1. Temporal Database Entries for the Springer Encyclopedia of Database Systems 2008

Abstract Versus Concrete Temporal Query LanguagesJan Chomicki, University at Buffalo, USA, http://www.cse.buffalo.edu/~chomicki David Toman, University of Waterloo, Canada, http://www.cs

Temporal Database Entries for the

Springer Encyclopedia of Database Systems

Christian S Jensen and Richard T Snodgrass (Editors)

May 22, 2008

TR-90

Title Temporal Database Entries for the

Springer Encyclopedia of Database SystemsCopyright c

TIMECENTERParticipants

Aalborg University, Denmark

Christian S Jensen (codirector), Simonas ˇSaltenis, Kristian Torp

University of Arizona, USA

Richard T Snodgrass (codirector), Sudha Ram

Individual participants

Yun Ae Ahn, Chungbuk National University, Korea; Michael H B¨ohlen, Free University of Bolzano, Italy; Curtis

E Dyreson, Utah State University, USA; Dengfeng Gao, IBM Silicon Valley Lab, USA; Fabio Grandi, sity of Bologna, Italy; Vijay Khatri, Indiana University, USA; Nick Kline, Microsoft, USA; Gerhard Knolmayer,University of Bern, Switzerland; Carme Mart´ın, Technical University of Catalonia, Spain; Thomas Myrach, Uni-versity of Bern, Switzerland; Kwang W Nam, Chungbuk National University, Korea; Mario A Nascimento,University of Alberta, Canada; John F Roddick, Flinders University, Australia; Keun H Ryu, Chungbuk Na-tional University, Korea; Dennis Shasha, New York University, USA; Paolo Terenziani, University of PiemonteOrientale “Amedeo Avogadro,” Alessandria, Italy; Vassilis Tsotras, University of California, Riverside, USA;Fusheng Wang, Siemens, USA; Jef Wijsen, University of Mons-Hainaut, Belgium; and Carlo Zaniolo, University

Univer-of California, Los Angeles, USA

For additional information, see The TIMECENTERHomepage:

URL:<http://www.cs.aau.dk/TimeCenter>

Any software made available via TIMECENTERis provided “as is” and without any express or implied warranties, including, without limitation, the implied warranty of merchantability and fitness for a particular purpose.

The TIMECENTERicon on the cover combines two “arrows.” These “arrows” are letters in the so-called Rune

alphabet used one millennium ago by the Vikings, as well as by their precedessors and successors The Runealphabet (second phase) has 16 letters, all of which have angular shapes and lack horizontal lines because theprimary storage medium was wood Runes may also be found on jewelry, tools, and weapons and were perceived

by many as having magic, hidden powers

The two Rune arrows in the icon denote “T” and “C,” respectively

In January 2007 Ling Liu and Tamer ¨Ozsu started work on an Encyclopedia of Database Systems to be lished by Springer We were asked to edit the encyclopedia entries that relate to the area of temporal databases.This report collects versions of the temporal database entries as of May, 2008 These entries are preliminary inseveral respects First, the entries have not been subjected to Springer’s final copyediting Second, they are onlyapproximately formatted: they will look much better in their final form Third, in contrast to the entries in theirfinal form, the entries in the technical report cannot be searched electronically (see below) And fourth, the reader

pub-does not get the benefit of the other entries available in the full encyclopedia Nonetheless, the content appearing

here is close to that which will appear in the final encyclopedia, and the entries included here provide a succinctand broad overview of the contributions and structure of the area of temporal databases

The complete encyclopedia, in which the final entries will appear, will be in multiple volumes It will constitute

a comprehensive and authoritative reference on databases, data management, and database systems Since it will

be available in both print and online formats, researchers, students, and practitioners will benefit from advancedsearch functionality and convenient interlinking possibilities with related online content The Encyclopedia’sonline version will be accessible on the SpringerLink platform (http://www.springer.com/computer/database+management+%26+information+retrieval/book/978-0-387-49616-0)

We thank the more than two dozen authors who contributed to these entries; some contributed to multipleentries We list those authors here

Arie ShoshaniRichard T Snodgrass

V S SubrahmanianAbdullah Uz TanselPaolo TerenzianiDavid TomanKristian TorpVassilis J Tsotras

