C. S. Jensen, R. T. Snodgrass, and M. D. Soo. Extending Existing Dependency Theory to Temporal Databases. IEEE Transaction on Knowledge and Data Engineering, to appear, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....to consider temporal extensions of relation schemas with one (or more) temporal attributes. Keys, normal forms, decompositions etc. as in relational databases. lmporal tunctlonal dependencies Many attempts to define temporal FDs for concrete temporal databases: latest and most general [Jensen et al. 1996] no logical formulation for dependencies technical problems [Chomicki, 1997] The approach of Jensen, Snodgrass and Soo is subsumed, generalized, and clarified by the classical approach [Chomicki, 1997] nstral nt uepenclencles Functional dependencies are equality generating. In temporal ....

Jensen, C., Snodgrass, R., and Soo, M. (1996). Extending Existing Dependency Theory to Temporal Databases. IEEE Transactions on Knowledge and Data Engineering, 8(4).

....share the same representation formalism, namely the relational model In particular, how accurate can time be modeled in this formalism These and similar questions underlie the research presented in this paper. Careful reading of the literature gives a number of useful hints. ffl Jensen et al. [12] study temporal dependencies, and mention [12, page 579] that their work can be generalized to spatial dimensions. This work, however, does not deal with temporal or spatial granularity. ffl Wang et al. 19, page 119] mention an approach where time is treated as a conventional attribute, and the ....

....makes explicit that only the temporal attribute (D) is subject to roll up. RUDs, unlike TFDs, allow to roll up any attribute, as illustrated in the motivating example. In particular, the RUD (1) cannot be expressed as a TFD. For a more extensive overview of temporal dependencies in databases, see [12, 19, 20]. 2.2 Roll Up Figure 1 illustrates spatial and temporal granularities. Time can be partitioned into (civil) years, fiscal years, semesters, and months. We assume that a fiscal year runs from July 1 to June 30 of the next (civil) year. Semesters run from January 1 to June 30, and from July 1 to ....

C. Jensen, R. Snodgrass, and M. Soo. Extending existing dependency theory to temporal databases. IEEE Trans. on Knowledge and Data Engineering, 8(4):563--582, 1996.

....because every month belongs to a single year. We also say that a month rolls up to its year. On the other hand, WEEK and MONTH are not comparable by because months do not divide evenly into weeks, nor vice versa. The level PRICE BRACKET denotes a set of consecutive price intervals, for example, [1 10], 11 20] 21 30] and so on. We have PRICE PRICE BRACKET, and a price rolls up to its containing price bracket. Roll up dependencies (RUDs) extend functional dependencies (FDs) by allowing attributes to be compared for equality at a specified level. For example, we may find that the tax ....

....the time indicator WEEK. In our formalism, this constraint is expressed by the RUD: H D WEEK RoomCharge : Only the temporal attribute (D : DATE) is subject to roll up. RUDs, unlike TFDs, allow us to roll up any attribute. For an extensive overview of temporal dependencies in databases, see [10, 16, 17]. Data Mining. We want to know whether there are certain spatial or temporal patterns in room charges. But the database contains a large number of expenditure records, giving such a profusion of detailed information that direct comparison is impossible. This information has first to be ....

C. Jensen, R. Snodgrass, and M. Soo. Extending existing dependency theory to temporal databases. IEEE Trans. on Knowledge and Data Engineering, 8(4):563-- 582, 1996.

....the timeslice operator renders a snapshot database called timeslice that contains the data valid at that particular time point. Static dependencies then haveavery natural interpretation in a temporal database: they are supposed to be satis#ed by any one timeslice. The temporal FDs proposed by Jensen et al. #1996# are an example. Besides the temporal re interpretation of classical dependency theory,achallenging task is to examine new formalism for expressing integrity constraints that are temporal by nature. Like in the non temporal case, we can roughly distinguish between two approaches. Under one ....

....of our TFDs. In subsection 7.2, we indicated a subtle, yet signi#cant, semantic di#erence between reasoning about Wang et al. s temporal FDs and our TFD C s. We argued that our axiomatization is closer to common sense temporal reasoning in certain situations. 9. 2 Temporal FD of Jensen et al. Jensen et al. #1996# essentially extend the notion of satisfaction of FDs by temporal relations: an FD X Y is satis#ed by a temporal relation if it is satis#ed by each timeslice. This corresponds to a TFD of the form c : X Current Y in our formalism. Jensen et al. develop a temporal dependency theory that is ....

