Y. E. Lien. On the equivalence of database models. Journal of the ACM, 29(2):333 -- 362, 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....developed for both strong and weak satisfaction of FDs. In the case of strong satisfaction the axioms coincide with the normal Armstrong s axioms [6] However, in the case of weak satisfaction, the transitivity rule in Armstrong s system is no longer valid and a modified system of axioms applies [8, 9, 37]. We also note that the definitions of weak and strong satisfaction just given are not particularly useful for testing satisfaction and more efficient syntactic equivalents gave been defined and shown to be equivalent to strong and weak satisfaction (see Lemmas 6.1 and 6.2 in [7] We now compare ....

Y. E. Lien. On the equivalence of database models. Journal of the ACM, 29(2):333 -- 362, 1982.

....Non relational Models: Schema conversion between different models has been extensively investigated. Historically, the trend for schema conversion has always been between consecutive models or models with overlapping time frames, as they have evolved (e.g. between Network and Relational models [8, 9], between ER and OO models [10, 11] or between UML and XML models [12, 13, 14, 15] For instance, 16] deals with conversion problems in OODB area; since OODB is a richer environment than RDB, their work is not readily applicable to our application. The logical database design methods and their ....

Lien, Y.E.: "On the Equivalence of Database Models". Journal of the ACM 29 (1982) 333--362

....new conceptual tools and applications which are made possible by the use of nulls. Generally recognized as useful, for instance, are the information preserving joins independently introduced in [13, 25] Also, null values have been found useful in mapping network schemas into relational schemas [15,26,27], in distributed databases, and in ensuring the universal relation assumption [6] There is a need for integrating these new concepts and ad hoc applications in a complete and consistent framework. This paper presents a new approach that avoids the dilemma of the unknown versus the ....

....whatever number we substitute for the where clause of QA evaluates to TRUE. Thus under the unknown interpretation, 4335, BROWN) should be included in IIQ H, Under the ni interpretation, however, the null value tilts in for both unknown and nonexistent values. Now, in conformity with [15,23], we assume that a nonexistent value does not satisfy any relational expression (i.e. one that involves a comparison operator, such as the three of Fig. 1) Therefore a TEI which does not exist is neither greater than 2634000, nor smaller than, nor equal to it. Thus, EMP tuples having a null ....

Y. E. LIEN, On the equivalence of database models, J. Assoc. Cornput. Mach. 29(2)(1982), 333-362.

....Y 1 , X Gammaffi Yn is removed in computing the dependency basis X Gammaffi W 1 j W 2 j : j Wm . In order to construct the minimum cover of the input set, conflicting GMVDs have to be removed. The notion of conflict free multivalued dependencies was originally introduced by Lien [13] in the study of the relationship between various database models. Here we extend this notion to GMVDs. Following Lee s argument [12] we show [20] that a modified Lien s decomposition algorithm generates a unique dependency structure (an acyclic hypergraph) from a set of conflict free GMVDs. Let ....

Y. Edmund Lien. On the equivalence of database models. Journal of the ACM, 29(2):336--362, October 1982.

....conditional independencies in (25) belongs to the BMVD class in (24) but not to the conflict free BMVD class in (26) We conclude this section by pointing out another similarity between relational databases and Bayesian networks. The notion of conflict free MVDs was originally proposed by Lien [22] in the study of the relationship between various database models. It has been shown [4] that a conflict free set of MVDs is equivalent to another data dependency called acyclic join dependency (AJD) defined below) That is, whenever any relation satisfies all of the MVDs in , then the relation ....

Y. E. Lien, "On the equivalence of database models," J. ACM, vol. 29, no. 2, pp. 336--362, Oct. 1982.

.... ############################################### Maths Naomi Eli # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # Figure 1 system for FDs holding in null relations was shown in [10]. Herein we define the concept of a FD being satisfied in a variable relation and show that the axiom system for FDs in null relations in [10] is also sound and complete for FDs holding in variable relations. In [6] an equivalence was shown between FDs that hold in relations and propositional ....

.... # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # Figure 1 system for FDs holding in null relations was shown in [10] Herein we define the concept of a FD being satisfied in a variable relation and show that the axiom system for FDs in null relations in [10] is also sound and complete for FDs holding in variable relations. In [6] an equivalence was shown between FDs that hold in relations and propositional implications in propositional logic. This equivalence is useful in practice, since the database designer can then take advantage of available ....

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Y.E. Lien, On the equivalence of database models, J. ACM 2 (1982), 333-362.

....in order that it hold in a nested relation over a NRS, R(T) Such a NFD is a member of the class of null extended data dependencies. We then define a NFD rule used for computing the extended chase of a nested relation with respect to a set of null extended data dependencies. DEFINITION 2.6. cf. [3, 22]. Let r be a flat relation over a set of attributes W U and let X, A U, where A is a single attribute. Then the NFD, X A, holds in r if and only if whenever there exist tuples t 1 , t 2 r such that t 1 [X] t 2 [X] i.e. t 1 and t 2 are X total) then t 1 [A] t 2 [A] i.e. t 1 and t ....

Y.E. LIEN, On the equivalence of database models. J. ACM 30, No. 2 (1982), 333-362.

....of null values. Since we allow the occurrence of null values in optional dimension levels, we have to be careful when working with functional dependencies. In this paper we consider inapplicable or non existent null values in conjunction with functional dependencies with nulls as introduced in [Lien82]: Let be a relation, i.e. a set of tuples, over a set of attributes , and let 4 . Relation (possibly with null values) satisfies the functional dependency with nulls , abbreviated NFD, if the following property holds: D ....

.... # , P Z , and , Proof. We recall that the Armstrong axioms form a sound and complete inference system for traditional functional dependencies (TFDs) i.e. FDs in the absence of null values (see, e.g. Vos00] furthermore, we recall from [Lien82] that the transitivity rule among the Armstrong axioms is no longer sound for NFDs and that by replacing the transitivity rule with a union 15 ID All Type Branch Subscribed Capital Legal Form Job Figure 4: Simple dependency graph. and a decomposition rule (which are also sound for TFDs) a sound ....

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Y.E. Lien, "On the Equivalence of Database Models," JACM 29 (2), 1982, 333--362.

....reflexivity, augmentation and transitivity. A fundamental result in relational database theory is that Armstrong s axiom system is sound and complete for FDs holding in complete relations. We denote the closure of a set of FDs F over R with respect to Armstrong s axiom system by F . Lien [LIEN82], and Atzeni and Morfuni [ATZE86] have shown that the inference rules: reflexivity, augmentation, decomposition and union, are sound and complete for FDs holding in incomplete relations; we call this axiom system, Lien and Atzeni s axiom system. That is, by dropping the transitivity rule from ....

....addition, we have shown in [LEVE94] that monodependence of a set of FDs F can be checked in polynomial time in the size of F. We observe that the two defining properties of monodependent sets of FDs correspond to the two defining properties of conflict free sets of multivalued dependencies (MVDs) [SCIO81, LIEN82, BEER86]. We further observe that the set of MVDs that is logically implied by a monodependent set of FDs may not be conflict free and thus monodependence is a weaker notion than conflictfreeness. For example, let F = fA B, B Ag, with sch(R) fA, B, Dg. It can easily be verified that R is ....

Y.E. Lien, On the equivalence of database models. Journal of the ACM 29, (1982), 333-362.

.... out such engineering processes as building a conceptual schema [Batini 1992; Batini 1993] schema normalization [Rauh 1995] DBMS schema translation [Hainaut 1993b; Rosenthal 1988; Rosenthal 1994] schema integration [Batini 1992] schema equivalence [D Atri 1984; Jajodia 1983; Kobayashi 1986; Lien 1982] data conversion [Navathe 1980] schema optimization [Hainaut 1993b; Halpin 1995] and others 1. According to the standard taxonomy of process models, this activity can best be described as a spiral process. 2 6 J L Hainaut 1998 15 12 98 [Blaha 1996; De Troyer 1993; Fahrner 1995] As will be ....

Lien, Y., E. 1982. On the equivalence of database models, JACM, 29, 2

....information is represented in SQL by using unk as a distinguished null value [DATE93] The theory of data dependencies in relational databases has been generalised in order to deal with incomplete databases. In particular, FDs have been generalised to null functional dependencies (NFDs) [LIEN82, ATZE86, LEVE94a], multivalued dependencies [ULLM88, ATZE93] have been generalised to null multivalued dependencies [LIEN82] and join dependencies [ULLM88, ATZE93] have been generalised to null join dependencies [LEVE92] More recently INDs have been generalised to null inclusion dependencies (NINDs) LEVE94b] A ....

....in relational databases has been generalised in order to deal with incomplete databases. In particular, FDs have been generalised to null functional dependencies (NFDs) LIEN82, ATZE86, LEVE94a] multivalued dependencies [ULLM88, ATZE93] have been generalised to null multivalued dependencies [LIEN82] and join dependencies [ULLM88, ATZE93] have been generalised to null join dependencies [LEVE92] More recently INDs have been generalised to null inclusion dependencies (NINDs) LEVE94b] A database schema R is a collection of relation schemas fR 1 ; R n g and each relation schema R i ....

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Y.E. Lien, On the equivalence of database models. Journal of the ACM 29, (1982), 333-362.

