interpretation.

The formalization of the general structure of the FIFA World Cup is completed by constraining thenumber of matches occourring in specific stages of the competition. For example, the number of groupmatches is controlled by the following axioms, which require groups with two, three and four teams tohave, respectively, one, three and six matches:

wc:TwoTeamsGroup v (≤ 1) top:hasChildEvent .wc:Match

wc:TwoTeamsGroup v ∃ top:hasChildEvent .wc:Match

wc:ThreeTeamsGroup v (= 3) top:hasChildEvent .wc:Match

wc:FourTeamsGroup v (= 6) top:hasChildEvent .wc:Match

Another aspect that need to be constrained regards the number of participating and/or qualified teams.Concerning the number of participants, it depends on the particular World Cup edition for the qualifi-cation and tournament stages, while for groups and knockout rounds it is known a-priori, and thus isformalized in this edition independent part of the module. The same applies for the number of teamsthat qualify to the next stage for intermediate knockout rounds. Participants to groups are orderedin a final ranking after group matches are played. Properties sport:hasWinner, sport:hasRunnerUp,sport:hasThirdPlace and sport:hasFourthPlace are used to specify the ranking, and are mandatory inthe different types of group. For example, for wc:ThreeTeamsGroup:

wc:ThreeTeamsGroup v ∃ sport:hasWinner .>wc:ThreeTeamsGroup v ∃ sport:hasRunnerUp .>wc:ThreeTeamsGroup v ∃ sport:hasThirdPlace .>

The last constrained aspect regards competition organizers. The World Cup itself, the tournament withits child stages and the qualification phase without its tournaments are all organized by FIFA (individualfb:fifa), while qualifification tournaments are organized by continental confederations. This is formalizedas follows:

wc:WorldCup v ∃ top:hasOrganizer .{ fb:fifa }wc:QualificationPhase v ∃ top:hasOrganizer .{ fb:fifa }

wc:QualificationTournament v ∀ top:hasOrganizer . fb:ContinentalConfederation

wc:Tournament v ∃ top:hasOrganizer .{ fb:fifa }wc:Tournament v ∀ top:hasChildEvent .(¬wc:Competitiont

∃ top:hasOrganizer { fb:fifa })

Edition-specific modelling The format of the FIFA World Cup has evolved since its first 1930 edition.The main differences in the format of the tournament phase – which is the focus of the modelling –are reported in [2] and consist in the following aspects: number of participants, qualification phase andaccess to World Cup, presence of the first and second group stage, presence and rounds of the knockoutstage, presence of third place playoff.

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In order to model the differences described above (as far as possible using OWL 2), several sub-classes wc:WorldCup1930, wc:WorldCup1934, . . . , wc:WorldCup2010 of class wc:WorldCup have beenintroduced one for each edition of the FIFA World Cup. Using these sub-classes, constraints specific toa subset of the World Cup editions can be formalized by GCI axioms having a disjunction of World Cupedition classes on the left hand side and a concept description specifying the constraint on the right handside.

The four axioms reported below restrict the number of participants for selected editions of the FIFAWorld Cup to 13, 16, 24 and 32 teams; note that in place of full wc:WorldCupX class identifiers theabbreviation wcX has been used, for ease of notation:

wc1930 t wc1950 v ∃ top:hasChildEvent .(wc:Tournamentu(= 13) top:hasParticipant .wc:Team )

wc1934 t wc1938twc1954 t . . . t wc1978

v ∃ top:hasChildEvent .(wc:Tournamentu(= 16) top:hasParticipant .wc:Team )

wcWorldCup1982 t . . . t wc1994 v ∃ top:hasChildEvent .(wc:Tournamentu(= 24) top:hasParticipant .wc:Team )

wc1998 t . . .wc2010 v ∃ top:hasChildEvent .(wc:Tournamentu(= 32) top:hasParticipant .wc:Team )

The presence or absence of the qualification phase is easily modelled by the following two axioms:

wc1930 v ¬∃ top:hasChildEvent .wc:QualificationPhase

wc1934 t . . . t wc2010 v ∃ top:hasChildEvent .wc:QualificationPhase

Note, however, that (as will be discussed in the following) the requirements on the host team and theWorld Cup holder team being automatically qualified cannot be modelled in OWL.

The presence / absence and the specific configuration of the first group stage is modelled by a com-plex concept description, which is then associated as a subsumer to the classes of the World Cup edi-tions the configuration applies to. Concept descriptions cover the number and type of groups formingthe group stage and the number of qualified teams for each group. The modelling of the second groupstage is similar to the one given for the first group stage.

Differences in the knockout stage are formalized by axioms specifying whether the knockout stageis present and which knockout rounds are played for each edition of the FIFA World Cup. The sameapplies for the presence or absence of the third place playoff.

Additional not modelled constraints Due to the limits of OWL (which correspond to the limits of theSROIQ Description Logic), the following constraints were not formalized even if deemed relevant forinclusion in the FIFA World Cup Module7:

1. Participation to sequential child stages. In the context of a stage consisting of a sequence of childstages (such as the tournament and the knockout stage) the following two constraints hold: (1) theteams participating to the first child stage are exactly the teams participating to the parent stage, and(2) the teams participating to the other child stages are the teams qualified in the previous child stage.

2. Participation to parallel child stages. In the context of a stage consisting of several child stagesheld in parallel (such as a group stage or the qualification phase) the following two constraints hold:(1) the teams participating to the parent stage are the disjoint union of the teams participating toits child stages and (2) the teams qualified in the parent stage are the disjoint union of the teamsqualified in the child stages.