X Sean WangJef WijsenYue ZhangAll entries were reviewed by several experts, underwent one or several revisions, and were eventually accepted

by an Associate Editor of the encyclopedia The authors represent in concert over three centuries of innovative

research in temporal databases, experience that informs the content of these entries

We thank Springer for providing useful online tools for managing the logistics of this large project and forinvesting heavily to ensure a highly useful and authoritative resource for the database community and for othersinterested in this technology Finally, we thank Jennifer Carlson and Simone Tavenrath, who so effectively andcheerfully managed the process at Springer; Jennifer Evans, also at Springer, who consistently supported thiseffort; and Ling and Tamer, for heading up this effort and insisting on the highest quality from the very beginning

Richard Snodgrass and Christian S Jensen

May 2008

i

ii

30 SQL-Based Temporal Query Languages 93

iv

C S Jensen and C E Dyreson (eds), M B¨ohlen, J Clifford, R Elmasri, S K Gadia, F Grandi, P Hayes,

S Jajodia, W K¨afer, N Kline, N Lorentzos, Y Mitsopoulos, A Montanari, D Nonen, E Peressi, B Pernici,J.F Roddick, N L Sarda, M R Scalas, A Segev, R T Snodgrass, M D Soo, A Tansel, R Tiberio and

G Wiederhold, “A Consensus Glossary of Temporal Database Concepts—February 1998 Version,” in TemporalDatabases: Research and Practice, O Etzion, S Jajodia, and S Sripada (eds.), LNCS 1399, Springer-Verlag,

pp 367–405, 1998

1

Abstract Versus Concrete Temporal Query Languages

Jan Chomicki, University at Buffalo, USA, http://www.cse.buffalo.edu/~chomicki David Toman, University of Waterloo, Canada, http://www.cs.uwaterloo.ca/~david

of data on time are captured by and represented in the underlying temporal data model

HISTORICAL BACKGROUND

Most databases store time-varying information On the other hand, SQL is often the language of choice fordeveloping applications that utilize the information in these databases Plain SQL, however, does not seem toprovide adequate support for temporal applications

Example To represent the employment histories of persons, a common relational design would use a schema

Employment(FromDate, ToDate, EID, Company),with the intended meaning that a person identified by EID worked for Company continuously from FromDate toToDate Note that while the above schema is a standard relational schema, the additional assumption that thevalues of the attributes FromDate and ToDate represent continuous periods of time is itself not a part of therelational model

Formulating even simple queries over such a schema is non-trivial: for example the query GAPS: “List all personswith gaps in their employment history, together with the gaps” leads to a rather complex formulation in, e.g.,SQL over the above schema (this is left as a challenge to readers who consider themselves SQL experts; for a list ofappealing, but incorrect solutions, including the reasons why, see [9]) The difficulty arises because a single tuple

in the relation is conceptually a compact representation of a set of tuples, each tuple stating that an employmentfact was true on a particular day

The tension between the conceptual abstract temporal data model (in the example, the property thatemployment facts are associated with individual time instants) and the need for an efficient and compactrepresentation of temporal data (in the example, the representation of continuous periods by their start andend instants) has been reflected in the development of numerous temporal data models and temporal querylanguages [3]

SCIENTIFIC FUNDAMENTALS

Temporal query languages are commonly defined using temporal extensions of existing non-temporal querylanguages, such as relational calculus, relational algebra, or SQL The temporal extensions can be categorized intwo, mostly orthogonal, ways:

The choice of the actual temporal values manipulated by the language This choice is primarily determined bythe underlying temporal data model The model also determines the associated operations on these values.The meaning of temporal queries is then defined in terms of temporal values and operations on them, andtheir interactions with data (non-temporal) values in a temporal database

The choice of syntactic constructs to manipulate temporal values in the language This distinction determineswhether the temporal values in the language are accessed and manipulated explicitly, in a way similar toother values stored in the database, or whether the access is implicit, based primarily on temporally extendingthe meaning of constructs that already exist in the underlying non-temporal language (while still using theoperations defined by the temporal data model).

