Conceptual models are an important repository for knowledge in companies and public institutions. The retrieval of this knowledge can prepare reorganisations projects and support IT investment decisions. However, so far this information source has hardly been utilized in automated analyses. We argue that if modelling languages are endowed with specific characteristics the resulting models can be analysed in an automatic manner. We formally show that with such languages: (1) type, synonym, homonym, and abstraction conflicts are eliminated as well as (2) the identification of semantically equivalent model elements can be traced back to finding syntactic ones.
Conceptual models are an important knowledge source for business decisions. They
are used in organisational design to describe the business objects, the processes, and
organisational structures of a company or public institution [
Automated knowledge retrieval from conceptual models significantly increases
their value in practice. So far the identification of reorganisation potential and
efficiency indicators has mainly been performed manually with high financial efforts.
Approaches for an analysis of conceptual models in an automatic manner as in other
domains, for example based on data warehouses or websites (e. g. [
Knowledge retrieval from conceptual models in an automated manner requires
specific modelling language characteristics. To perform an analysis with models that
exhibit an arbitrary structure hampers the identification of semantically meaningful
results [
The remainder of this paper will proceed as follows: In the next section we will provide the basic vocabulary to discuss the retrieval of knowledge from conceptual models. Formal definitions of the terms conceptual model as well as conceptual modelling grammar are given and modelling rules are specified. Subsequently, we will explain the need for an equivalence notion between model elements as basis for an analysis. Formal definitions of the different conflicts that can emerge during a model analysis are given. Subsequently, these conflicts are solved by specific language properties. The paper closes with a summary of the main results and an outlook to further research. 2
Informally, a conceptual model can be defined as a representation of an application
domain expressed in a semi-formal, mostly visual language with the purpose of
facilitating information systems development and organisational design [
A description of the internal model IM is denoted as DIM. DIM is a linguistic artefact
which provides the intentional semantics of IM [
Existing formalisms for conceptual models and modelling grammars (e. g. [
CMG is a conceptual model grammar iff C, R, V, G and Z exist such that: − CMG = C, R,V ,G, Z − C is a non-empty set of constructs, including object types and relationship types − R is the set of permitted relations between the constructs with R ⊆ C × C , c represents the incoming construct of the pair (c, c′) ∈ R , c′ is the outgoing construct − V is a set of well-formedness rules which restrict the conceptual models of the grammar − G is a set of graphical symbols − Z assigns constructs to graphical symbols with Z ⊆ C × G A CMG defines the concrete syntax of a visual conceptual modelling language. A CMG without G and Z represents the abstract syntax of a conceptual modelling language. In the following the terms CMG and conceptual modelling language are used synonymous.
Domain specific languages are created to solve problems within a particular area of
concern [
CM is a conceptual model iff E, F, S, and A exist such that: − CM = E, F , S, A − E is a non- empty set of model elements, members of E are instantiations of members of C with E ⊆ C × N and N as the set of natural numbers − F is the set of relations between model elements with F ⊆ E × E , e represents the incoming model element of the pair (e, e′) ∈ F , e′ is the outgoing model element, all undirected edges have the same direction − S is a set of actual linguistic statements that describe the internal model IM with