....and then used in the definition of the model. The second point is that there is no clear notion of when a translation is correct. In fact, a lot of research has been conducted in the last decades on scheme equivalence with reference to the relational model [1, 7, 12] or to heterogeneous frameworks [9, 10, 11], but there is no general, agreed definition. Therefore, we followed a pragmatic approach. We assume that the constructs that correspond to the same metaconstruct have the same semantics, and then we define translations that operate on individual constructs (or simple combinations thereof) as ....

Y.E. Lien. On the equivalence of database models. Journal of the ACM, 29(2):333--362, 1982.

....the corresponding type could be introduced in the metamodel. Since there is no clear notion of when a translation is correct (a lot of research has been conducted in the last decades on scheme equivalence with reference to the relational model [2, 10, 15] or to heterogeneous frameworks [1, 12, 13, 14], but there is no general, agreed definition) we follow a pragmatic approach. We assume that the constructs that correspond to the same metaconstruct have the same semantics, and then we define translations that operate on individual constructs (or simple combinations thereof) as follows: for each ....

Y.E. Lien. On the equivalence of database models. Journal of the ACM, 29(2):333-- 362, 1982.

....if the given set of MVDs is conflict free, then the nested normal form decomposition is also dependency preserving. Finally, we show that if M is conflict free, then the set of root to leaf paths of scheme trees in nested normal form decomposition is precisely the unique 4NF decomposition [Fa, L2] of U with respect to M. 1. Introduction A relational database [Co] is a collection of relations where each relation is at least in First Normal Form (1NF) i.e. tuple components of a relation are atomic (nondecomposable) values. However, for non business database applications such as text ....

....is equivalent to M. Moreover, the path set of T R , i.e. COURSE, TEXT) COURSE, SECTION, DAY) COURSE, SECTION, GRADER) is the unique 4NF decomposition [Fa] of U with respect to M, which is also in Split Free Normal Form (SFNF) BK2] Note that M in Example 1. 1 is a conflict free set of MVDs [L2, BFMY]. Given U and a set M of MVDs, we present a decomposition of U into a set of NNF relations (Section 4) Since the scheme of an NNF relation is a normal scheme tree, such a decomposition F= T 1 , T n is called a normal scheme forest (NSF) decomposition of U with respect to M. In addition to ....

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Lien, Y.E., On the Equivalence of Database Models, JACM, April 1982, pp. 333-362.

....such as 4NF decomposition can be found in [YO] A set of attributes X splits R U, if there are two dependents V 1 and V 2 of X such that V 1 R and V 2 R are nonempty. R is split by a set M of MVD s if there is at least one X in LHS(M) such that X splits R. A set M of MVD s is conflict free [L2, BFMY] if (1) M does not split any X in LHS(M) and (2) DEP(X) DEP(Y) DEP(X Y) for any X, Y in LHS(M) Conflict free sets of MVDs have several desirable properties [BFMY] Moreover, it is claimed [Sc] that real world sets of MVD s are conflict free. In fact, R U is decomposable w.r.t. X ....

....that there exist W 1 , W n such that X W i , i = 1, n, n 0, is nontrivial and right reduced, and X W i i = 1, n = X W. That is, M 1 = M . By Lemma 3.2, M = M 1 . It follows that M = M . Elements in LHS(M ) are called keys of M. Note that, in [BFMY, L1, L2], keys of M are defined as the elements of LHS(M) but not as the elements of LHS(M ) Since we consider reduced MVD s, referring to the elements of LHS(M ) as keys of M is more convenient in our context. RDEP(X) denotes the set W W DEP(X) and X W is reduced . By definition, ....

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Lien, Y.E., On the Equivalence of Database Models, JACM, April 1982, pp. 333-362.

....FDs in the closure of F such that the righthand side of each of the two FDs splits the left hand side of the other FD. The two defining properties of monodependent sets of FDs correspond to the two defining properties of conflict free sets of multivalued dependencies (MVDs) Sciore 1981; Lien 1982; Beeri et al. 1983; Beeri and Kifer 1986] in Section 4 we exhibit a simple example showing that, in general, monodependence does not imply conflictfreeness. The main result in [Levene and Loizou 1997] shows that satisfaction is additive with respect to the class of all incomplete relations and ....

....relevant whether we allow incomplete relations in the database or not. Our results show an interesting correspondence between monodependence as a desirable property, when the data dependencies are FDs, and conflict freeness as a desirable property, when the data dependencies are MVDs [Sciore 1981; Lien 1982; Beeri et al. 1983; Beeri and Kifer 1986] The layout of the rest of the paper is as follows. In Section 2 we formalise the notion of incomplete relations. In Section 3 we define the notion of an FD being satisfied in an incomplete relation. In Section 4 we introduce monodependent sets of FDs. In ....

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Lien, Y. 1982. On the equivalence of database models. Journal of the ACM 29, 333--362.

....g, connecting O 1 and O 3 . For schema (b) and FD fO 1 ; Dg fLg, two paths connecting O 3 with O 6 and two paths between O 1 and O 3 can be found. Usually, different paths correspond to different semantics and a database modeler has one of these paths in mind when specifying a dependency (cf. Lie82] This ambiguity is also known from the universal relation approach ( MUV84] Obviously an O 3 (b) O O O 3 O O O 1 2 4 5 6 p r q O 1 O O O 2 4 5 (a) s t u v A B C D E F G H K L p q r t s Figure 3: Ambiguity of an FD at schema level FD can be satisfied with respect to one path and ....

....object types O 1 and O 2 , both directly connected to type O, and extensions given for these. g specifies (value based) entries that allow to retrieve objects of type O by navigating along the relationships connecting O 1 , O 2 and O. We will denote this as navigational semantics of OFD g (cf. Lie82] Given a combination of values for A and B, and using G g under the given state, at most one O object is retrieved if g is valid. As described in Section 5.2 this navigational view does also fit for non type canonical OFDs, i.e. for combinations of sink objects. Suppose we want to retrieve an ....

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Y. E. Lien. On the equivalence of database models. Journal of the ACM, 29(2):333-- 362, 1982.

....some collection of join consistent tuples from a connected subset of the relations R 1 ; Rn , padded out with nulls, and b) There is no additional relation among the R i s with a tuple that is join consistent with t. The set of tuples described in the proof of Theorem 2. 1 is exactly what Lien [1982] calls maxtrav (maximal traversals) He shows the equivalence of maxtrav to the set of tuples we described by conditions (A C) above. Lein [1982] also gives a result (equivalence to network database schemes ) about the same class of hypergraphs that we consider in this paper connected, ....

Lien, Y. E. [1982]. "On the equivalence of database models," J. ACM 29:2, pp. 333--363.

....Armstrong relations exist for SFDs and WFDs. Keywords: incomplete relations; functional dependencies; axiom system; Armstrong relations 1 Introduction It is very rare in practice that all the information in a database is complete. This has lead researchers to extend the relational database model [CODD79, LIEN82, ATZE86, IMIE89] so as to handle incomplete information. Codd s original proposal [CODD79] suggested the addition to the database domains of an unmarked null value, whose meaning is value at present unknown , which we denote by unk. We call such relations, whose tuples may contain the null value unk, incomplete ....

....model. A sound and complete axiom system for FDs holding in (complete) relations was first given in [ARMS74] see also [ULLM88, ATZE93] and is known as Armstrong s axiom system. When considering the satisfaction of FDs in incomplete relations the transitivity rule is no longer sound. Thus, Lien [LIEN82] and Atzeni and Morfuni [ATZE86] extended FDs so as to deal with missing information, suggesting the interpretation of inapplicable or nonexistent and no information , respectively, of the unmarked null value. A sound and complete axiom system for FDs holding in incomplete relations was ....

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Y.E. Lien, On the equivalence of database models. Journal of the ACM 2, (1982), 333-362.

....preservation of dependencies, normal forms such as 3NF, BCNF, 4NF [Ul] and acyclicity [BFMY] Informally, we say a database scheme is desirable with respect to a given set of dependencies if it is acyclic, in 4NF, and dependency preserving. We restrict the data dependencies to FDs and MVDs as in [BFMY, BK, L1, L2, Ka, YO]. Even for such a restricted class of dependencies, the design problem is still difficult; and no necessary and sufficient condition for a desirable database scheme has been found. Below, we briefly review some of the related results. In the context of only MVDs, it was shown [L2, BFMY] that the ....

....BK, L1, L2, Ka, YO] Even for such a restricted class of dependencies, the design problem is still difficult; and no necessary and sufficient condition for a desirable database scheme has been found. Below, we briefly review some of the related results. In the context of only MVDs, it was shown [L2, BFMY] that the necessary and sufficient condition for a desirable database scheme is the given set of MVDs being conflict free. Moreover, in this case the desirable database scheme is unique, and can be obtained in polynomial time [L1] However, when FDs and MVDs are brought together there is no such ....

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Lien, Y.E., On the Equivalence of Database Models, JACM, April 1982, pp. 333-362.

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Y. E. Lien. On the equivalence of database models. Journal of the ACM, 29(2):333 -- 362, 1982.

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Y.E. Lien. On the equivalence of database models. Journal of the ACM, 29(2):336--362, October 1982.

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Lien, Y.E.: "On the Equivalence of Database Models". J. ACM 29 (1982) 333--362

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Y. E. Lien, `On the equivalence of database models', Database Res. Rep. 3, Bell Labs, Holmdel, NJ, 1980.

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Y.E. Lien. On the equivalence of database models. Journal of the ACM, 29(2):333--362, 1982.

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