Table Of ContentTime Granularities in Databases, Data Mining,
and Temporal Reasoning
Springer-Verlag Berlin Heidelberg GmbH
Claudio Bettini • Sushil Jajodia • Sean Wang
Time Granularities
in Databases, Data Mining,
and Temporal Reasoning
With 44 Figures and 4 Tables
, Springer
Prof.Dr.Claudio Bettini Prof.Dr.Sushil[ajodia
Prof.Dr.X.Sean Wang
UniversityofMilan
InformationScience Department George MasonUniversity
ViaComelico,39 DepartmentofInformation
20135Milan,Italy andSoftwareEngineering
Fairfax,VA22030-4444,USA
bettinits'dsi.unimi.it
{jajodia, xywang}@gmu.edu
LibraryofCongressCataloging-in-PublicationData
Bettini,C.(Claudio), 1963-
Timegranularitiesindatabases,datarnining,andtemporalreasoninglC.Bettini,
S.[ajodia,X.S.Wang.
p.cm.
Includesbibliographicalreferencesandindex.
1.Databasemanagement.2.Temporaldatabases.3.Datamining. I.Iajodia,Sushil.
II.Wang,X.S.(X.Sean),1960- III.Title.
QA76.9.D3B4872000
006.3-dc21 00-030792
ACMComputing Classification (1998): H.4.I,H.2.8, FA.I, 1.204,J.7
ISBN978-3-642-08634-2 ISBN978-3-662-04228-1 (eBook)
DOI 10.1007/978-3-662-04228-1
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Preface
Calendar units, such as months and days, clock units, such as hours and
seconds, and specialized units, such as business days and academic years,
serve major roles in a wide range of information system applications. System
support for reasoning about these units, called granularities in this book, is
important for the efficient design, use, and implementation of such applica
tions. Consider these typical examples:
• In a relational database, a standard way to incorporate time is to extend
a relational schema to include some time attribute. Values of this time at
tribute come from some fixed granularity. Users and applications, however,
may require the flexibility of viewing the temporal information contained
in the corresponding relation in terms of different granularities. In the ab
sence of any system support, users must understand the semantics of the
granularity used in the relation, formulate their queries according to this
granularity, and then convert (manually or by application programs) the
responses in the desired granularity.
• In a federated database environment, different constituent databases may
use different granularities to store temporal information. When these
databases are combined to process a query at the federation level, a uni
fying framework is needed to resolve any mismatches involving different
granularities.
• Several problems in Artificial Intelligence can be formulated as constraint
satisfaction problems (CSPs). In a temporal CSP, variables are used to
represent event occurrences and constraints are used to represent their
temporal relationships. Several problems in scheduling, planning, diagnosis,
and natural language understanding can be formulated as temporal CSPs,
often involving multiple granularities. In this case, system support is needed
to check the consistency of the given constraints, and to derive implicit
constraints involving different time granularities.
• A huge amount of data is collected every day in the form of event-time
sequences. Common examples are the recording of different values of stock
shares during a day, every access to a computer by an external network,
bank transactions, or events related to malfunctions in an industrial plant.
These sequences represent valuable sources of information, not only what
is explicitly registered, but also for deriving implicit information and for
VI Preface
predicting the future behavior of the process that we are monitoring. The
latter activity requires an analysis of the frequency of certain events, dis
covery of their regularity, or discovery of sets of events that are related by
particular temporal relationships. Such frequency, regularity, and relation
ships are very often expressed in terms of multiple granularities, and thus
analysis and discovery tools must be able to deal with these granularities.
This book provides a unifying model for expressing granularities, neces
sary for designing, using, and implementing reasoning about these granular
ities. The presented model is then applied to several areas:
• Investigation of symbolic representations and of relationships among gran-
ularities (Chap. 2)
• Logical design of temporal databases with multiple granularities (Chap. 3)
• Querying temporal databases with multiple views (Chap. 4)
• Networks of temporal constraints with granularities (Chap. 5)
• Mining of large event sequences for complex temporal relationships
(Chap. 6)
Other areas could also benefit from the granularity model; some of these are
discussed in Chap. 7.
Intended audience
This book addresses several aspects of temporal information. It is intended for
computer scientists and engineers who are interested in the formal models and
technical development of specific issues. Practitioners Gan learn about critical
aspects that must be considered when designing and implementing databases
supporting temporal information. Lecturers may find this book useful in an
advanced course on databases. They may also use this book to supplement
an existing course on databases or knowledge bases. Moreover, any graduate
student working on time representation and reasoning, either in databases or
knowledge bases, should definitely read this book.
Acknowledgments
Some of the material in this book has appeared elsewhere. We gratefully ac
knowledge the IEEE Computer Society for permission to use material from
"Temporal semantic assumptions and their use in database query evalua
tion," IEEE Transactions on Knowledge and Data Engineering, Vol. 10, No.
2, Marchi April 1998, pp. 277-296 in Chap. 4; and "Discovering temporal
relationships with multiple granularities in time sequences," IEEE Transac
tions on Knowledge and Data Engineering, Vol. 10, No.2, Marchi April 1998,
pp. 222-237 in Chap. 6. We also acknowledge the Association for Computing
Machinery for allowing us to use material from "Logical design for tempo
ral databases with multiple granularities," ACM Transactions on Database
Systems, Vol. 22, No.2, June 1997, pp. 115-170 in Chap. 3; and Baltzer Sci
ence Publishers for allowing us to use material from "A general framework
for time granularity and its application to temporal reasoning," Annals oj
Preface VII
Mathematics and Artificial Intelligence, Vol. 22, No. 1,2, 1998, pp. 29-58 in
Chaps. 2 and 5.