Jensen, C., Snodgrass, R., and Soo, M. 1996. Extending existing dependency theory to temporal databases. IEEE Trans. on Knowledge and Data Engineering 8, 4, 563#582.

....timeslice operator renders a snapshot database called timeslice that contains the data valid at that particular time point. Static dependencies then have a very natural interpretation in a temporal database: they are supposed to be satisfied by any one timeslice. The temporal FDs proposed by Jensen et al. 1996] are an example. Besides the temporal re interpretation of classical dependency theory, a challenging task is to examine new formalism for expressing integrity constraints that are temporal by nature. Like in the non temporal case, we can roughly distinguish between two approaches. Under one ....

....our TFDs. In subsection 7.2, we indicated a subtle, yet significant, semantic difference between reasoning about Wang et al. s temporal FDs and our TFD C s. We argued that our axiomatization is closer to common sense temporal reasoning in certain situations. 9. 2 Temporal FD of Jensen et al. Jensen et al. 1996] essentially extend the notion of satisfaction of FDs by temporal relations: an FD X Y is satisfied by a temporal relation if it is satisfied by each timeslice. This corresponds to a TFD of the form c : X Current Y in our formalism. Jensen et al. develop a temporal dependency theory that is ....

Jensen, C., Snodgrass, R., and Soo, M. 1996. Extending existing dependency theory to temporal databases. IEEE Trans. on Knowledge and Data Engineering 8, 4, 563--582.

....which means that the salary never changes. The classical relational database design theory is still applicable. BRICS Mini course on Temporal Databases 110 2 Temporal functional dependencies Many attempts to define temporal FDs for concrete temporal databases: ffl latest and most general [Jensen et al. 1996] ffl no logical formulation for dependencies ffl technical problems [Chomicki, 1997] The approach of Jensen, Snodgrass and Soo is subsumed, generalized, and clarified by the classical approach [Chomicki, 1997] BRICS Mini course on Temporal Databases Valid time: t v , transaction time t t . ....

Jensen, C., Snodgrass, R., and Soo, M. (1996). Extending Existing Dependency Theory to Temporal Databases. IEEE Transactions on Knowledge and Data Engineering, 8(4).

....of these is specific to a particular data model, and thus appropriates the inherent peculiarities of its data model. Furthermore, these normal forms often deviate substantially in nature from conventional normal forms and are in some sense not true extensions of these, for a variety of reasons [JSS96] We adopted a different approach. Since relations in the BCDM can be related to those of other temporal data models, then functional dependencies and normal forms expressed in terms of the BCDM can also be mapped into other data models. We thus chose to apply dependency theory to the BCDM. ....

....and hence for all past states of r . Hence, the same functional dependency must hold for all snapshots of r (this insight first appeared over a decade ago [CW83] A similar argument can be applied to valid time relations and to bitemporal relations, yielding the following characterization [JSS96] 21 R. A temporal functional dependency , denoted X Y , exists on R if for all meaningful instance r of R, c t (r) s 1 [X ] s 2 [X ] s 1 [Y ] s 2 [Y ] ut For example, the instance empSal in Figure 11(a) satisfies the dependency EName Sal. In the definition of a ....

[Article contains additional citation context not shown here]

C. S. Jensen, R. T. Snodgrass, and M. D. Soo. Extending Existing Dependency Theory to Temporal Databases. IEEE Transaction on Knowledge and Data Engineering, to appear, 1996.

....operator was first defined by Clifford and Croker [CC87] who named it the natural timejoin. We showed in earlier work that the temporal natural join plays the same important role in reconstructing normalized temporal relations as does the snapshot natural join for normalized snapshot relations [JSS96] Most previous work in temporal join evaluation has addressed, either implicitly or explicitly, the implementation of the temporal natural join (or the closely related temporal equijoin) 2.6 Outerjoins and Outer Cartesian Products Like the snapshot outerjoin, temporal outerjoins and Cartesian ....

....previous section, an adequate empirical investigation of the performance of temporal join algorithms has not been performed. We concentrate on the temporal equijoin, defined in Section 2.4. This join and the related temporal natural join, are needed to reconstruct normalized temporal relations [JSS96] To perform a study of implementations of this join, we must first provide state of the art implementations of the 17 different types of algorithms outlined for this join. In this section, we discuss our implementation choices. 18 Table 3: Existing Algorithms and Taxonomy Counterparts ....