7 Note that constraints 1, 2 and 4 can be actually generalized to any sport competition (e.g. by introducing the concepts ofparallel and sequential competition), in which case they can be moved to the Sport Module.

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3. Participation to third place playoff. Teams participating to the third place playoff are the runner-upteams of the semi-finals.

4. Qualification in knockout rounds. Teams qualified in a knockout round are the winners of the matchesin that knockout round.

5. Qualification in groups. Teams qualified in a group are the winner and runner-up of the group (iftwo teams qualifies for each group) or just the winner (if only one team qualifies).

6. Ranking of FIFA World Cup. The ranking (winner / runner-up / third place / fourth place) of theWorld Cup corresponds to the ranking of the tournament stage.

7. Ranking of tournament stage. The ranking of the tournament stage consists in the winner of the final,the runner-up of the final, the winner of the third place playoff and the runner-up of the third placeplayoff.

8. Registration with continental confederations. Teams participating to the qualification tournament ofa continental zone must be registered with the continental confederation administering that zone.

9. Host team definition. A host team for a FIFA World Cup tournament is a team representing one ofthe hosting countries of the competition.

10. Host team inclusion. For certain editions of the FIFA World Cup, host teams are automaticallyqualified.

11. Holder team inclusion. For certain editions of the FIFA World Cup, the team that won the previousedition is automatically qualified.

Apparently, most of these constraints seem to be addressable by exploiting the HasSelf self restrictionOWL 2 construct (see section 8.2.4 of the OWL 2 specification [4]) and the property chain construct (seesection 9.2.1 of the specification), in conjunction with the introduction of special self-loop propertieswhich act as markers. The idea is to introduce new properties derived by the composition of existingproperties applied to certain classes, these classes denoted by the “marker” properties, and then usethese composite properties to formalize complex constraints; marker properties can be defined by meansof the HasSelf concept constructor, which denotes the individuals connected to themselves by meansof a specific property. The following example shows a concrete application of the approach to modelconstraint 9 by defining a wc:hasHostTeam property:

wc:Team v HasSelf (wc:teamMarker )

wc:Tournament v HasSelf (wc:tournamentMarker )

wc:tournamentMarker ◦ sport:hasHostCountry◦ top:hasCountry − ◦ wc:teamMarker

v wc:hasHostTeam

The first two axioms force each instance of wc:Team or wc:Tournament to be connected to itself viathe marker properties wc:teamMarker and wc:tournamentMarker. The third axiom consider the compo-sition of sport:hasHostCountry and top:hasCountry−, which leads from a generic competition to anyindividual related to the country hosting that competition. This path, too vague, is refined by means ofthe two marker properties, whose addition cause only paths from FIFA World Cup tournaments to hostFIFA World Cup teams to be considered. Given the “direction” of the inclusion axiom, each time such apath is encountered the derived property wc:hasHostTeam can be inferred.

Using this technique, other constraints can be formalized. Continuing the example, the propertywc:hasHostTeam just defined can be used to model constraint 10 as reported below, where propertywc:tournamentWithQualifiedHostMarker is a marker for tournaments for which host teams are auto-matically qualified:

wc:Tournament u ∃ top:hasParentEvent.(wc:WorldCup2010 t . . .)

v HasSelf (wc:tournamentWithQualifiedHostMarker )

wc:tournamentWithQualifiedHostMarker◦ sport:hasHostTeam

v top:hasParticipant

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The technique discussed above presents three limitations, which together motivate the fact it was notapplied in the modelling:

1. It is cumbersome, due to the introduction of a large number of artificial marker properties.2. Due to a limit in OWL 2 aimed to preserve decidability (section 9.2.1 of the OWL 2 specification),

property chains may appear only as the left hand side of a role inclusion axiom. This prevents to de-fine a property as exactly equivalent to the composition of other properties. In the wc:hasHostTeamexample, this means that any team can be explicitly asserted as being an host team without beingassociated to an hosting country, with the ontology remaining consistent.

3. Due to other limits in OWL 2 (section 11.2 of the specification), transitive properties and propertiesthat can be inferred via property chains with their super properties are not simple properties, whichmeans that they cannot be used in cardinality restrictions, self restrictions and disjoint constraints,and that they cannot be declared as functional, inverse functional, irreflexive and asymmetric. Thisis a severe limitation: in the example above, it would apply to property wc:hasParticipant, thus pre-venting any cardinality restriction to be declared on it and, consequently, requiring several importantaxioms on the number of participants to competition stages to be dropped.

References

1. Loris Bozzato, Francesco Corcoglioniti, Mathew Joseph, and Luciano Serafini. Evaluation of contextual queries. Tech-nical Report TR-FBK-DKM-2011-2, Fondazione Bruno Kessler, Trento, Italy, 2011. https://dkm.fbk.eu/index.php/Resources.

2. FIFA. Formats of the FIFA World Cup final competitions 1930 - 2010. http://www.fifa.com/mm/document/fifafacts/mcwc/ip-201 04e fwc formats slots 8821.pdf. [Online; accessed 03-August-2011].

3. Martin Homola, Luciano Serafini, and Andrei Tamilin. Modeling contextualized knowledge. In Proc. of InternationalWorkshop on Context, Information And Ontologies (CIAO10), Portugal, 2010.

4. Boris Motik, Bijan Parsia, and Peter F. Patel-Schneider. OWL 2 Web Ontology Language structural specifi-cation and functional-style syntax. W3C recommendation, W3C, October 2009. http://www.w3.org/TR/2009/REC-owl2-syntax-20091027/.

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