Additional design considerations relate to compatibility with existing query languages, e.g., the notion of temporalupward compatibility

However, as illustrated above, an additional hurdle stems from the fact that many (early) temporal querylanguages allowed the users to manipulate a finite underlying representation of temporal databases rather thanthe actual temporal values/objects in the associated temporal data model A typical example of this situationwould be an approach in which the temporal data model is based on time instants, while the query languageintroduces interval-valued attributes Such a discrepancy often leads to a complex and unintuitive semantics ofqueries

In order to clarify this issue, Chomicki has introduced the notions of abstract and concrete temporal databasesand query languages [2] Intuitively, abstract temporal query languages are defined at the conceptual level of thetemporal data model, while their concrete counterparts operate directly on an actual compact encoding of temporaldatabases The relationship between abstract and concrete temporal query languages is also implicitly present

in the notion of snapshot equivalence [7] Moreover, Bettini et al [1] proposed to distinguish between explicitand implicit information in a temporal database The explicit information is stored in the database and used toderive the implicit information through semantic assumptions Semantic assumptions about fact persistence play

a role similar to mappings between concrete and abstract databases, while other assumptions are used to addresstime-granularity issues

Abstract Temporal Query Languages

Most temporal query languages derived by temporally extending the relational calculus can be classified asabstract temporal query languages Their semantics is defined in terms of abstract temporal databases which, inturn, are typically defined within the point-stamped temporal data model, in particular without any additionalhidden assumptions about the meaning of tuples in instances of temporal relations

Example The employment histories in an abstract temporal data model would most likely be captured by asimpler schema “Employment(Date, EID, Company)”, with the intended meaning that a person identified by EIDwas working for Company on a particular Date While instances of such a schema can be potentially very large(especially when a fine granularity of time is used), formulating queries is now much more natural

Choosing abstract temporal query languages over concrete ones resolves the first design issue: the temporal valuesused by the former languages are time instants equipped with an appropriate temporal ordering (which is typically

a linear order over the instants), and possibly other predicates such as temporal distance The second designissue—access to temporal values—may be resolved in two different ways, as exemplified by the following twodifferent query languages:

•Temporal Relational Calculus (TRC): a two-sorted first-order logic with variables and quantifiers explicitlyranging over the time and data domains (see the entry Temporal Relational Calculus)

•First-order Temporal Logic (FOTL): a language with an implicit access to timestamps using temporalconnectives (see the entry Temporal Logic in Database Query Languages)

Example The GAPS query is formulated as follows:

TRC: ∃t1, t3.t1< t2< t3∧ ∃c.Employment(t1, x, c) ∧ (¬∃c.Employment(t2, x, c)) ∧ ∃c.Employment(t3, x, c)FOTL: 3∃c.Employment(x, c) ∧ (¬∃c.Employment(x, c)) ∧ 2∃c.Employment(x, c)

Here, the explicit access to temporal values (in TRC) using the variables t1, t2, and t3can be contrasted with theimplicit access (in FOTL) using the temporal operators3 (read “sometime in the past”) and 2 (read “sometime

in the future”) The conjunction in the FOTL query represents an implicit temporal join The formulation in

2

TRC leads immediately to an equivalent way of expressing the query in SQL/TP [9], an extension of SQL based

on TRC (see the entry SQL-based Temporal Query Languages)

Example The above query can be formulated in SQL/TP as follows:

SELECT t.Date, e1.EID

FROM Employment e1, Time t, Employment e2

WHERE e1.EID = e2.EID AND e1.Date < e2.Date

AND NOT EXISTS ( SELECT *

FROM Employment e3WHERE e1.EID = e3.EID AND t.Date = e3.DateAND e1.Date < e3.Date AND e3.Date < e2.Date )The unary constant relation Time contains all time instants in the time domain (in our case, all Dates) and isonly needed to fulfill syntactic SQL-style requirements on attribute ranges However, despite of the fact that theinstance of this relation is not finite, the query can be efficiently evaluated [9]

Note also that in all the above cases, the formulation is exactly the same as if the underlying temporal databaseused the plain relational model (allowing for attributes ranging over time instants)

The two languages, FOTL and TRC, are the counterparts of the snapshot and timestamp models (cf the entryPoint-stamped Data Models) and are the roots of many other temporal query languages, ranging from the moreTRC-like temporal extensions of SQL, to more FOTL-like temporal relational algebras (e.g., the conjunction intemporal logic directly corresponds to a temporal join in a temporal relational algebra, as both of them induce

an implicit equality on the associated time attributes) The precise relationship between these two groups oflanguages is investigated in the entry Temporal Logic in Database Query Languages

