Representing Social Reality in OWL 2?

Abstract

This paper introduces a design pattern that allows for the OWL 2 DL representation of concepts central to social reality: roles. The work presented here is motivated by experiences in the development of the LKIF Core ontology of basic legal concepts [10,8]. This paper applies modelling steps identi ed in earlier work for the representation of transactions [9] to the domain of roles. This is done by building on Searle's theory of social reality [14]. We use the new features of OWL 2 to approximate a rei ed relation, and show how the approach of [9] can be reused to de ne a pattern for capturing roles, intentional concepts and n-ary relations [13].

Introduction

This paper introduces a design pattern that allows for the OWL 2 DL representation of relational roles in social reality, and n-ary relations in general. We apply the pattern to two use cases: the representation of n-ary relations by the SWBP of the W3C3 [ 13 ] and a description of social reality [ 14 ].

The work presented here is motivated by experiences in the development of the LKIF Core ontology of basic legal concepts [ 10,8 ]. To be able to adequately capture the contents of legal norms [ 17 ], this ontology had to be equipped with a large number of concepts for describing social reality: roles, beliefs, desires, obligations, permissions, intentions etc. The problem of representing roles such as `student' has been discussed at length in the literature [ 15,12 ]: they can be seen both as a class (`Jane is a Student') and as a relation (e.g. the student relation between Jane and her university). The same duality holds for intentional categories such as beliefs and desires. While a class conveys a stronger ontological commitment than the relation, the relation is often more convenient and succinct for practical use.

The representational construct in existing Semantic Web languages that comes closest to capturing this duality is rei cation. Rei cation allows one to address the relation between two or more resources (e.g. an RDF triple) as a ? This paper is a signi cantly revised version of a section in [ 8 ] 3 SWBP: Semantic Web Best Practices and Deployment group. See http://www.w3.

org/2001/sw/BestPractices. primary entity (a resource). It is a sensitive subject, and is often associated with messy modelling and has complicated semantics, especially when di erent levels of rei cation are not strati ed. On the other hand, rei cation is becoming increasingly important as a candidate approach to attaching metadata to individual triples, e.g. for the purposes of provenance tracking.

Unfortunately, the built-in rei cation capabilities of RDF are not su cient to our purposes. Namely, the existence of a rei cation (an RDF statement) does not entail the existence of the corresponding relation [ 6 ]. Furthermore, OWL 2 DL [ 2 ] is not expressive enough to represent rei ed relations either, even though these form a core part of use cases in social reality.

Current Semantic Web languages fall short in another, related respect: they do not provide means to express n-ary relations. This issue was addressed by the SWBP in the identi cation of a (famous) design pattern that represents the n-ary relation as a class with multiple properties relating it to the relata of the n-ary relation [ 13 ]. Unavoidably, this pattern has an e ect similar to that of RDF rei cation: the original relation between the relata is lost.

This paper applies modelling steps identi ed in earlier work for the representation of transactions [ 9 ] to the domain of roles. This is done by building on Searle's theory of social reality [ 14 ]. We use the complex role inclusion axioms of OWL 2 to approximate a rei ed relation. We show how the new features of OWL 2 can be used to de ne a pattern for capturing intentional concepts, speech acts, and the n-ary relations examples of the SWBP document [ 13 ].

Section 2 describes the problems of representing social roles and n-ary relations in more detail. section 3 applies the steps of [ 9 ] to construct the design pattern, and subsection 3.1 applies this pattern to the use cases described above. 2

The Problem

The LKIF Core ontology distinguishes three levels: physical reality, an intentional level and a legal level. Each consecutive level builds on and expands the level below it with more descriptive power. The distinction between these levels is inspired by Valente's functional ontology, where legal knowledge is considered to be an abstraction of commonsense knowledge [ 16 ].

Categories described at the intentional level and above, are social constructs that can be attributed to, or imposed on brute facts [ 14 ]. Brute facts are phenomena of which the existence does not depend on human agreement. This is similar to the way in which intentional and functional notions are generalised over physical phenomena in the design and intentional stance of Dennett [ 1 ]. According to Searle, institutional facts are constructed by means of constitutive and regulative rules. These are rules of the form:

X counts as Y in context C Examples of constitutive and regulative rules are, respectively: { Bills issued by the Bureau of Engraving and Printing (X) count as money (Y) in the United States (C). { For the purposes of this law (C), a house boat (X) is deemed to be a house (Y).

