Tài liệu Managing time in relational databases- P18 doc

The predicate for this relationship, as it holds between two time periods expressed as pairs of dates using the closed-open con-vention, is: eff_beg_dt 1 > eff_beg_dt 2 AND eff_beg_dt 1

The inverse of this relationship is: P2 [overlaps
1] P1 In the superscripted relationship, the first time period is the later one The predicate for this relationship, as it holds between two time periods expressed as pairs of dates using the closed-open con-vention, is:

(eff_beg_dt 1 > eff_beg_dt 2 ) AND (eff_beg_dt 1 < eff_end_dt 2 ) AND (eff_end_dt 1 > eff_end_dt 2 )

It says that P1 starts after P2 starts and before P2 ends, and ends after P2ends

Consider the following request for information: which policies began before the Diabetes Management Wellness Pro-gram for 2009, and ended while that proPro-gram was still going on? The SQL written to fulfill this request is:

SELECT * FROM V_Allen_Example WHERE pol_eff_beg_dt < wp_eff_beg_dt AND pol_epis_end_dt > wp_eff_beg_dt AND pol_epis_end_dt < wp_epis_end_dt

P1[intersects] P2 This not an Allen relationship It is the node in our taxonomy

of Allen relationships which includes the [starts], [starts
1], [finishes], [finishes
1], [during], [during
1], [equals], [overlaps] and [overlaps
1] relationships In other words, it combines the [overlaps] relationships with the [fills] relationships

In the non-superscripted relationship, the first time period is the earlier one The predicate for this relationship, as it holds between two time periods expressed as pairs of dates using the closed-open convention, is:

(eff_beg_dt 1 <¼ eff_beg_dt 2 ) AND (eff_end_dt 1 > eff_beg_dt 2 )

It says that P1starts no later than P2starts, and ends after P2

starts The idea behind it is that it includes every relationship in which P1and P2 have at least one clock tick in common and in which P1is the earlier time period

The limiting case is that in which P1ends at the same time

P2 starts So let P1 be [4/15/2010 – 5/13/2010] and let P2 be [5/12/2010 – 9/18/2010] The clock tick they share is 5/12/2010 The inverse of this relationship is: P1 [intersects
1] P2 The first time period in this non-superscripted relationship is the later one The predicate for this relationship, as it holds between

two time periods expressed as pairs of dates using the

closed-open convention, is:

(eff_beg_dt 1 >¼ eff_beg_dt 2 )

AND (eff_beg_dt 1 < eff_end_dt 2 )

It says that P2starts no later than P1starts, and ends after P1

starts The idea behind it is that it includes every relationship in

which P1and P2 have at least one clock tick in common and in

which P1is the earlier time period

All pairs of time periods that share at least one clock tick

sat-isfy one or the other of these two predicates So the predicate

that expresses the truth condition for all time periods that share

at least one clock tick is:

((eff_beg_dt 1 < eff_end_dt 2 )

AND (eff_end_dt 1 > eff_beg_dt 2 ))

It says that either one of the clock ticks in P1is also in P2or that

one of the clock ticks in P2is also in P1 The idea behind it is that it

covers all the cases where two time periods have at least one clock

tick in common, regardless of which is the later time period

It is interesting to look at this relationship in terms of what

falls outside its scope For any two relationships that share at

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Equals | -|

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Intersects Overlaps Fills Occupies Starts Finishes During | -|

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Aligns | -|

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Time Period Relationships Along a Common Timeline

Figure 14.10 P1[intersects] P2

least one clock tick, neither ends before the other begins Other-wise, they could not share a clock tick Looking at [includes] in terms of what falls outside its scope, we can express it as follows: NOT(eff_end_dt 1 <¼ eff_beg_dt 2 ) AND NOT(eff_beg_dt 1

>¼ eff_end_dt 2 ) And for those who like as few NOTs as possible, a logical rule (one of the transformation rules known as the De Morgan’s equi-valences) gives us the following predicate:

NOT((eff_end_dt 1 <¼ eff_beg_dt 2 ) OR (eff_beg_dt 1

>¼ eff_end_dt 2 ))

In other words, if two things are both not true, then it isn’t true that either of them is true! On such profundities are the rules of logic constructed

Consider the following request for information: which policies share any clock tick with the Diabetes Management Wellness Program for 2009?