Temporal integrity constraints over point-stamped temporal databases can also be conveniently expressed inTRC or FOTL (see the entry Temporal Integrity Constraints)

Multiple Temporal Dimensions and Complex Values While the abstract temporal query languages are typicallydefined in terms of the point-based temporal data model, they can similarly be defined with respect to complextemporal values, e.g., pairs (or tuples) of time instants or even sets of time instants In these cases, in particular

in the case of set-valued attributes, it is important to remember that the set values are treated as indivisibleobjects, and hence truth (i.e., query semantics) is associated with the entire objects, but not necessarily withtheir components/subparts For a detailed discussion of this issue, see the entry Telic Distinction in TemporalDatabases

Concrete Temporal Query Languages

Although abstract temporal query languages provide a convenient and clean way of specifying queries, theyare not immediately amenable to implementation: the main problem is that, in practice, in temporal databasesfacts persist over periods of time Storing all true facts individually for every time instant during a period would

be prohibitively expensive or, in the case of infinite time domains such as dense time, even impossible

Concrete temporal query languages avoid these problems by operating directly on the compact encodings oftemporal databases (see the discussion of compact encodings in the entry on Point-stamped Temporal Models).The most commonly used encoding is the one that uses intervals However, in this setting, a tuple that associates

a fact with such an interval is a compact representation of the association between the same fact and all the timeinstants that belong to this interval This observation leads to the design choices that are commonly present insuch languages:

•Coalescing is used, explicitly or implicitly, to consolidate representations of (sets of) time instants associatedwith the same fact In the case of interval-based encodings, this leads to coalescing adjoining or overlappingintervals into a single interval (see the entry Temporal Coalescing) Note that coalescing only changes theconcrete representationof a temporal relation, not its meaning (i.e., the abstract temporal relation); hence

it has no counterpart in abstract temporal query languages

•Implicit set operations on time values are used in relational operations For example, conjunction (join)

3

typically uses set intersection to generate a compact representation of the time instants attached to the facts

in the result of such an operation

Example For the running example, a concrete schema for the employment histories would typically be defined

as “Employment(VT, EID, Company)”, where VT is a valid time attribute ranging over periods (intervals) TheGAPS query can be formulated in a calculus-style language corresponding to TSQL2 (see the entry on TSQL2)along the following lines:

∃I1, I2.[∃c.Employment(I1, x, c)] ∧ [∃c.Employment(I2, x, c)] ∧ I1precedes I2∧ I = [end(I1) + 1, begin(I2) − 1]

In particular, the variables I1 and I2 range over periods and the precedes relationship is one of Allen’s intervalrelationships The final conjunct, I = [end(I1) + 1, begin(I2) − 1], creates a new period corresponding to the timeinstants related to a person’s gap in employment; this interval value is explicitly constructed from the end andstart points of I1and I2, respectively For the query to be correct, however, the results of evaluating the bracketedsubexpressions, e.g., “[∃c.Employmeent(I1, x, c)] ,” have to to be coalesced Without the insertion of the explicitcoalescing operators, the query is incorrect To see that, consider a situation in which a person p0is first employed

by a company c1, then by c2, and finally by c3, without any gaps in employment Then without coalescing ofthe bracketed subexpressions of the above query, p0 will be returned as a part of the result of the query, which isincorrect Note also that it is not enough for the underlying (concrete) database to be coalesced

The need for an explicit use of coalescing makes often the formulation of queries in some concrete SQL-basedtemporal query languages cumbersome and error-prone

An orthogonal issue is the difference between explicit and implicit access to temporal values: this distinctioncarries over to the concrete temporal languages as well Typically, the various temporal extensions of SQL arebased on the assumption of an explicit access to temporal values (often employing a built-in valid time attributeranging over intervals or temporal elements), while many temporal relational algebras have chosen to use theimplicit access based on temporally extending standard relational operators such as temporal join or temporalprojection

All Timestamp/Snapshot Temporal Databases

Finitely Representable Temporal Databases

Interval-encoded Temporal Databases

{ (1998, John), (1999, John),

, (2002, John) } Q(D) -

{ ([1990, 1997], John, IBM), ([2003, 2008], John, MS), ([1992, 2005], Sue, MS), ([2005, +∞], Sue, SAP) }