S ⊆ DL , the statements consists of technical terms from the application domain − A assigns technical terms to model elements with A ⊆ E × S Suppose a simplified grammar CMG ERM consisting of entity types (ET), relationship types (RT) and links (L) with C ERM = {ET , RT , L} . The conceptual model CM B given in Fig. 1 based on CMGERM can be specified with CM B = E B , F B , S B , AB : − E B = {(ET ,1),(ET ,2),(RT ,1),(L,1),(L,2)} − F B = {((ET ,1),(L,1)),((L,1),(RT ,1)),((RT ,1),(L,2)),((L,2),(ET ,2))} − S B = {Writer, writes, Book} − AB = {((ET ,1),Writer),((ET ,2), Book),((RT ,1), writes)}
For a proper representation of the internal model IM with {IM } = M (CM IM ) the conceptual model CMIM must be adequate and complete. This requires that the modelling language and the domain language are comprehensive enough to describe IM. Therefore, necessary conditions for {IM } = M (CM IM ) can be formulated: • All elements of IM must be describable with constructs of the modelling language: ∀ε ∈ IE, ∃c ∈ C :ε ∈ M (Dc )
s ∈ S ↔ ∃e ∈ E : (e, s) ∈ A • A domain statement is part of the conceptual model CM if it can be assigned to a model element: • A domain statement is assigned to a model element if the domain statement exactly describes the corresponding element of the internal model, the construct associated with the model element has a more general meaning (larger extension) than the domain statement and no other domain statement is already connected with the model element: • All relations within the internal model IM must be describable in terms of permitted relations between constructs of the modelling language: • For all elements of IM there is an equipollent statement within the domain language: ∀(ε ,ε ′) ∈ IR, ∃(c, c′) ∈ R :ε ∈ M (Dc ) ∧ε ′ ∈ M (Dc′ )
∀ε ∈ IE, ∃s ∈ DL : {ε } = M (Ds )
If the conditions R1 to R3 are fulfilled then the modelling language and the domain language are called applicable. That means CMG and DL can be used to explicate the internal model IM.
For a more convenient presentation some abbreviations are useful. The type of a model element e ∈ E is its corresponding construct c ∈ C . The function τ : E → C , τ (e) = τ ((c, k )) = c provides the type of a model element. The auxiliary relation Ψ ⊆ IE × E establishes an one to one mapping between elements of the internal model IM and elements of the conceptual model CM. (ε , e) ∈ Ψ holds iff: (∀ε ′ ∈ IE : (ε ′, e) ∈ Ψ → ε ′ = ε ) ∧ (∀e′ ∈ E : (ε , e′) ∈ Ψ → e′ = e) .
In order to preserve the meaning and structure of IM during the explication the following conditions are required: • A model element e ∈ E refers to exactly one element of the internal model ε ∈ IE and its corresponding construct is able to describe ε :
e ∈ E ↔ ∃∈ IE : (ε , e) ∈ Ψ ∧ε ∈ M (Dτ (e) ) • Each relation between model elements f ∈ F is assigned to exactly one relation between elements of the internal model ρ ∈ IR and the modelling grammar permits the relation: (e, e′) ∈ F ↔ ∃(ε ,ε ′) ∈ IR : (ε , e) ∈ Ψ ∧ (ε ′, e′) ∈ Ψ ∧ (τ (e),τ (e′)) ∈ R (R5) (R1) (R2) (R3) (R4) (R6) (R7)
From a set theoretic perspective the modelling language constructs do not have any impact on the extensional semantics of the conceptual model. ε ∈ M (Dτ (e) ) (R4) and {ε } = M (Ds ) (R7) show that s is more general than c =τ (e) . M (Dτ (e) ) ⊃ M (Ds ) (R7) ensures that the relationship is a strict one. That means that the modelling language construct c is redundant from an extensional point of view. The value of c within the model is an intentional one. The construct c emphasises a certain aspect of s and thus helps to structure the domain. For example a modelling construct “entity type” instantiated with the domain statement “colour” tells that colour is considered as an object on its own and not as an attribute. However, this information has no influence on the extension of the domain statement colour. The extension is still blue, green, red, and so on. Without the condition M (Dτ (e) ) ⊃ M (Ds ) the construct would lose its role as a structuring element and the domain statement would take over this job. However, this would destroy the original function of a construct.
These formalisations are used in the following to propose and prove mechanisms for the elimination of semantic analysis conflicts. Such mechanisms are required in order to reach the objective of this paper to enable the analysis of conceptual models in an automated manner.