A regulative rule imposes additional restrictions on something (i.e. a house boat) to create an institutional fact (the house-boat-as-house) which can exist independently from that rule. The constitutive rule determines (in part) the possibility of existence of the institutional fact. Because of the normative character of regulative rules, the counts-as relation has received a lot of attention in AI and Law, most recently in [ 4 ].

Constitutive rules are deceptively similar to subsumption, but are very distinct in three ways. Firstly, the counts-as relation is ontologically subjective and observer relative, and therefore contextual. It only holds in relation to a certain context, within a system of constitutive rules created by (collective) intentionality. Secondly, the counts-as relation limits inheritance, and does not permit substitutability of the syntactic elements of rules. For instance, the statement \Money is the root of all evil" in conjunction with the constitutive rule introduced before, does not make that \Bills issued by the Bureau of Engraving and Printing count as the root of all evil in the United States.". This is because the context of the counts-as relation is intensional; the institutional fact cannot be de ned by reference to statements outside the context. And thirdly, the countsas relation can be used to connect anti-rigid with rigid classes [ 5 ]. For example, where \bills issued by the Bureau of Engraving and Printing" is rigid, \money" is anti-rigid.

These characteristics of the counts-as relation make that it cannot be represented using the subsumption relation, which is contextless, extensional and subject to ontological restrictions concerning its relata. In the following section we brie y discuss existing approaches to this problem. 2.1

Existing Approaches Social constructs are often conceived of as a relation between the brute fact and its context. A well known example is the duality of roles as relations and classes [ 15,12 ]. [ 15 ] identi es three ways to represent roles, as named places in relations, as specialisation or generalisation, or as adjunct instances. Of these only the rst and last conform to the intensional character of the counts-as relation.

Representing roles as adjunct instances means that the role itself and its player are de ned as two distinct classes, with a played by relation. For each occurrence where some entity plays a role, two individuals need to be asserted in the ABox. For some purposes this representation may be non intuitive or overly verbose. In the named places approach, roles can be represented as inverse properties. The drawback is that the relation between role player, role and context is ` attened' to a relation between role player and role. The role-as-relation approach is enticing in cases where the role-as-class approach involves an apparent circularity. To give an example, it is hard to consider the role Student independently from a student of relation with a University class. De ning Student in terms of that relation is rather tautological. A similar example is the interplay between a propositional attitude Belief, and the proposition that is believed by an agent. In the development of LKIF Core, we encountered various other occasions where this pattern emerged (see subsection 3.1).

[ 7 ] describe a methodology for de ning roles in OWL as a separate ontology. Bridge axioms de ned using `canPlay' properties indicate applicability of these roles to classes in a `base ontology'. For reasoning, the base ontology and role ontology can be integrated in a single ontology where all natural types are de ned as superclasses of the roles they can play. This approach has the nice property of keeping a strict separation of roles and natural types. However, it cannot cater for the duality of role-as-class vs. role-as-relation.

The structure required for notions in social reality is very similar to one of the most prominent design patterns discussed by the Noy and Rector in a note of the Semantic Web Best Practices and Deployment (SWBP) working group: n-ary relations, relations between more than two entities [ 13 ]. One could say that a role is an n-ary relation between role player, role and context. Noy and Rector represent n-ary relations as a class with n properties that rei es the relation.4 For instance, a high probability has diagnosis relation between Christine, Breast Tumor Christine is represented as an individual of type Diagnosis Relation with properties value Breast Tumor Christine and probability high. This solution is similar to the association class in class diagrams of UML that directly represents some association (relation) between two classes. The association class itself can then have additional properties. Association classes can only be used to reify a binary relation where the relation itself has additional properties (see Figure 1).

In [ 8 ] we discuss that this solution is not arbitrary: the rei cation makes explicit some knowledge about the domain which would be left implicit in the n-ary relation. For instance, a structured representation of an action explicates the thematic roles played by its participants. In an n-ary relation, these roles are just positions in a predicate. In other words, the restriction to binary relations in OWL enforces a more ontologically concise representation. The drawback is that exactly because of this commitment, the n-ary relation itself can no longer be represented. The question we try to answer here is whether we can devise a design pattern that can reclaim some of the relational character of the rei cation. 3