The SQL written to fulfill this request is:

SELECT * FROM V_Allen_Example WHERE pol_eff_beg_dt < wp_epis_end_dt AND pol_epis_end_dt > wp_eff_beg_dt Notice how this SQL is much simpler than the OR’d collection

of all of the conditions that make up the leaf nodes of its Allen relationships

P1[before] P2

This is a pair of relationships, one the inverse of the other

In the non-superscripted relationship, the first time period is the earlier one

Time Period Relationships Along a Common Timeline

Excludes

Before

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Figure 14.11 P1[before] P2

The predicate for this relationship, as it holds between two

time periods expressed as pairs of dates using the closed-open

convention, is:

(eff_end_dt 1 < eff_beg_dt 2 )

It says that after P1ends, there is at least one clock tick before

P2 begins For example, consider the case where eff_end_dt1 is

5/13/2014 and eff_beg_dt2 is 5/14/2014 Because of the

closed-open convention, the last clock tick in P1 is 5/12/2014, and so

there is one clock tick gap between the two time periods, that

clock tick being 5/13/2014

The inverse of this relationship is: P1 [before
1] P2 In the

superscripted relationship, the first time period is the later one

The predicate for this relationship, as it holds between two time

periods expressed as pairs of dates using the closed-open

convention, is:

(eff_beg_dt 1 > eff_end_dt 2 )

It says that before P1 begins, there is at least one clock tick

after P2 ends For example, consider the case where eff_beg_dt1

is 5/14/2014 and eff_end_dt2 is 5/13/2014 Because of the

closed-open convention, the last clock tick in P2 is 5/12/2014,

and so there is one clock tick gap between the two time periods,

that clock tick being 5/13/2014

Throughout this book, if it isn’t important which time period

comes first, we will simply say that the two time periods are

non-contiguous

This is a particularly useful pair of relationships because they

distinguish episodes of the same object from one another

Two adjacent versions—versions of an object with no other

ver-sion of the same object between them—belong to different

episodes just in case the earlier one is [before] the later one

Of two adjacent episodes of the same object, one is [before]

the other, and the other is [before
1] the former

Consider the following request for information: which

policies ended at least one date before the Diabetes

Manage-ment Wellness Program for 2009 began?

The SQL written to fulfill this request is:

SELECT * FROM V_Allen_Example

WHERE pol_epis_end_dt < wp_eff_beg_dt

P1[meets] P2

This is a pair of relationships, one the inverse of the other

In the non-superscripted relationship, the first time period is

the earlier one

The predicate for this relationship, as it holds between two time periods expressed as pairs of dates using the closed-open convention, is:

(eff_end_dt 1 ¼ eff_beg_dt 2 )

It says that after P1ends, P2begins on the very next clock tick There is no clock tick gap between them Say that both dates are 5/13/2004 This means that the last clock tick in P1is 5/12/2004 and the first clock tick in P2 is 5/13/2004, and so there are no clock ticks between the two time periods

The inverse of this relationship is: P2[meets
1] P1 In the super-scripted relationship, the first time period is the later one The pred-icate for this relationship, as it holds between two time periods expressed as pairs of dates using the closed-open convention, is: (eff_beg_dt 1 ¼ eff_end_dt 2 )

It says that before P1 begins, P2 ends on the previous clock tick There is no clock tick gap between them

This is a particularly useful relationship because it defines a collection of versions of the same object that belong to the same episode Every adjacent pair of versions of the same object that

do not share any clock ticks, i.e in which neither includes the other, and which also do not have a single clock tick between them, belong to the same episode The earlier version of the pair meets the later one; the later version is met by the earlier one Throughout this book, if it isn’t important which of two time periods that meet come first, we will simply say that the two time periods are contiguous

Consider the following request for information: which policies ended immediately before the Diabetes Management Wellness Program for 2009 began?

Time Period Relationships Along a Common Timeline

Excludes

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Meets

Figure 14.12 P1[meets] P2

The SQL written to fulfill this request is:

SELECT * FROM V_Allen_Example

WHERE pol_epis_end_dt ¼ wp_eff_beg_dt

P1[excludes] P2

This not an Allen relationship It is the node in our taxonomy

of Allen relationships which includes the [before], [before
1],

[meets] and [meets
1] relationships

In the non-superscripted relationship, the first time period is

the earlier one The predicate for this relationship, as it holds

between two time periods expressed as pairs of dates using the

closed-open convention, is:

(eff_end_dt 1 <¼ eff_beg_dt 2 )

It says that P2starts either immediately after the end of P1, or

later than that The idea behind it is that it includes every

rela-tionship in which P1 and P2 have no clock ticks in common

and in which P1is the earlier time period

The inverse of this relationship is: P1[excludes
1] P2 The first

time period in this non-superscripted relationship is the later

one The predicate for this relationship, as it holds between

two time periods expressed as pairs of dates using the

closed-open convention, is:

(eff_beg_dt 1 >¼ eff_end_dt 2 )