An analysis of conceptual models requires that certain reoccurring element structures can be identified in the models. Based on a match between model elements and predefined semantic patterns, meaningful statements about the domain can be derived. Thus, the identification of semantically equivalent conceptual model elements is a prerequisite for a semantic analysis aiming at knowledge retrieval. As semantic patterns represent sections from models, in the following they will be considered as conceptual models themselves. When a conceptual model CM is searched for the pattern CM’ then the elements of both artefacts must be compared.
The comparison of conceptual model elements can be divided into a syntactical
and semantical one [
Two model elements e ∈ E and e′ ∈ E ′ are syntactically equivalent ( e = syn e′ ) if they share the same type and have a syntactically identical domain statement associated. e = syn e′ iff: − τ (e) =τ (e′) (S1) − ∀s ∈ S : (e, s) ∈ A → (e′, s) ∈ A′ (S2) − ∀s′ ∈ S ′ : (e′, s′) ∈ A′ → (e, s′) ∈ A (S3)
Semantically equivalent model elements require, in addition to the syntactic ones,
that the meanings of the constructs as well as the domain statements are considered.
So far there is no algorithm that allows for a semantic comparison of conceptual
model elements [
Two model elements eεCMG,DL and eε′CMG,DL are semantically equivalent ( e = sem e′ ) if they are syntactically equivalent, the types of the corresponding model elements have identical semantics, and the associated domain statements share the same meaning. e = sem e′ iff: − e = syn e′ (S4) − M (Dτ (e) ) = M (Dτ (e′) ) (S5) − ∀s ∈ S,∀s′ ∈ S : (e, s) ∈ A ∧ (e′, s′) ∈ A′ → M (Ds ) = M (Ds′ ) (S6)
There are a couple of conflicts that can arise when a semantic analysis of a conceptual model is performed (taxonomies of these conflicts can be found for example in [2427]).
Type conflicts arise whenever the same fact of the application domain is represented by using different constructs of the modelling language. They result if there are choices in the modelling language about what construct is to be used in a certain situation. There is a type conflict between a model CMICMMG E, F, S, A and a semantic pattern CM I′MCMG E′, F ′, S ′, A′ iff: ∃e ∈ E, ∃e′ ∈ E′, ∃s ∈ S : s ∈ S ′ ∧ (e, s) ∈ A ∧ (e′, s) ∈ A′ ∧τ (e) ≠τ (e′) (C1)
Synonym conflicts occur when two different domain statements have the same meaning. There is a synonym conflict between a model CM IM E, F , S , A and a semantic pattern CM I′M E′, F ′, S′, A′ iff:
∃s ∈ S, ∃s′ ∈ S ′ : s ≠ s′ ∧ M (Ds ) = M (Ds′ )
Homonym conflicts emerge due to domain statements which have more than one meaning. This is the case if for one domain statement there is a different, adequate and complete description with a varying extension. There is a homonym conflict between a model CM IM E, F , S, A and a semantic pattern CM I′M′ E′, F ′, S ′, A′ iff: ∃s ∈ S : s ∈ S ′ ∧ M (Ds ) ≠ M (Ds′ ) (C2) (C3)
Abstraction conflicts result from the representation of the application domain at deviating levels of abstraction. Different modellers use more general or more precise domain statements for the same fact. There is an abstraction conflict between a model CM IM E, F , S, A and a semantic pattern CM I′M′ E′, F ′, S ′, A′ iff: (C4)
Type conflicts, synonym conflicts and abstraction conflicts lead to an underestimation of the semantic similarity of two model elements. Homonym conflicts can cause an overestimation of the similarity.
The general approach of this paper is to eliminate the semantic analysis conflicts through the adoption of rules for modelling grammars which simplify the examination of conceptual models.
Type conflicts can be avoided, if all modelling language constructs are required to be semantically disjoint.
Proposition 1 (Type Conflicts): With ∀c, c′ ∈ C, c ≠ c′ : M (Dc ) ∩ M (Dc′ ) = ∅ type conflicts between a model CM ICMMG and a semantic pattern CMI′MCMG are not feasible. Proof: If it is possible to show that from ∀c, c′ ∈C, c ≠ c′ : M (Dc ) ∩ M (Dc′ ) = ∅ follows that (e, s) ∈ A ∧ (e′, s) ∈ A′ →τ (e) =τ (e′) type conflict cannot arise. In order that (e, s) ∈ A holds it is necessary that: M (Dτ (e) ) ⊃ M (Ds ) (R7). From the condition ∀c, c′ ∈C, c ≠ c′ : M (Dc ) ∩ M (Dc′ ) = ∅ the following conclusion can be derived: ∀e&, &e&∈ E, e& ≠ &e&: M (Dτ (e&) ) ∩ M (Dτ (&e&) ) = ∅ . Thereof one can follow that there is at least one cˆ =τ (e) to meet the condition: M (Dτ (e) ) ⊃ M (Ds ) . Consequently, it must also hold for (e′, s) ∈ A′ that: M (Dτ (e′) ) ⊃ M (Ds ) . The application of the same modelling grammar leads to the identical: cˆ = τ (e′) . Hence, it follows that: τ (e) =τ (e′) if (e, s) ∈ A and (e′, s) ∈ A′ .
Homonym and synonym conflicts can be eliminated if these language defects are removed from the domain language.
synonym conflicts between a model CM ICMMG and a semantic pattern CMI′MCMG are not feasible.
Proof: From the definition of a CM it follows that S ⊆ DL . Consequently, if there are no synonyms in DL there are also no synonym conflicts caused by S. Proposition 3 (Homonym Conflicts): With ∀s ∈ DL : M (Ds ) = M (Ds′ ) homonym conflicts between a model CM ICMMG and a semantic pattern CMI′MCMG are not feasible. Proof: If there are no homonyms in DL there are also no homonym conflicts caused by S.
Subsequently, the implications of proposition 1 and proposition 2 on an identification of syntactical equivalence are evaluated. It is claimed that if the same internal model coupled with an identical modelling language as well as the same domain language are employed, and according to the propositions all synonyms are eliminated as well as all modelling language constructs are disjoint, then two syntactically equivalent model elements arise. This means that different modellers who share the same internal model will come to a syntactically identical result.
− ∀c, c′ ∈ C, c ≠ c′ : M (Dc ) ∩ M (Dc′ ) = ∅ − ∀s, s′ ∈ DL, s ≠ s′ : M (D ) ≠ M (Ds′ )
s imply that eεCMG ,DL = syn eε′CMG ,DL .
Proof: ∀c, c′ ∈ C, c ≠ c′ : M (Dc ) ∩ M (Dc′ ) = ∅ and R1 imply that: ∀ε ∈ IE, ∃c ∈ C :ε ∈ D(M c ) and ∀ε ∈ IE, ¬∃c′ ∈ C, c′ ≠ c :ε ∈ D(M c′ ) . Thus, c is the only construct in C that can describe ε . R3 and ∀s, s′ ∈ DL, s ≠ s′ : M (Ds ) ≠ M (Ds′ ) analogical imply: ∀ε ∈ IE, ∃s ∈ S : {ε } = D(M s ) and ∀ε ∈ IE,¬∃s′∈S, s′ ≠ s :{ε }∈D(Ms′ ) . Thus, s is the only domain statement in DL that can describe the element of the internal model ε ∈ IE . Consequently, each ε is associated with exactly one pair (c, s) which can be used to represent it. Because of R4 and the properties of Ψ for each ε exactly one e is instantiated with τ (e) = c . Thus, for each ε the pair (c, s) can be extended to a triple (e, c, s) . − If M (Dc ) ⊂ M (Ds ) then because of R7 e is labelled with s. This is expressed by the relation (e, s) ∈ A . Because of R6 it follows that: s ∈ S . − If M (Dc ) = M (Ds ) then because of R7 and R6 (e, s) ∉ A and s ∉ S . − M (Dc ) ⊃ M (Ds ) contradicts R1 and R3.
For each ε& there is also only one corresponding c& which is instantiated as e& . Due to R5 and R2 for each (ε ,ε&) ∈ IR exactly one (e, e&) ∈ F is created. In the case of two model elements eεCMG,DL and eε′CMG,DL for each ε ∈ IM there is exactly one triple (e, c, s) with e ∈ E and exactly one triple (e′, c′, s′) with e′ ∈ E′ (R4). Because CMG and DL are the same for both model elements, it follows that c = c′ and s = s′ . Because of S1-S3 from c = c′ and s = s′ follows that: eεCMG ,DL = syn eε′CMG ,DL .
The idea of proposition 3 is now transferred to the constructs of a conceptual modelling grammar. Also, in the set of constructs there must not be homonyms: ∀c ∈ C : M (Dc ) = M (Dc′ ) . Suppose two model elements which were created with the same modelling language and an identical domain language. It is claimed that if these model elements are syntactically equivalent and neither the domain language nor the modelling language contain homonyms then the two model elements are also semantically equivalent.
− eCMG ,DL = syn e′CMG ,DL − ∀c ∈ C : M (Dc ) = M (Dc′ ) − ∀s ∈ DL : M (Ds ) = M (Ds′ ) imply that eCMG ,DL = sem e′CMG ,DL .
Proof: From ∀c ∈ C : M (Dc ) = M (Dc′ ) follows that: c = c′ implies M (Dc ) = M (Dc′ ) because both models apply the same modelling language. From ∀s ∈ DL : M (Ds ) = M (Ds′ ) it follows that: s = s′ implies M (Ds ) = M (Ds′ ) , because both models apply an identical domain language. Every e ∈ E belongs to a triple (e, c, s) , each e′ ∈ E′ is part of (e′, c′, s′) . The syntactical equivalence of eCMG ,DL = syn e′CMG ,DL implies that τ (e) =τ (e′) (S1) and where applicable s = s′ (S2, S3). Consequently it holds that: M (Dτ (e) ) = M (Dτ (e′) ) (S5) and M (Ds ) = M (Ds′ ) (S6). Hence, it follows: eCMG ,DL = sem e′CMG ,DL .
Proposition 4 and Proposition 5 have important consequences. They assure that
under the conditions:
− ∀c, c′ ∈ C, c ≠ c′ : M (Dc ) ∩ M (Dc′ ) = ∅ (D1)
− ∀s, s′ ∈ DL, s ≠ s′ : M (Ds ) ≠ M (Ds′ ) (D2)
− ∀c ∈ C : M (Dc ) = M (Dc′ ) (D3)
− ∀s ∈ DL : M (Ds ) = M (Ds′ ) (D4)
the identification of two syntactically equivalent model elements can be traced back
to a syntactical pattern. Starting from two identical internal models semantically and
syntactically equivalent model elements are explicated. It is not necessary to apply a
semantic analysis operation on conceptual models as a syntactic analysis operation is
sufficient to identify a specific pattern. This in turn implies that if D1-D4 hold then a
semantic analysis of conceptual models can be completely automated. The process
modelling and analysis method PICTURE contains a language that has been built
based upon these criteria and that can be used for automated knowledge retrieval [
The proposed construction rules for conceptual modelling languages represent a theoretical result that needs further practical evaluation. Languages that meet these criteria have only a limited scope of application and loose the ability to be used in situations where different abstraction levels are needed or a flexible use of domain language is required. It is due to further research to investigate on how some of the criteria can be relaxed without increasing the analysis efforts.
So far conceptual models have been mainly considered as spin-off products of the
software development process or of reengineering projects. However, as they contain
valuable domain knowledge they are an important artifact on their own. The
consequence is that the models are not created for a single purpose anymore but have
a lifecycle in which they are modified and extended to keep up with the changes in
the environment. The definition of operations on conceptual models like
transformation, integration or search helps to address this issue [
Acknowledgments. The work published in this paper is partly funded by the European Commission through the STREP PICTURE. It does not represent the view of European Commission or the PICTURE consortium and the authors are solely responsible for the paper's content.