The Design Pattern

Current representations of social reality and n-ary relations involve an important commitment to either a relation oriented approach or a class centred representation: these options are mutually exclusive. The class centred approach is ontologically more concise, but also more verbose. For many applications it is useful, or simply convenient, to abstract away from this ontological commitment. Therefore, an explicit methodology for creating (or inferring) an abstraction of 4 [ 13 ] avoid the use of this term because of di ering interpretation of the term in TopicMaps and RDF. C1

object Rn pred. Rn subject predicate object Rr

R subject predicate object subject

object R

Rs C1

C2

C1

C2

Rn

C2 ontologically concise, but verbose representations can be very useful for ontology reuse. A reusing ontology may adopt just the abridged version of `properties' without compromising its ontological commitment. Figure 1 shows the rei cation Rr of relation R as an individual with explicit subject, predicate and object relations, and the converse abstraction Rs of individual R as a relation between classes C1 and C2.

The following outlines a design pattern that allows us to infer the abstraction of a rei ed relation. This pattern is based on the ve design steps identi ed in [ 9,8 ]: create initial class description, constrain the number of role llers, disambiguate role llers, traverse the tree, and introduce domain dependence. First, we describe the general principle in terms of the construction of social roles. This is then elaborated to show its application for n-ary relations and propositional attitudes.

Consider the de nition of a simple social role: a student is a person who is enrolled as such at some university. Using [ 14 ]'s counts-as rule, we can rephrase this as: \A person (X) counts as a student (Y) if enrolled at some university (C)". Casting this into OWL axioms, we can de ne the Student class as follows:

counts as some Person u context some University This de nition does not constrain the number of and type of entities that are valid values for the context and counts as properties. At a more general level, a subjective entity (de ned in LKIF Core) is de ned as an entity imposed on another entity using a counts-as rule:5

Subjective Entity

imposed on some owl:Thing u context some owl:Thing v imposed on exactly 1 owl:Thing u context exactly 1 owl:Thing imposed on

counts as A Social Role is a role that can only be played by a single agent, in a single context. It inherits a cardinality restriction on the played by and context properties 5 Note the way in which the equivalent class and subclass of axioms on Subjective Entity are used to ensure that any entity that is attributed in some context is both recognised as a Subjective Entity, but also enforced to be attributed to exactly one entity in a single context [ 9 ]. For a more restrictive de nition we could de ne imposed on and context as functional properties.

Observer relative fact At this point, we have said nothing about how the classes Person and University are related.6 The cardinality restrictions on the played by and context properties allow us to infer that, since Student is a subclass of Social Role, the Person class must be subclass of Agent. To prevent the University from being a student in the context of itself, the imposed on and context properties are made disjoint.

A straightforward abstraction of this rei cation can be speci ed as role inclusion axioms that simulate the respective named places: context o plays

v student plays o context v university An OWL 2 reasoner can infer a student relation between some university U and person P , and its inverse. Because in role inclusion axioms the property chain is a sub property of the property, the abstraction is subject to a similar limitation as RDF rei cation, but in the exact opposite direction. It can only infer the relation given the rei ed structure; while RDF rei cation only infers the rei ed structure, given the relation. Also, the abstraction cannot be used to identify an explicit predicate (cf. rdf:predicate) for the rei ed relation between the summarised class (Student) and the relation (student). 6 The same problem as with the de nition of Transaction in [ 9 ]

The role inclusion axiom will infer the relation for any context and brute fact connected through a Role. We therefore need to introduce domain dependence [ 9 ] and de ne the student relation in terms of some of the elements particular to the structure of the Student class. There are two ways to do this: either by re ning the properties involved, or by using self restrictions. The drawback of the rst approach is that for every type of role, we need to add a domain dependent property and axiom for each of the properties in its de nition. Furthermore, such properties can only be used local to the role being de ned, and the properties cannot be used to infer class membership (as they need to be given in advance). A more economical approach is to introduce a single property that uniquely identi es a class in the RBox. For our Student role, we introduce the is student property, that will relate any student individual to itself. We can ensure this by specifying a self restriction on the Student class:

Student is student some self

Any individual that is related to itself via the is student property will be identi ed as an instance of Student, and any individual asserted as instance of Student will be related to itself via that property. We can now rephrase the student abstraction axiom as follows:7

context o is student o played by v student This section gives an overview of how this pattern can be applied to various other contexts: n-ary relations, propositional attitudes and speech acts. The main di erence between the rei cation of binary relations and n-ary relations is that the latter have multiple subjects or objects, but share a single predicate, see Rn in Figure 1. In fact, [ 13 ] point out, n-ary relations typically have multiple objects, but a single subject. For instance, we can extend the de nition of a Diagnosis Relation as follows:

Diagnosis Relation

is diagnosis some self has diagnosis o is diagnosis o diagnosis value v diagnosis has diagnosis o is diagnosis o diagnosis prob v diagnosis We can easily extend this pattern to express more speci c kinds of diagnosis, or add informative properties such as a has cancer prob property that relates the 7 The university property can be expressed by reversing the direction of the context and played by properties.