Financial support for our research presented in this book was provided
by the Defense Advanced Research Projects Agency, National Science Foun
dation, and Army Research Office. We are deeply grateful to the respective
program managers, Gio Wiederhold, Maria Zemankova, and David Hislop, for
their support. In a way, work on this book began when Gio Wiederhold ap
proached one of us (Jajodia) for joint work on a paper dealing with temporal
granularities.
Many people contributed to the research results presented in this book.
In particular, Elisa Bertino actively supported a very fruitful cooperation
between the research groups at the University of Milan and George Mason
University, and shared with us her insights on specific issues of semantic
assumptions in temporal databases. Curtis Dyreson and Richard Snodgrass
had extensive discussions with us on granularity relationships, which led to
some of the definitions included in this book. Graduate students Roberto
De Sibi, Giovanni Gabrielli, Jia-Ling Lin, Roberto Marceca, Peng Ning, and
Nicola Piccioni participated in the research and made contributions to the
subjects as well.
Finally, it is a pleasure to acknowledge Dr. Hans W6ssner, Executive
Editor for Springer-Verlag, whose enthusiasm and support for this project
were most helpful.
Milan, Italy and Fairfax, Virginia Claudio Bettini
April, 2000 Sushil Jajodia
X. Sean Wang
Contents
Preface................................................... V
Part I. Time Granularities
1. Introduction.............................................. 3
1.1 Formal Notion of Time Granularity. . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Temporal Databases with Multiple Granularities ........... 8
1.3 Bibliographic Notes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10
2. Granularity Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11
2.1 Introduction........................................... 11
2.2 Formal Notions ........................................ 12
2.2.1 Granularity Relationships ......................... 13
2.2.2 Properties....................................... 17
2.3 Granularity Conversion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19
2.4 Granularity Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19
2.5 Symbolic Representation ................................ 23
2.5.1 The Grouping-Oriented Operations. . . . . . . . . . . . . . . .. 24
2.5.2 Granule-Oriented Operations ...................... 27
2.5.3 Syntactic Restrictions on Algebra Operations . . . . . . .. 31
2.5.4 Examples ....................................... 32
2.5.5 Granularity Conversion ........................... 33
2.5.6 Accommodating Restrictions on Index/Label Sets. . .. 34
2.6 Expressiveness and Alternative Representations. . . . . . . . . . .. 35
2.6.1 Alternative Representations. . . . . . . . . . . . . . . . . . . . . . .. 37
2.6.2 Collections and Slices. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 37
2.6.3 Expressiveness and Relationships. . . . . . . . . . . . . . . . . .. 39
2.7 Bibliographic Notes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 42
X Contents
Part II. Applications to Databases
3. Design of Temporal Databases with Multiple Granularities 47
3.1 Introduction........................................... 47
3.1.1 Temporal Dimension of Logical Design. . . . . . . . . . . . .. 48
3.2 Temporal Functional Dependencies. . . . . . . . . . . . . . . . . . . . . .. 50
3.2.1 Inference Axioms for TFDs . . . . . . . . . . . . . . . . . . . . . . .. 52
3.2.2 Closure of Attributes ............................. 56
3.3 Temporal Normalization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 57
3.4 Temporal Boyce-Codd Normal Form. . . . . . . . . . . . . . . . . . . . .. 63
3.4.1 Decomposing Temporal Module Schemas into TBCNF 64
3.5 Preservation of Dependencies ............................ 68
3.6 Temporal Third Normal Form. . . . . . . . . . . . . . . . . . . . . . . . . . .. 69
3.6.1 Decomposing Temporal Module Schemas into T3NF .. 70
3.7 Discussion............................................. 73
3.8 Conclusion............................................ 77
3.9 Bibliographic Notes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 78
4. Querying Temporal Databases with Multiple Views. . . . . .. 83
4.1 Introduction........................................... 83
4.2 Data Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 87
4.2.1 The Query Language MQLF. .. .... .... . . .. .. . . .. . .. 87
4.3 Point-Based Assumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 89
4.3.1 An Example: Persistence. . . . . . . . . . . . . . . . . . . . . . . . .. 89
4.3.2 Syntax and Semantics of Point-Based Assumptions. .. 90
4.4 Properties of Temporal Modules with Assumptions. . . . . . . .. 92
4.5 Querying a Database with Point-Based Assumptions. . . . . . .. 94
4.6 Interval-Based Assumptions. . . . . . . . . . . .. . . . . . . . . . . . . . . . .. 98
4.6.1 An Example: Liquidity. . . . . . . . . . . . . . . . . . . . . . . . . . .. 98
4.6.2 Syntax and Semantics. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 99
4.7 Querying a Database with Interval-Based Assumptions ...... 101
4.8 Combining Point-Based and Interval-Based Assumptions .... 104
4.9 Semantic Assumptions on TSQL2 Temporal Relations ....... 106
4.10 Discussion and Conclusion ............................... 110
4.11 Bibliographic Notes ..................................... 112
Part III. Reasoning with Time Granularities and Its Applications
5. Constraint Reasoning ..................................... 117
5.1 Introduction ........................................... 117
5.2 Temporal Constraint Networks with Granularities .......... 120
5.2.1 Complexity of Consistency Checking ................ 123
5.3 A Complete Algorithm .................................. 124
