The Object Role Modelling (ORM2) is a conceptual modelling approach combining both textual specifications and graphical language, similar to UML and ER, and adopted by Visual Studio, the integrated development environment designed by Microsoft. This paper introduces a new linear syntax and corresponding complete set-theoretic semantics for a generalization of ORM2 language. A core fragment of ORM2 is defined, for which a provably correct encoding into ALCQI description logic is presented. Based on these results, an extensive and systematic critique of alternative approaches to the formalisation of ORM2 in (description) logics published so far is provided. A first prototype has been implemented, which o ers a back-end for the automated support of consistency and entailment checks for ORM2 conceptual schemas along with its translation into ALCQI knowledge bases.
Automated support to enterprise modelling has increasingly become a subject of
interest for organisations seeking solutions for storage, distribution and analysis of
knowledge about business processes [
The NIAM language (‘Natural-language Information Analysis Method’), ancestor
ORM, has been equipped with an FOL-based semantics for the first time in 1989 [
This paper addresses the main problem of providing a logic formalism, equipped
with sound and complete reasoning services, that captures the expressiveness of ORM2.
The first contribution of the paper is thus the introduction of a completely new linear
syntax and a set-theoretic semantics for ORM2 matching the usage patterns in the
community. The new syntax can be used to express the full set of ORM2 graphical symbols
introduced in [10]. The second contribution of the paper is driven by a practical
objective. On the basis of well known results developed in the Description Logics (DLs)
community, we identified a ‘core’ fragment of ORM2 that can be translated in a sound
and complete way into the ExpTime-complete logic ALCQI [
The rest of the paper is organised as follows: Section 2 is about the introduction, through examples, of the ORM2 graphical notation and intended semantics in the framework of the fact modelling approach; Section 3 introduces the new linear syntax by means of expressing the example from the previous section in this syntax. The encoding of the corresponding set-theoretic semantics into the DL logic ALCQI is the main topic of Section 4. Finally, Section 5 gives an overview of the implemented reasoning support prototype, its interface and gives an example of its usage. 2
Basic ORM2 objects are: entities (e.g. a house or a car) and values (e.g. character string or number). Moreover, entities and values are described in terms of the types they belong to: a type (e.g. House, Car) is a set of possible instances. In order to avoid ambiguity among the possible instances of a given type, entities are identified also by means of a particular reference mode and a value. The roles played by the entities in a given domain are introduced by means of logical predicates; each predicate (or relation) has a given set of roles according to its arity. Each role is connected to exactly one object type, indicating that the role is played only by possible instances of that type.
The first step of the ORM2 design procedure thus concerns the specification of the relevant object types (i.e. entity and value types), predicates and reference modes. All the subsequent steps in the procedure mostly deal with the specification of static constraints. Let us consider the example in Fig. 1: As mentioned before, the modelling activity in ORM2 is supported by several tools that provide user friendly graphical interfaces to build complex conceptual schemas. However, none of the available design tools o ers automated reasoning support on specific combinations of ORM2 constraints. The automated verification of schema consistency and consistency of an object type over a conceptual schema strictly depends on the possibility to perform reasoning and make inferences on it by means of a semantic-based logic representation of the schema itself.
With this goal in mind, we propose a linear syntax that fully covers the set of
graphical symbols of ORM2. Table 1, using the example from previous section, shows how
a new introduced syntax can be used to encode conceptual schemas that have been
originally specified in graphical terms. For each construct in the syntax, its
corresponding set-theoretic semantics expressed in relational algebra is also introduced in
table 2 (where O denotes an object type).
With the main aim of relying on available reasoning tools to reason in an e ective
way on ORM2 schemas, we present here the encoding in the logic ALCQI, for which
tableaux-based reasoning algorithms with a tractable computational complexity have
been developed [
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ALCQI corresponds to the basic DL ALC equipped with qualified cardinality
restrictions and inverse roles, and it can also be viewed as a fragment of DLR [
The ORM2zero fragment considers the following constraints: ORM2zero = fTYPE; FREQ ; MAND; R-SET ; O-SETIsa; O-SETTot; O-SETEx; OBJg, where: (i) FREQ can be applied to only one role at time, and (ii) R-SET applies either to a pair of relations of the same arity or to two single roles. The encoding of the semantics of ORM2zero is shown in table 3.
Given the encoding above, a fragment of ALCQI KB corresponding to the schema from the Fig. 1 is the following (where reified relations have been prefixed with ‘R-’): Example 1: 9 (reportsTo.sub) :R-reportsTo v Admin 9 (reportsTo.obj) :R-reportsTo v AreaManager
Admin v 9 (reportsTo.sub) :R-reportsTo The correctness of the introduced encoding is guaranteed by the following theorem: Theorem 1. Let zero be an ORM2zero conceptual schema and ALCQI the ALCQI knowledge base constructed as described above. Then an entity/value type O is consistent in zero if and only if the concept O is satisfiable w.r.t. ALCQI.
The ORM2 automated reasoning support tool is implemented in Java and includes a parser for ORM2 linear syntax, a set of Java classes representing the ORM2 knowledge database, a translator into an OWL2 ontology and a modal reasoning engine using HermiT or FaCT++ as an underlying reasoner. The graphical user interface of a tool is introduced on Figure 2 and contains controls which allow to select an input file, underlying reasoner, output file and output format for resulting ontology (if needed). The consistency check for an input ORM2 schema is performed after loading the input file and the result of the check is communicated by visual flag as well as by a detailed log in the corresponding window. Let us now consider the following example in ORM2 linear syntax. This model describes a domain of university personnel, which is partitioned into three mutually exclusive categories: research sta , administration and some lazy people. We then introduce an entity type Student as a part of university personnel, which is claimed to be neither researchers nor administration sta .