C. S. Jensen, R. T. Snodgrass and M. D. Soo. Extending Existing Dependency Theory to Temporal Databases. IEEE Transactions on Knowledge and Data Engineering, 8(4):563--582, August, 1996.

....can take different forms. They have been expressed using first order temporal logic (FOTL) 8, 9] Alternatively, one can study restricted classes of FOTL formulas, which may be called temporal dependencies. A comprehensive overview of temporal dependencies has been given by Jensen et al. [20]. In this paper, we introduce a new temporal dependency, called trend dependency (TD) which captures a significant class of data evolution constraints. Two examples of such constraints, taken from recent work, are Salaries of employees should never decrease [8] and A faculty s rank cannot ....

....implies oe, denoted Sigma j= oe, iff every temporal relation satisfying Sigma also satisfies oe. 2 Defining a temporal relation as a time series of snapshot relations is not uncommon in theoretical research. See for example [8, 28] Also the work on temporal dependency theory of Jensen et al. [20] departs from the idea that temporal relations can be timesliced. Of course, more advanced structures for storing time related data have been proposed in the literature. See for example [27, 10] However, such representation issues are somehow peripheral to this study. Intuitively, one may think ....

[Article contains additional citation context not shown here]

C. Jensen, R. Snodgrass, and M. Soo. Extending existing dependency theory to temporal databases. IEEE Trans. on Knowledge and Data Engineering, 8(4):563--582, 1996.

....of these is specific to a particular data model, and thus appropriates the inherent peculiarities of its data model. Furthermore, these normal forms often deviate substantially in nature from conventional normal forms and are in some sense not true extensions of these, for a variety of reasons [JSS96] We adopted a different approach. Since relations in the BCDM can be related to those of other temporal data models, then functional dependencies and normal forms expressed in terms of the BCDM can also be mapped into other data models. We thus chose to apply dependency theory to the BCDM. ....

....and hence for all past states of r 0 . Hence, the same functional dependency must hold for all snapshots of r (this insight first appeared over a decade ago [CW83] A similar argument can be applied to valid time relations and to bitemporal relations, yielding the following characterization [JSS96] Definition: Let X and Y be sets of non timestamp attributes of a bitemporal relation schema R. A temporal functional dependency , denoted X T Y , exists on R if for all meaningful instance r of R, 8c v ; c t 8s 1 ; s 2 2 V c v (ae B c t (r) s 1 [X ] s 2 [X ] s 1 [Y ] s 2 ....

[Article contains additional citation context not shown here]

C. S. Jensen, R. T. Snodgrass, and M. D. Soo. Extending Existing Dependency Theory to Temporal Databases. IEEE Transaction on Knowledge and Data Engineering, to appear, 1996.

....and hence for all past states of r # . Hence, the same functional dependency must hold for all snapshots of r (this insight first appeared over a decade ago [4] A similar argument can be applied to valid time relations and to bitemporal relations, yielding the following characterization [22]. TEMPORALLY ENHANCED DATABASE DESIGN 917 Definition 2 Let X and Y be sets of non timestamp attributes of a bitemporal relation schema R.Atemporal functional dependency, denoted X T #Y , exists on R if for all meaningful instance r of R, #c v ,c t #s 1 ,s 2 # # V c v (# B c t ....

....functional dependencies and temporal functional dependencies means that inference rules such as Armstrong s axioms have close temporal counterparts that play the same role in the temporal context as do the non temporal rules in the non temporal context. Next, we can also define temporal keys [22]. For example, the explicit attributes X of a temporal relation schema R form a (temporal) key if X T #R. Finally, we can generalize snapshot normal forms in a similar manner. Example 3 These are some of the dependencies that hold in the rental car database schema (this schema was shown in ....

[Article contains additional citation context not shown here]

C. S. Jensen, R. T. Snodgrass, and M. D. Soo. Extending Existing Dependency Theory to Temporal Databases. IEEE Transaction on Knowledge and Data Engineering, 8(4):563--582 (1996).

.... 2 4 C102 T1245 5 7 5 now C102 T1245 8 UC 5 7 C102 T1234 9 9 9 11 C102 T1234 10 13 9 13 C102 T1234 14 15 9 now C102 T1234 16 UC 9 15 CustomerID TapeNum [2,Now] Theta [2,4] C101 [2,Now] Theta [2,4] T1234 [5,7] Theta [5,1] C102 [5,7] Theta [5,1] T1245 [8,Now] Theta [5,7] 8,Now] Theta [5,7] [9,9] Theta [9,11] 9,9] Theta [9,11] T1234 [10,13] Theta [9,13] 10,13] Theta [9,13] 14,15] Theta [9,1] 14,15] Theta [9,1] 16,Now] Theta [9,15] 16,Now] Theta [9,15] Figure 2: Alternative Representations of the CheckedOut Instance which is assumed to conform to the ANSI X3 SPARC ....