{ ([1990, 1997], John, IBM), ([2003, 2008], John, MS), ([1992, 1999], Sue, MS), ([2000, 2005], Sue, MS), ([2005, +∞], Sue, SAP) }

{([1998, 2002], John)}

{([1998, 1999], John), ([2000, 2002], John) } eval(Q)(E1) -

6k.k

Figure 1: Query Evaluation over Interval Encodings of Point-stamped Temporal Databases

4

Compilation and Query Evaluation An alternative to allowing users direct access to the encodings of temporaldatabases is to develop techniques that allow the evaluation of abstract temporal queries over these encodings.The main approaches are based on query compilation techniques that map abstract queries to concrete queries,while preserving query answers More formally:

Q(kEk) = keval(Q)(E)k,where Q an abstract query, eval(Q) the corresponding concrete query, E is a concrete temporal database, andk.k a mapping that associates encodings (concrete temporal databases) with their abstract counterparts (cf.Figure 1) Note that a single abstract temporal database, D, can be encoded using several different instances ofthe corresponding concrete database, e.g., E1 and E2 in Figure 1

Most of the practical temporal data models adopt a common approach to physical representation of temporaldatabases: with every fact (usually represented as a tuple), a concise encoding of the set of time points at which thefact holds is associated The encoding is commonly realized by intervals [6, 7] or temporal elements (finite unions

of intervals) For such an encoding it has been shown that both First-Order Temporal Logic [4] and TemporalRelational Calculus [8] queries can be compiled to first-order queries over a natural relational representation ofthe interval encoding of the database Evaluating the resulting queries yields the interval encodings of the answers

to the original queries, as if the queries were directly evaluated on the point-stamped temporal database Similarresults can be obtained for more complex encodings, e.g., periodic sets, and for abstract temporal query languagesthat adopt the duplicate semantics matching the SQL standard, such as SQL/TP [9]

KEY APPLICATIONS

Temporal query languages are primarily used for querying temporal databases However, because of theirgenerality they can be applied in other contexts as well, e.g., as an underlying conceptual foundation for queryingsequences and data streams [5]

CROSS REFERENCE

Allen’s relations, bitemporal relation, constraint databases, key, nested relational model, non first normal form(N1NF), point-stamped temporal models, relational model, snapshot equivalence, SQL, telic distinction intemporal databases, temporal coalescing, temporal data models, temporal element, temporal granularity, temporalintegrity constraints, temporal join, temporal logic in database query languages, temporal relational calculus andalgebra, time domain, time instant, TSQL2, transaction time, valid time

on Database Systems, 26(2):145–178, 2001

[5] Y.-N Law, H Wang, and C Zaniolo Query Languages and Data Models for Database Sequences and Data Streams

In International Conference on Very Large Data Bases, pages 492–503, 2004

[6] S B Navathe and R Ahmed Temporal Extensions to the Relational Model and SQL In A Tansel, J Clifford,

S Gadia, S Jajodia, A Segev, and R T Snodgrass, editors, Temporal Databases: Theory, Design, andImplementation, pages 92–109 Benjamin/Cummings, 1993

[7] R T Snodgrass The Temporal Query Language TQuel ACM Trans Database Syst., 12(2):247–298, 1987

[8] D Toman Point vs Interval-based Query Languages for Temporal Databases In ACM Symposium on Principles ofDatabase Systems, pages 58–67, 1996

[9] D Toman Point-based Temporal Extensions of SQL In International Conference on Deductive and Object-OrientedDatabases, pages 103–121, 1997

5

ALLEN’S RELATIONS

Peter Revesz, University of Nebraska-Lincoln, http://www.cse.unl.edu/~revesz/

Paolo Terenziani Universita’ del Piemonte Orientale “Amedeo Avogadro”,

A (convex) time interval I is the set of all time points between a starting point (usually denoted

time intervals [1] There are 13 different possibilities, depending on the relative positions of the endpoints of the intervals

For example, “There will be a guest speaker during the Database System class” can be

considering the relative position of the endpoints; point relations are discussed in the entry