ENTITYTYPES: fUNI-Personnel,LazyPeople,Student,Admin,RTStaffg
O-SETtot(fLazyPeople,RTStaff,Adming,UNI-Personnel) O-SETex(fLazyPeople,RTStaff,Adming,UNI-Personnel) O-SETisa(fStudentg,UNI-Personnel) O-SETex(fStudent,RTStaffg,UNI-Personnel)
O-SETex(fStudent,Adming,UNI-Personnel) The resulting encoding in ALCQI will look like the following:
UNI-Personnel v RTStaff t Admin t LazyPeople
RTStaff v :Admin t :LazyPeople
Admin v :LazyPeople Student v :RTStaff t :Admin
Student v UNI-Personnel After loading the linear syntax input file, the corresponding conceptual schema is automatically checked for consistency (see Figure 2). As a result of the consistency check we obtain the message ’The given ORM2 schema is internally consistent’, which confirms the correctness of the schema.
Implemented entailment check functionality allows user to analyze the conceptual schema and to discover interesting inferences. For example, let us analyze the entity type Student, which is claimed to be part of the university personnel. However, since the partition of UNI-Personnel described above is total, the only possibility for Student to be non-empty is to be equivalent to the entity type LazyPeople. Which is indeed confirmed by the inference engine of the implemented prototype when performing entailment check for the following ORM2 statement (see Figure 2):
O-SETisa(fStudentg,LazyPeople) 6
In the last few years, several papers addressed the issue of encoding ORM2
conceptual schema into DL knowledge bases [15,14,13,11]. Among those proposals, [15] can
be taken as the only one going through the encoding with a formal perspective. In
particular, [15] pretends to start from the Halpin’s FOL semantics, and introduces an
encoding of a fragment of ORM2 into the logic DLRi f d [
As regards to [14], we mostly rely here on the extensive review already made by Keet in [15]. Starting from this, it should be also noticed that subsequent attempts, focused on the possibilities of encoding ORM2 into the the web ontology language OWL2 [13,11], su er from the same formal inconsistencies and limitations of [14]. In particular, [14] is misleading with respect to the underlying DL formalism: distinct DL languages (e.g. DLR, plus DLR-Lite, plus SROIQ, plus ‘role composition’ operator) are there arbitrary mixed together. No special semantics is provided by [14] in correspondence with these combinations, nor theorems showing the complexity of reasoning with them.
Another paper focused on the encoding of ORM2 in OWL has also been recently
published [16]. The paper introduces a set of informal ‘rules’ devoted to the mapping of
a subset of ORM2 constructs into OWL Manchester Syntax [
In this paper we introduced a linear syntax and a complete set-theoretic semantics for the ORM2 conceptual modelling language. A decidable, and computationally tractable, fragment of ORM2 has been clearly identified and mapped into the DL logic ALCQI. Finally, a first reasoning support prototype for ORM2 has been implemented, which enables consistency and entailment checks for the defined fragment of ORM2. Future theoretic works will be mainly focused on the extension of the ORM2zero towards the identification of a more expressive, still decidable, ‘object role’ modelling language. The practical objectives of the research will be directed towards full integration of the prototype into third-party solutions providing graphical user interface for designing ORM2 conceptual schemas (e.g. NORMA plugin for Microsoft Visual Studio). In particular, such integration will benefit from reasoning capabilities of the tool by providing the user with a list of all meaningful inferences entailed by the original schema. 10. Halpin, T., Morgan, T.: Information modeling and relational databases: from conceptual analysis to logical design. Morgan Kaufmann, 2nd edn. (2001) 11. Hodrob, R., Jarrar, M.: ORM to OWL2 DL mapping. In: International conference on intelligent semantic web: applications and services. ACM (2010) 12. Horrocks, I., Sattler, U., Tobies, S.: Practical reasoning for expressive description logics.
In: Proceedings of the 6th International Conference on Logic Programming and Automated Reasoning. pp. 161–180. LPAR ’99, Springer-Verlag, London, UK (1999), http: //dl.acm.org/citation.cfm?id=645709.664314 13. Jarrar, M.: Mapping ORM into the SHOIN/OWL description logic – towards a methodological and expressive graphical notation for ontology engineering. In: OTM 2007 workshops: Proceedings of the International Workshop on Object-Role Modeling (ORM’07). LNCS, vol. 4805, pp. 729–741. Springer (November 2007) 14. Jarrar, M.: Towards automated reasoning on ORM schemes. mapping ORM into the DLRi f d description logic. In: Proceedings of the 26th International Conference on Conceptual Modeling (ER 2007). LNCS, vol. 4801, pp. 181–197. Springer (November 2007) 15. Keet, M.: Mapping the Object-Role Modeling language ORM2 into description logic language DLRi f d. Tech. Rep. KRDB07-2, KRDB Research Centre, Faculty of Computer Science, Free University of Bozen-Bolzano (2007) 16. Wagih, H.M., ElZanfaly, D.S., Kouta, M.M.: Mapping Object Role Modeling 2 schemes to OWL2 ontologies. In: Ting, Z. (ed.) Proceedings of the 3rd IEEE International Conference on Computer Research and Development (ICCRD), Shanghai, China, March 11-13, 2011. vol. 4, pp. 126–132. IEEE Press (2011)