.... 5 7 5 now C102 T1245 8 UC 5 7 C102 T1234 9 9 9 11 C102 T1234 10 13 9 13 C102 T1234 14 15 9 now C102 T1234 16 UC 9 15 CustomerID TapeNum [2,Now] Theta [2,4] C101 [2,Now] Theta [2,4] T1234 [5,7] Theta [5,1] C102 [5,7] Theta [5,1] T1245 [8,Now] Theta [5,7] 8,Now] Theta [5,7] 9,9] Theta [9,11] [9,9] Theta [9,11] T1234 [10,13] Theta [9,13] 10,13] Theta [9,13] 14,15] Theta [9,1] 14,15] Theta [9,1] 16,Now] Theta [9,15] 16,Now] Theta [9,15] Figure 2: Alternative Representations of the CheckedOut Instance which is assumed to conform to the ANSI X3 SPARC three level ....

[Article contains additional citation context not shown here]

C. S. Jensen, R. T. Snodgrass, and M. D. Soo. Extending Existing DependencyTheory to Temporal Databases, IEEE Transactions on Knowledge and Data Engineering, 8(4):563--582, August 1996.

....of these is specific to a particular data model, and thus appropriates the inherent peculiarities of its data model. Furthermore, these normal forms often deviate substantially in nature from conventional normal forms and are in some sense not true extensions of these, for a variety of reasons [44]. We adopted a different approach. Since relations in the BCDM can be related to those of other temporal data models, then functional dependencies and normal forms expressed in terms of the BCDM can also be mapped into other data models. We thus chose to apply dependency theory to the BCDM. ....

....and hence for all past states of r 0 . Hence, the same functional dependency must hold for all snapshots of r (this insight first appeared over a decade ago [13] A similar argument can be applied to valid time relations and to bitemporal relations, yielding the following characterization [44]. Definition 2 Let X and Y be sets of non timestamp attributes of a bitemporal relation schema R. A temporal functional dependency , denoted X T Y , exists on R if for all meaningful instance r of R, 8c v ; c t 8s 1 ; s 2 2 V c v (ae B c t (r) s 1 [X ] s 2 [X ] s 1 [Y ] s ....

[Article contains additional citation context not shown here]

C. S. Jensen, R. T. Snodgrass, and M. D. Soo. Extending Existing Dependency Theory to Temporal Databases. IEEE Transaction on Knowledge and Data Engineering, to appear (1996).

....An example might be The higher the degree, the higher the salary. This type of dependencies turns out very useful in temporal databases as it allows capturing meaningful trends. Nearly all temporal dependencies that have so far been proposed in the literature compare attributes for equality only [JSS96], which greatly limits their expressivity. For example, consider the relational schema fSS#, Rank, Salg. A tuple fSS#:x, Rank:y, Sal:zg means that the employee with the social security number x has rank y and salary z. Ranks are numbers between 1 and 5. Assume that I 1 and I 2 are two relations ....

....with two time instances has in it the full complexity of the data mining problem we are going to explore, while it considerably simplifies the technical treatment. 2 Related Work Lately and independently of data mining, there has been a growing interest in dependencies for temporal databases [JSS96, WBBJ97]. All temporal dependencies found in the extensive overview of Jensen et al. JSS96] compare attributes by using equality only. Our TD s compare attributes by operators of f ; 6=g; they generalize the dynamic functional dependencies proposed by Wijsen [Wij95] Association rules can take ....

[Article contains additional citation context not shown here]

C.S. Jensen, R.T. Snodgrass, and M.D. Soo. Extending existing dependency theory to temporal databases. IEEE Trans. on Knowledge and Data Engineering, 8(4):563--582, 1996.

No context found.

C. S. Jensen, R. T. Snodgrass, and M. D. Soo. Extending existing dependency theory to temporal databases. IEEE Transactions on Knowledge and Data Engineering, 8#4#:563#582, 1996.

No context found.

C.S. Jensen, R.T. Snodgrass, and M.D. Soo. Extending Existing Dependency Theory to Temporal Databases. IEEE Transaction on Knowledge and Data Engineering, 8(4), August 1996.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC