A formal comparison of conceptual data modeling languages

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1 A formal comparison of conceptual data modeling languages A prelude to intelligent CASE tools C. Maria Keet Faculty of Computer Science, Free University of Bozen-Bolzano, Italy keet@inf.unibz.it Knowledge Systems Group, Meraka Institute, Pretoria, July

2 Presentation is based on the EMMSAD 08 presentation & paper, of which a shorter version is available as DL 08 paper: Keet, C.M. A formal comparison of conceptual data modeling languages. 13th International Workshop on Exploring Modeling Methods in Systems Analysis and Design (EMMSAD 08). Montpellier, France, June CEUR-WS Vol-337, pp Keet, C.M. Unifying industry-grade class-based conceptual data modeling languages with CM com. 21st International Workshop on Description Logics (DL 08), May 2008, Dresden, Germany. CEUR-WS, Vol-353.

3 1 Background Motivation Methodology 2 Overview DLR ifd syntax and semantics CM com 3 ER and EER UML class diagrams ORM and ORM2 4

4 Long-term scopes Background Motivation Methodology Requests for automated, online, interoperability among diverse conceptual data models and compatibility between industry-grade conceptual data modeling languages. (Semi-)Standards, such as Barker ER, IE, IDEF1X, and UML Implementations in CASE tools, such as VisioModeler, NORMA, CaseTalk, RationalRose, VP-UML, and SmartDraw Interest in reasoning over conceptual models and other online usage of conceptual models is growing from the side of modelers and early-adopter industry.

5 What do we have? Background Motivation Methodology From conceptual modeling: diagram-based transformations between the main languages [H01] Problems: for each new notation a new mapping scheme has to be identified, m : n mesh with (k 1)k/2 required mappings among k languages, and informal transformations From computational logic: unify class-based modeling languages through the DLR family of Description Logic languages, avenue for formal 1:n mappings [CLN99] Problems: worked out flexibly for restricted versions of ER and frame-based systems only but not full EER, UML or ORM/ORM2, and more expressive DLRs are available now

6 What do we have? Background Motivation Methodology From conceptual modeling: diagram-based transformations between the main languages [H01] Problems: for each new notation a new mapping scheme has to be identified, m : n mesh with (k 1)k/2 required mappings among k languages, and informal transformations From computational logic: unify class-based modeling languages through the DLR family of Description Logic languages, avenue for formal 1:n mappings [CLN99] Problems: worked out flexibly for restricted versions of ER and frame-based systems only but not full EER, UML or ORM/ORM2, and more expressive DLRs are available now

7 Methodology Background Motivation Methodology Q: What is the greatest common denominator (or core) of the industry-grade conceptual data modeling languages? First steps: compare ER, EER, UML class diagrams, ORM, and ORM2 and identify greatest common denominator Extend and refine [CGLNR98, CLN98, CLN99] by integrating previously obtained results on mappings between conceptual modelling languages and characteristics of the DL languages taking into account standardized (UML, IDEF1X) and semi-standardized (Barker ER, IE, ORM, ORM2) languages and their implementations (a.o., VisioModeler, NORMA, CaseTalk, RationalRose, VP-UML, and SmartDraw)

8 Methodology Background Motivation Methodology Q: What is the greatest common denominator (or core) of the industry-grade conceptual data modeling languages? First steps: compare ER, EER, UML class diagrams, ORM, and ORM2 and identify greatest common denominator Extend and refine [CGLNR98, CLN98, CLN99] by integrating previously obtained results on mappings between conceptual modelling languages and characteristics of the DL languages taking into account standardized (UML, IDEF1X) and semi-standardized (Barker ER, IE, ORM, ORM2) languages and their implementations (a.o., VisioModeler, NORMA, CaseTalk, RationalRose, VP-UML, and SmartDraw)

9 Motivation Methodology Methodology and look ahead to results DLR ifd used to formally define the generic common conceptual data modeling language CM com, i.e., with syntax and (model-theoretic) semantics This CM com is used to formally define and compare ER, EER, UML class diagrams, ORM, and ORM2. Need to resolve main issues: Establish what exactly is, or is not, part of the ER and EER, include textual or OCL constraints Decide what to do with an officially informal conceptual modeling language (UML) or if there are alternative formalisations (ORM)

10 Motivation Methodology Methodology and look ahead to results DLR ifd used to formally define the generic common conceptual data modeling language CM com, i.e., with syntax and (model-theoretic) semantics This CM com is used to formally define and compare ER, EER, UML class diagrams, ORM, and ORM2. Need to resolve main issues: Establish what exactly is, or is not, part of the ER and EER, include textual or OCL constraints Decide what to do with an officially informal conceptual modeling language (UML) or if there are alternative formalisations (ORM)

11 Description Logics Background Overview DLR ifd syntax and semantics CM com The basic ingredients of all DL languages are concepts and roles, where a DL-role is an n-ary predicate (n 2) A DL language has several constructs, thereby giving greater or lesser expressivity and efficiency of automated reasoning DL knowledge bases are composed of the Terminological Box (TBox) with axioms at the concept-level, and the Assertional Box (ABox) with assertions about instances A TBox corresponds to a formal conceptual data model or can be used to represent a type-level ontology

12 The base language: DLR Overview DLR ifd syntax and semantics CM com Take atomic relations (P) and atomic concepts A as the basic elements of DLR, which allows us to construct arbitrary relations (arity 2) and arbitrary concepts according to the syntax: R n P ($i/n : C) R R 1 R 2 C 1 A C C 1 C 2 [$i]r k[$i]r i denotes a component of a relation; if components are not named, then integer numbers between 1 and n max are used, where n is the arity of the relation. Only relations of the same arity can be combined to form expressions of type R 1 R 2, and i n

13 The base language: DLR Overview DLR ifd syntax and semantics CM com The model-theoretic semantics of DLR is specified through the usual notion of interpretation, where I= ( I, I), and the interpretation function I assigns to each concept C a subset C I of I and to each n-ary R a subset R I of ( I ) n, such that the conditions are satisfied following: ( k[$i]r) = {d {(d 1,..., d n ) R1 d i = d } k} I n ( I ) n (R 1 R 2 ) I = R I 1 R I 2 P I I n ( C) I = I \ C I ( R) I = I n \ R I (C 1 C 2 ) I = C1 I CI 2 A I I ($i/n : C) I = {(d 1,..., d n ) I n d i C I } I 1 = I ( [$i]r) I = {d I (d 1,..., d n ) R I.d i = d}

14 The base language: DLR Overview DLR ifd syntax and semantics CM com A knowledge base is a finite set KB of DLR (or DLR ifd ) axioms of the form C 1 C 2 and R 1 R 2. An interpretation I satisfies C 1 C 2 (R 1 R 2 ) if and only if the interpretation of C 1 (R 1 ) is included in the interpretation of C 2 (R 2 ), i.e. C I(t) 1 C I(t) 2 (R I(t) 1 R I(t) 2 ). 1 denotes the interpretation domain, n for n 1 denotes a subset of the n-cartesian product of the domain, which covers all introduced n-ary relations. ($i/n : C) denotes all tuples in n that have an instance of C as their i-th component.

15 Relations between the 5 DLRs Overview DLR ifd syntax and semantics CM com ORM2 DLR muifd ORM UML DLR ifd DLR mu DLR reg DLR us EER ER DLR Relationship between "fragments of ORM2" w.r.t. the common CDM languages Extensions to DLR Existing formal partial transformations between CDM languages Existing diagram-based partial transformations between CDM languages

16 Overview DLR ifd syntax and semantics CM com DLR ifd DLR ifd has two additional constructs compared to DLR: identification assertions on a concept C, which has the form (id C[i 1 ]R 1,..., [i h ]R h ), where each R j is a relation and each i j denotes one component of R j. Non-unary functional dependency assertions on a relation R, which has the form (fd R i 1,..., i h j), where h 2, and i 1,..., i h, j denote components of R Syntax and semantics as for DLR

17 CM com syntax Background Overview DLR ifd syntax and semantics CM com Definition (Conceptual Data Model CM com syntax) A CM com conceptual data model is a tuple Σ = (L, REL, ATT, CARD, ISA C, ISA R, ISA U, DISJ, COVER, KEY, EXTK, FD, OBJ, REX, RDM) such that: - L is a finite alphabet partitioned into the sets: C (class symbols), A (attribute symbols), R (relationship symbols), U (role symbols), and D (domain symbols); the tuple (C, A, R, U, D) is the signature of the conceptual data model Σ. - REL is a function that maps a relationship symbol in R to an U-labeled tuple over C, REL(R) = U 1 : C 1,..., U k : C k, and k is the arity of R. -...

18 Overview DLR ifd syntax and semantics CM com Example: syntax for CM com ISA for, e.g., Author ISA Person cardinality constrains, CARD(Author, Writes, auth) = (1, n) DISJ and COVER where {Author, Editor} DISJ Person and {Author, Editor} COVER Person KEY(Person) = id Equivalent representation in DLR ifd as: Author Person (subsumption), Author [auth]writes (at least one), Author Editor (disjoint), Person Author Editor (covering), and Person =1 [From]id, 1 [To](id [From] : Person) (key)

19 Overview DLR ifd syntax and semantics CM com Example: syntax for CM com ISA for, e.g., Author ISA Person cardinality constrains, CARD(Author, Writes, auth) = (1, n) DISJ and COVER where {Author, Editor} DISJ Person and {Author, Editor} COVER Person KEY(Person) = id Equivalent representation in DLR ifd as: Author Person (subsumption), Author [auth]writes (at least one), Author Editor (disjoint), Person Author Editor (covering), and Person =1 [From]id, 1 [To](id [From] : Person) (key)

20 Overview DLR ifd syntax and semantics CM com Example: syntax for CM com B A For each Person, exactly one of the following holds: some Author is that Person; some Editor is that Person. It is possible that more than one Author writes the same Book and that the same Author writes more than one Book. Each Book, Author combination occurs at most once in the population of Author writes Book. Each Author writes some Book. For each Book, some Author writes that Book. C {disjoint,complete} Figure: Examples of graphical syntax for CM com with ORM2 drawn in NORMA (A), UML class diagram drawn in VP-UML (B), and EER drawn with SmartDraw (C).

21 CM com semantics Background Overview DLR ifd syntax and semantics CM com Definition (CM com Semantics) Let Σ be a CM com conceptual data model. An interpretation for the conceptual model Σ is a tuple B = ( B B D, B), such that: B is a nonempty set of abstract objects disjoint from B D ; B D = D i D B D i is the set of basic domain values used in Σ; and B is a function that maps: Every basic domain symbol D D into a set D B = B D i.... Every attribute A A to a set A B B B D, such that, for each C C, if ATT(C) = A 1 : D 1,..., A h : D h, then, o C B ( i {1,..., h}, a i. o, a i A B i a i. o, a i A B i a i B D i ).

22 Overview DLR ifd syntax and semantics CM com Definition (CM com Semantics cont d) B is said a legal database state or legal application software state if it satisfies all of the constraints expressed in the conceptual data model: For each C 1, C 2 C: if C 1 ISA C C 2, then C B 1 CB 2. For each R 1, R 2 R: if R 1 ISA R R 2, then R B 1 RB 2. For each U 1, U 2 U, R 1, R 2 R, REL(R 1 ) = U 1 : o 1,..., U n : o n, REL(R 2 ) = U 2 : o 2,..., U m : o m, n = m, R 1 R 2 : if U 1 ISA U U 2, then U B 1 UB 2....

23 Overview DLR ifd syntax and semantics CM com Definition (CM com Semantics cont d) For each C C, R h R, h 1, REL(R h ) = U : C, U 1 : C 1,..., U k : C k, k 1, k + 1 the arity of R h, such that EXTK(C) = [U 1 ]R 1,..., [U h ]R h, then for all o a, o b C B and for all t 1, s 1 R1 B,..., t h, s h Rh B we have that: o a = t 1 [U 1 ] =... = t h [U h ] o b = s 1 [U 1 ] =... = s h [U h ] implies o a = o b t j [U] = s j [U], for j {1,..., h}, and for U j where o a is an instance of C that is the U j -th component of a tuple t j of R j, for j {1,..., h}, and o b is an instance of C that is the U j -th component of a tuple s j of R j, for j {1,..., h}, and for each j, t j agrees with s j in all components different from U j,...

24 Overview DLR ifd syntax and semantics CM com Definition (CM com Semantics cont d)..., then o a and o b are the same object. For each R R, U i, j U, for i 2, i j, REL(R) = U 1 : C 1,..., U i : C i, j : C j, FD(R) = U 1,..., U i j, then for all t, s R B, we have that t[u 1 ] = s[u 1 ],..., t[u i ] = s[u i ] implies t j = s j.... For each U i U, i 2, R i R, each R i has the same arity m (with m 2), C j C with 2 j i(m 1) + 1, and REL(R i ) = U i : C i,... U m : C m (and, thus, R i Ri B and o j Cj B ), if {U 1, U 2,... U i 1 } REX U i, then i {1,..., i}.o j Cj B CMIN(o j, r i, u i ) 1 u i u 1... u i u i 1 where u i Ui B, r i Ri B.

25 Overview Background ER and EER UML class diagrams ORM and ORM2 ORM2 DLR muifd ORM UML DLR ifd DLR mu DLR reg DLR us EER ER DLR Relationship between "fragments of ORM2" w.r.t. the common CDM languages Extensions to DLR Existing formal partial transformations between CDM languages Existing diagram-based partial transformations between CDM languages

26 ER and EER UML class diagrams ORM and ORM2 Definition (CM ER ) A CM ER conceptual data model is a tuple Σ = (L, REL, ATT, CARD, KEY, EXTK) adhering to CM com syntax and semantics except that CARD is restricted to any of the values { 0, 1, 1}, denoted in Σ with CARD. Definition (CM EER ) A CM EER conceptual data model is a tuple Σ = (L, REL, ATT, CARD, ISA C, DISJ, COVER, KEY, EXTK) adhering to CM com syntax and semantics.

27 ER and EER UML class diagrams ORM and ORM2 Definition (CM UML ) A CM UML conceptual data model is a tuple Σ = (L, REL, ATT, CARD, ISA C, ISA R, DISJ, COVER, KEY, EXTK, FD, OBJ, PW) adhering to CM com syntax and semantics, except for the aggregation association PW, with syntax PW = U 1 : C 1, U 2 : C 2, that has no defined semantics.

28 ER and EER UML class diagrams ORM and ORM2 Definition (CM ORM ) A CM ORM conceptual data model is a tuple Σ = (L, REL, ATT, CARD, ISA C, ISA R, ISA U, KEY, EXTK, FD, OBJ, REX, RDM, JOIN, KROL, RING ) adhering to CM com syntax and semantics, and, in addition, such that: - JOIN comprises the following constraints: {join-subset, join-equality, join-exclusion} over 2 n-ary relations, n 2, as defined in [H89]. - KROL comprises the following constraints: {subset over k roles, multi-role frequency, set-equality over k roles, role exclusion over k roles} over an n-ary relation, n 3, and k < n, as defined in [H89]. - RING comprises the following constraints: {intransitive, irreflexive, asymmetric}, as defined in [H89].

29 ER and EER UML class diagrams ORM and ORM2 Definition (CM ORM2 ) A CM ORM2 conceptual data model is a tuple Σ = (L, REL, ATT, CARD, ISA C, ISA R, ISA U, DISJ, COVER, KEY, EXTK, FD, OBJ, REX, RDM, JOIN, KROL, RING) adhering to the syntax and semantics as defined for CM com, and such that: - KROL and JOIN are as in Definition 9. - RING comprises the following constraints: {intransitive, irreflexive, asymmetric, antisymmetric, acyclic, symmetric}, as defined in [H89, H01].

30 Discussion Background trivial (almost) with the 5 definitions Four finer-grained issues With ORM formalization of [H89], CM UML not a proper fragment of CM ORM (total exclusive subtypes but OCL). CM UML fragment of CM ORM2 (dismiss PW) KEY is for single attribute keys (± ORM reference scheme), EXTK for multiple-attribute keys. no enforcing of elementary fact type Attributes (UML, ER, EER) vs. attribute-free (ORM, ORM2). Semantics of ATT, an n-ary relation with as range(s) data type(s) Some features of ORM and ORM2 missing in CM com...

31 Discussion Background trivial (almost) with the 5 definitions Four finer-grained issues With ORM formalization of [H89], CM UML not a proper fragment of CM ORM (total exclusive subtypes but OCL). CM UML fragment of CM ORM2 (dismiss PW) KEY is for single attribute keys (± ORM reference scheme), EXTK for multiple-attribute keys. no enforcing of elementary fact type Attributes (UML, ER, EER) vs. attribute-free (ORM, ORM2). Semantics of ATT, an n-ary relation with as range(s) data type(s) Some features of ORM and ORM2 missing in CM com...

32 Discussion Background Why a comparison with DLR ifd and CM com and not FOL? DLs are well-studied FOL fragments, and by looking at (non-) correspondences, one gains better insight in properties of CM languages as well CM UML, CM ER, and CM EER are in ExpTime-complete (DLR ifd is) Knowledge about computationally more appealing fragments in NP or NLogSpace [ACKRZ07, KS06, SCS07]

33 Discussion Background Why a comparison with DLR ifd and CM com and not FOL? DLs are well-studied FOL fragments, and by looking at (non-) correspondences, one gains better insight in properties of CM languages as well CM UML, CM ER, and CM EER are in ExpTime-complete (DLR ifd is) Knowledge about computationally more appealing fragments in NP or NLogSpace [ACKRZ07, KS06, SCS07]

34 Features [KR07] Language OWL DL-Lite DLR Feature Lite DL v1.1 F R A ifd µ reg Role hierarchy N-ary roles (where n 2) ± ± ± Role concatenation Role acyclicity Symmetry Role values Qualified number restrictions One-of, enumerated classes Functional dependency Covering constraint over concepts Complement of concepts Complement of roles Concept identification Range typing Reflexivity Antisymmetry Transitivity Asymmetry ± - Irreflexivity

35 Features [KR07] Language OWL DL-Lite DLR Feature Lite DL v1.1 F R A ifd µ reg Role hierarchy N-ary roles (where n 2) ± ± ± Role concatenation Role acyclicity Symmetry Role values Qualified number restrictions One-of, enumerated classes Functional dependency Covering constraint over concepts Complement of concepts Complement of roles Concept identification Range typing Reflexivity Antisymmetry Transitivity Asymmetry ± - Irreflexivity

36 Restrictions on DLR µifd (tentative) THEOREM Given a knowledge base K = (T, R, A, F) of DLR µifd, where DLR µifd = (DLR ifd, DLR µ ), satisfiability and logical implication DLR µifd is ExpTime-complete, provided the following conditions are met: Least (greatest) fixpoint µx.c (νx.c) is used only with binary roles R b R; R b does not occur in any identification assertion, i.e., for (id C[i 1 ]R 1,..., [i h ]R h ) then R b R 1,..., R b R h.

37 Discussion Background Why a comparison with DLR ifd and CM com and not FOL? DLs are well-studied FOL fragments, and by looking at (non-) correspondences, one gains better insight in properties of CM languages as well CM UML, CM ER, and CM EER are in ExpTime-complete (DLR ifd is) Knowledge about computationally more appealing fragments in NP or NLogSpace [ACKRZ07, KS06, SCS07] DLR ifd most expressive common denominator; thus far, best trade-off expressiveness & computation With unambiguously defined syntax and semantics, modelers can keep using their preferred diagram-based language (or make a new one), have common language at the interchange automated transformations

38 Discussion Background Why a comparison with DLR ifd and CM com and not FOL? DLs are well-studied FOL fragments, and by looking at (non-) correspondences, one gains better insight in properties of CM languages as well CM UML, CM ER, and CM EER are in ExpTime-complete (DLR ifd is) Knowledge about computationally more appealing fragments in NP or NLogSpace [ACKRZ07, KS06, SCS07] DLR ifd most expressive common denominator; thus far, best trade-off expressiveness & computation With unambiguously defined syntax and semantics, modelers can keep using their preferred diagram-based language (or make a new one), have common language at the interchange automated transformations

39 Discussion Background Why a comparison with DLR ifd and CM com and not FOL? DLs are well-studied FOL fragments, and by looking at (non-) correspondences, one gains better insight in properties of CM languages as well CM UML, CM ER, and CM EER are in ExpTime-complete (DLR ifd is) Knowledge about computationally more appealing fragments in NP or NLogSpace [ACKRZ07, KS06, SCS07] DLR ifd most expressive common denominator; thus far, best trade-off expressiveness & computation With unambiguously defined syntax and semantics, modelers can keep using their preferred diagram-based language (or make a new one), have common language at the interchange automated transformations

40 Conclusions and current work ER, EER, UML class diagrams, and ORM are different proper fragments of ORM2 ER, EER, UML class diagrams are in ExpTime Results obtained with CM com simplifies (semi-)automated interoperability of conceptual data models in different graphical languages DLR µifd for ORM s ring constraints, temporal extensions with DLR US and ER VT

41 Conclusions and current work ER, EER, UML class diagrams, and ORM are different proper fragments of ORM2 ER, EER, UML class diagrams are in ExpTime Results obtained with CM com simplifies (semi-)automated interoperability of conceptual data models in different graphical languages DLR µifd for ORM s ring constraints, temporal extensions with DLR US and ER VT

42 Artale, A., Calvanese, D., Kontchakov, R., Ryzhikov, V., Zakharyaschev, M. Reasoning over Extended ER Models. Proc. of ER 07, Springer LNCS 4801, Calvanese, D., De Giacomo, G., Lenzerini, M., Nardi, D., Rosati, R. Description logic framework for information integration. In Proc. of KR 98, Calvanese, C., De Giacomo, G., Lenzerini, M. On the decidability of query containment under constraints. In: Proc. of PODS 98, , Calvanese, D., Lenzerini, M., Nardi, D. Description logics for conceptual data modeling. In: Chomicki, J., Saake, G. (Eds.), Logics for Databases and Information Systems. Kluwer, Amsterdam Calvanese, D., Lenzerini, M. & Nardi, D. Unifying class-based representation formalisms. JAIR, 11: , Calvanese, D. & De Giacomo, G. Expressive description logics. In: The DL Handbook: Theory, Implementation and Applications, Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P. (Eds). Cambridge University Press, pages Halpin, T.A. A logical analysis of information systems: static aspects of the data-oriented perspective. PhD Thesis, University of Queensland, Australia

43 Halpin, T. Information Modeling and Relational Databases. San Francisco: Morgan Kaufmann Publishers, Kaneiwa, K., Satoh, K. Consistency Checking Algorithms for Restricted UML Class Diagrams. In: Proc. of FoIKS 06, Springer LNCS 3861, Keet, C.M. and Rodríguez, M. Toward using biomedical ontologies: trade-offs between ontology languages. AAAI 2007 Workshop on Semantic e-science (SeS 07), 23 July 2007, Vancouver, Canada. AAAI 2007 TR WS-07-11, Smaragdakis, Y., Csallner, C., Subramanian, R. Scalable automatic test data generations from modeling diagrams. In: Proc. of ASE 07, Nov. 5-9, Atlanta, Georgia, USA

44 Thank you for your attention

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