Propositional Attitude

PA

PA holds towards Proposition

context PAs attitude Ag

P Context is an agent holds o PA o towards -> PAs SA creates

CA SA actor

Ag utters CAs states

CA

Expression

E Context is an agent

utters o states -> CAs agent- o SA o creates -> utters patient to the probability of such a particular diagnosis: This representation can be extended in a straightforward manner to cover more complex n-ary relations (see [ 8 ]).

Besides roles, other subjective and mental entities play an important role in the LKIF Core ontology. Propositional attitudes, such as beliefs, intentions and convictions are central to the representation (and resolution) of legal cases. A conviction of either murder or manslaughter hinges on the presence of an intent to kill. Propositional attitudes subjective entities that have a relational character very similar to roles. Consider the sentence: \Mary believes that John killed Susan.". The propositional content of the belief is \John killed Susan". However, the belief is inclusive of both the attitude and the content, i.e. it is \that John killed Suzan". We can rephrase the example as \Mary holds a belief towards the proposition `John killed Suzan'.".

To express these attitudes, we have to introduce the properties towards and holds as sub properties of imposed on and context . A propositional attitude is anything held by an Agent towards some Proposition (see Figure 3). This is easily re ned to a de nition of Belief, its corresponding marker property, and the abstraction property chain:

Belief

is belief some self We successfully applied the pattern to cover more complex classes such as speech acts: actions that create a communicated attitude such as declarations, assertions and promises (see Figure 3, [ 8 ]).

AR

I P

intends towards is_intention_to_act action_context context performs plays actor

Ag initiates

agentive_cause holds counts_as context

P The preceding section gives an overview of a design pattern for representing social reality using abstractions over rei ed relations. This pattern relies heavily on the new features of OWL 2, namely the ability to assert property disjointness (between counts as and context), role inclusion axioms, self restrictions and punning. It reuses modelling steps identi ed in earlier work [ 9 ], and we applied it to several modelling problems including the well known issue of representing n-ary relations. One application of the pattern, in [ 8 ], was the de nition of the relation between actions and processes, where actions are subjective entities in the context of the agent that performs the action. This resulted in a combination of four abstraction patterns (see Figure 4). Experience with this exercise has shown that extending the combination of patterns further is hindered by the fact that the super-property of role chains is a complex property, which restricts the types of OWL axioms allowed (e.g. no cardinality restrictions). The problem here is that without cardinality restrictions, the pattern is no longer able to distinguish between the di erent llers of the three positions of the triangle.

In the introduction to the pattern, it was mentioned that abstractions of rei cations could contribute to a more practical reusability of ontologies. The broad range of use cases for the summarisation pattern discussed in this paper clearly shows that its applicability is far reaching. Without abstraction, the choice between a relation or class oriented representation of is an important ontological commitment. And more importantly, this choice would have to be made individually, for each of the use cases we discussed. The result is often a hodgepodge of relation and class oriented solutions, within a single ontology.

Reuse of the LKIF Core ontology in applications that use expressive features of OWL 2, such as the versioning mechanism of [ 11 ] and normative assessment described in [ 17 ], is quite demanding because of the large number of complex class axioms in the LKIF ontology itself (see [ 10,8 ]). Abstractions allow us to combine the conciseness of relations with the verbose ontological correctness of classes within an ontology. A lightweight version of the ontology can be constructed by creating direct class axioms for abstraction properties, while discarding the axioms related to their rei cation. The resulting ontology is much more succinct, both qua ontological commitment and qua expressiveness. While abstraction properties are complex in the original ontology, the lightweight ontology represents them as simple. The latter consequently does not involve any cardinality constraints nor does it assert expressive property types over these properties. Of course ontologies that reuse the lightweight ontology may add such restrictions on those properties without violating any of the global restrictions in OWL 2 [ 2 ], but this would not be a safe reuse of the original ontology [ 3 ].

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