“Temporal Constraints” of this Encyclopedia) Moreover, any subset of the 13 relations,

relations in Allen’s Algebra) Such subsets are used in order to denote ambiguous cases, in

has been the first application of Allen’s relations A graphical representation of the basic 13 Allen’s relations is shown in the following figure

Allen’s relations are specific cases of temporal constraints (see the entry “Temporal Constraints”

of this Encyclopedia): namely, they are qualitative temporal constraints between time intervals

Given a set of such constraints, qualitative temporal reasoning can be used in order to make

inferences (e.g., to check whether the set of constraints is consistent; see in the entry

“Qualitative temporal reasoning” of this Encyclopedia)

Finally, notice that, in many entries of this Encyclopedia, the term (time) period has been used with the same meaning of (time) interval in this entry

APPLICABILITY PERIOD

Christian S Jensen Aalborg University, Denmark

Richard T Snodgrass University of Arizona http://www.cs.arizona.edu/people/rts/

SYNONYMS

none

DEFINITION

The applicability period (or period of applicability) for a modification (generally an insertion, deletion,

or update) is the time period for which that modification is to apply to Generally the modification is asequenced modification and the period applies to valid time This period should be distinguished fromlifespan

For insertions, the applicability period is the valid time of the fact being inserted The following states that Ben

is in the book department for one month in 2007

INSERT INTO EMPLOYEE

VALUES (’Ben’, ’Book’)

VALID PERIOD ’[15 Feb 2007, 15 Mar 2007]’

For a deletion, the applicability period states for what period of time the deletion is to apply The followingmodification states that Ben in fact wasn’t in the book department during March

DELETE FROM EMPLOYEE

WHERE Name = ’Ben’

VALID PERIOD ’[1 Mar 2007, 31 Mar 2007]’

After this modification, the lifespan would be February 15 through February 28

Similarly, the applicability period for an UPDATE statement would affect the stored state just for the applicabilityperiod

A current modification has a default applicability period that either extends from the time the statement isexecuted to forever or, when now-relative time is supported, from the time of execution to the ever-increasingcurrent time for insertions

R T Snodgrass, Developing Time-Oriented Database Applications in SQL, Morgan Kaufmann ers, Inc., San Francisco, CA, July 1999, 504+xxiv pages.

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When associated with a fact, a bitemporal interval then identifies an interval (valid time) during whichthat fact held (or holds or will hold) true in reality, as well as identifies an interval (transaction time)when that belief (that the fact was true during the specified valid-time interval) was held, i.e., was part

of the current database state

MAIN TEXT

In this definition, a time interval denotes a convex subset of the time domain Assuming a discrete time domain,

a bitemporal interval can be represented with a non-empty set of bitemporal chronons or granules

C S Jensen and C E Dyreson (eds), M B¨ohlen, J Clifford, R Elmasri, S K Gadia, F Grandi, P Hayes,

S Jajodia, W K¨afer, N Kline, N Lorentzos, Y Mitsopoulos, A Montanari, D Nonen, E Peressi, B Pernici,J.F Roddick, N L Sarda, M R Scalas, A Segev, R T Snodgrass, M D Soo, A Tansel, R Tiberio and

G Wiederhold, “A Consensus Glossary of Temporal Database Concepts—February 1998 Version,” in TemporalDatabases: Research and Practice, O Etzion, S Jajodia, and S Sripada (eds.), LNCS 1399, Springer-Verlag,

pp 367–405, 1998

1

MAIN TEXT

In this definition, “bi” refers to the capture of exactly two temporal aspects An alternative definition states that

a bitemporal relation captures one or more valid times and one or more transaction times In this definition, “bi”refers to the existence of exactly two types of times

One may adopt the view that the data in a relation represents a collection of logical statements, i.e., statementsthat can be assigned a truth values The valid times of these so-called facts are the times when these are true

in the reality modeled by the relation In cases where multiple realities are perceived, a single fact may havemultiple, different valid times This might occur in a relation capturing archaeological facts for which there noagreements among the archaeologists In effect, different archaeologists perceive different realities

Transaction times capture when database objects are current in a database In case an object migrates from onedatabase to another, the object may carry along its transaction times from the predecessor databases This thencalls for relations that capture multiple transaction times

The definition of bitemporal is used as the basis for applying bitemporal as a modifier to other concepts such as

“query language.” A query language is bitemporal if and only if it supports any bitemporal relation Hence, mostquery languages involving both valid and transaction time may be characterized as bitemporal

Relations are named as opposed to databases because a database may contain several types of relations Mostrelations involving both valid and transaction time are bitemporal according to both definitions

Concerning synonyms, the term “temporal relation” is commonly used However, it is also used in a generic andless strict sense, simply meaning any relation with time-referenced data

Next, the term “fully temporal relation” was originally proposed because a bitemporal relation is capable ofmodeling both the intrinsic and the extrinsic time aspects of facts, thus providing the “full story.” However, thisterm is no longer used

The term “valid-time and transaction-time relation” is precise and consistent with the other terms, but is alsolengthy

CROSS REFERENCE*

Temporal Database, Transaction Time, Valid Time

REFERENCES*

C S Jensen and C E Dyreson (eds), M B¨ohlen, J Clifford, R Elmasri, S K Gadia, F Grandi, P Hayes,

S Jajodia, W K¨afer, N Kline, N Lorentzos, Y Mitsopoulos, A Montanari, D Nonen, E Peressi, B Pernici,J.F Roddick, N L Sarda, M R Scalas, A Segev, R T Snodgrass, M D Soo, A Tansel, R Tiberio and

G Wiederhold, “A Consensus Glossary of Temporal Database Concepts—February 1998 Version,” in TemporalDatabases: Research and Practice, O Etzion, S Jajodia, and S Sripada (eds.), LNCS 1399, Springer-Verlag,

1

pp 367–405, 1998.

2

MAIN TEXT

Calendars are most often cyclic, allowing human-meaningful time values to be expressed succinctly For example,dates in the common Gregorian calendar may be expressed in the form <month day, year > where the month andday fields cycle as time passes

The concept of calendar defined here subsumes commonly used calendars such as the Gregorian calendar, theHebrew calendar, and the Lunar calendar, though the given definition is much more general This usage isconsistent with the conventional English meaning of the word

Dershowitz and Reingold’s book presents complete algorithms for fourteen prominent calendars: the present civilcalendar (Gregorian), the recent ISO commercial calendar, the old civil calendar (Julian), the Coptic an Ethiopiccalendars, the Islamic (Muslim) calendar, the modern Persian (solar) calendar, the Bah´a’´ı calendar, the Hebrew(Jewish) calendar, the Mayan calendars, the French Revolutionary calendar, the Chinese calendar, and both theold (mean) and new (true) Hindu (Indian) calendars One could also envision more specific calendars, such as anacademic calendar particular to a school, or a fiscal calendar particular to a company

N Dershowitz and E M Reingold, Calendrical Calculations, Cambridge, 1977

C S Jensen and C E Dyreson (eds), M B¨ohlen, J Clifford, R Elmasri, S K Gadia, F Grandi, P Hayes,

S Jajodia, W K¨afer, N Kline, N Lorentzos, Y Mitsopoulos, A Montanari, D Nonen, E Peressi, B Pernici,J.F Roddick, N L Sarda, M R Scalas, A Segev, R T Snodgrass, M D Soo, A Tansel, R Tiberio and

G Wiederhold, “A Consensus Glossary of Temporal Database Concepts—February 1998 Version,” in TemporalDatabases: Research and Practice, O Etzion, S Jajodia, and S Sripada (eds.), LNCS 1399, Springer-Verlag,

pp 367–405, 1998

B Urgun, C E Dyreson, R T Snodgrass, J K Miller, N Kline, M D Soo, and C S Jensen, “IntegratingMultiple Calendars using τ Zaman,” Software—Practice and Experience 37(3):267-308, 2007

1

MAIN TEXT

A calendric system is the abstraction of time available at the conceptual and logical (query language) levels As anexample, a Russian calendric system could be constructed by considering the sequence of five different calendarsused in that region of the world In prehistoric epochs, the Geologic calendar and Carbon-14 dating (another form

of calendar) are used to measure time Later, during the Roman empire, the lunar calendar developed by theRoman republic was used Pope Julius, in the first Century B.C., introduced a solar calendar, the Julian calendar.This calendar was in use until the 1917 Bolshevik revolution when the Gregorian calendar, first introduced byPope Gregory XIII in 1572, was adopted In 1929, the Soviets introduced a continuous schedule work week based

on four days of work followed by one day of rest, in an attempt to break tradition with the seven-day week Thisnew calendar, the Communist calendar, had the failing that only eighty percent of the work force was active onany day, and it was abandoned after only two years in favor of the Gregorian calendar, which is still in use today.The term “calendric system” has been used to describe the calculation of events within a single calendar However,the given definition generalizes that usage to multiple calendars in a very natural way

CROSS REFERENCE*

Calendar, Temporal Database, Time Interval

REFERENCES*

C S Jensen and C E Dyreson (eds), M B¨ohlen, J Clifford, R Elmasri, S K Gadia, F Grandi, P Hayes,

S Jajodia, W K¨afer, N Kline, N Lorentzos, Y Mitsopoulos, A Montanari, D Nonen, E Peressi, B Pernici,J.F Roddick, N L Sarda, M R Scalas, A Segev, R T Snodgrass, M D Soo, A Tansel, R Tiberio and

G Wiederhold, “A Consensus Glossary of Temporal Database Concepts—February 1998 Version,” in TemporalDatabases: Research and Practice, O Etzion, S Jajodia, and S Sripada (eds.), LNCS 1399, Springer-Verlag,

pp 367–405, 1998

1

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Current Semantics

Free Univerity of Bozen-Bolzano, Italy, Aalborg University, Denmark and

University of Arizona, USA

Specif-MAIN TEXT

Current semantics [3] requires that queries and views on a temporal database consider the current informationonly and work exactly as if applied to a non-temporal database For example, a query to determine who managesthe high-salaried employees should consider the current database state only Constraints and assertions also workexactly as before: they are applied to the current state and checked on database modification

Database modifications are subject to the same constraint as queries: they should work exactly as if applied to

a non-temporal database Database modifications, however, also have to take into consideration that the currenttime is constantly moving forward Therefore, the effects of modifications must persist into the future (untiloverwritten by a subsequent modification)

The definition of current semantics assumes a timeslice operator τ [t](Dt

) that takes the snapshot of a temporaldatabase Dt

at time t The timeslice operator takes the snapshot of all temporal relations in Dt

and returns theset of resulting non-temporal relations

Let now be the current time [2] and let t be a time point that does not exceed now Let Dt

be a temporaldatabase instance at time t Let M1, , Mn, n ≥ 0 be a sequence of non-temporal database modifications.Let Q be a non-temporal query Current semantics requires that for all Q, t, Dt

, and M1, , Mn the followingequivalence holds:

Q(Mn(Mn−1( (M1(Dt

) )))) = Q(Mn(Mn−1( (M1(τ [now](Dt

))) )))Note that for n = 0 there are no modifications, and the equivalence becomes Q(Dt

) = Q(τ [now](Dt

)), i.e., anon-temporal query applied to a temporal database must consider the current database state only

An unfortunate ramification of the above equivalence is that temporal query languages that introduce new reservedkeywords not used in the non-temporal languages they extend will violate current semantics The reason is thatthe user may have previously used such a keyword as an identifier (e.g., a table name) in the database Toavoid being overly restrictive, it is reasonable to consider current semantics satisfied even when reserved wordsare added, as long as the semantics of all statements that do not use the new reserved words is retained by thetemporal query language

Temporal upward compatibility [1] is a synonym that focuses on settings where the original temporal database isthe result of rendering a non-temporal database temporal

CROSS REFERENCE

Nonsequenced Semantics, Now in Temporal Databases, Sequenced Semantics, Snapshot equivalence, TemporalDatabase, Temporal Data Model, Temporal Query Languages, Timeslice Operator

REFERENCES

[1] J Bair, M H B¨ohlen, C S Jensen, and R T Snodgrass Notions of Upward Compatibility of Temporal QueryLanguages Wirtschaftsinformatik, 39(1):25–34, February 1997.

[2] J Clifford, C Dyreson, T Isakowitz, C S Jensen, and R T Snodgrass On the Semantics of “NOW” in Databases.ACM Transactions on Database Systems, 22:171–214, June 1997

[3] R T Snodgrass Developing Time-Oriented Database Applications in SQL Morgan Kaufmann, 1999

2