It says that P2ends either immediately before the start of P1,

or earlier than that The idea behind it is that it includes every

relationship in which P1and P2have no clock ticks in common

and in which P1is the later time period

All pairs of time periods that share no clock ticks satisfy one

or the other of these two predicates So the predicate that

Time Period Relationships

Along a Common Timeline

Excludes

Before Meets

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Figure 14.13 P1[excludes] P2

designates all and only those time periods that share no clock ticks is:

(eff-end-dt 1 <¼ eff-beg-dt 2 ) OR (eff-beg-dt 1 >¼ eff-end-dt 2 )

It says that either P2 starts after P1 ends or ends before P2

starts The idea behind it is that regardless of which time period comes first, they share no clock ticks

It should be the case that two time periods [exclude] one another if and only if they do not [intersect] one another If so, then if we put a NOT in front of the predicate for the [intersects] relationship, we should get a predicate which expresses the [excludes] relationship.2Putting a NOT in front of the [intersects] relationship, we get:

NOT((eff_beg_dt 1 < eff_end_dt 2 ) AND (eff_end_dt 1 > eff_beg_dt 2 )) This is a statement of the form NOT(X AND Y) The first thing

we will do is transform it, according to the De Morgan’s rules, into (NOT-X OR NOT-Y) This gives us:

NOT(eff_beg_dt 1 < eff_end_dt 2 )

OR NOT(eff_end_dt 1 > eff_beg_dt 2 ) Next, we can replace NOT(eff_beg_dt1 < eff_end_dt2) with (eff_beg_dt1>¼ eff_end_dt2), and NOT(eff_end_dt1> eff_beg_dt2) with (eff_end_dt1<¼ eff_beg_dt2) This gives us:

(eff_beg_dt 1 >¼eff_end_dt 2 ) OR (eff_end_dt 1 <¼ eff_beg_dt 2 ) Finally, by transposing the two predicates, we get:

(eff_end_dt 1 <¼ eff_beg_dt 2 ) OR (eff_beg_dt 1 >¼ eff_end_dt 2 ) And this is indeed the predicate for the [excludes] relation-ship, demonstrating that [excludes] is indeed logically equivalent

to NOT[intersects]

Consider the following request for information: which policies either ended before the Diabetes Management Wellness Program for 2009 began, or began after that program ended? The SQL written to fulfill this request is:

SELECT * FROM V_Allen_Example WHERE (pol_epis_end_dt <¼ wp_eff_beg_dt

OR pol_eff_beg_dt >¼ wp_epis_end_dt)

2 Since, at the time we are writing this paragraph, we haven’t done this, it is an excellent way of finding out if we have made any logical mistakes so far.

Point in Time to Period of Time Queries

A point in time is a period of time that includes only one

clock tick Thus, using the closed-open convention, a point in

time, T1, is identical to the period of time [T1– T2] where T2 is

the next clock tick after T1 The only difference is in the notation

In the following discussions, we will use the simpler notation,

T1, for the point in time

In this section, we consider periods of time that are longer

than a single clock tick Periods of time that are one clock tick

in length are points in time, and we consider Allen relationships

between two points in time later

Given that P1is longer than a single clock tick, it may or may

not share a clock tick with T1 If it does, then T1 [occupies] P1

Otherwise, either one is [before] the other, or else they [meet]

In Asserted Versioning databases, all temporal periods are

delimited with the same point in time granularities When

compar-ing time periods to time periods, the logic in the AVF does not

depend on the granularity of the clock ticks used in temporal

parameters, as long as all of them are the same The clock ticks

could be months (as they are in the examples throughout this book),

days, seconds or microseconds of any size As we noted in Chapter 3,

the AVF can carry out its temporal logic without caring about

granularity specifically because of the closed-open convention

However, when comparing a point in time to a period of time,

we must be aware of the granularity of the clock tick, and must

often either add a clock tick to a point or period in time, or

sub-tract a clock tick from a point or period in time Consequently,

we need to specify the clock tick duration used in the specific

implementation to correctly perform this arithmetic We will

use “fCTD”, standing for “clock tick duration”, as the name of a

function that converts an integer into that integer number of

clock ticks of the correct granularity So, for example, in:

eff_end_dt – fCTD(1)

f CTD takes on the value of one clock tick If the granularity is a

month, as it is in most of the examples in this book, the result will

be to subtract one month from the effective end date If the

gran-ularity is a millisecond-level timestamp, it will subtract one

milli-second from that date The fCTD function determines the

granularity for a specific Asserted Versioning database from the

miscellaneous metadata table, shown as Figure 8.7 in Chapter 8

Different DBMSs use different date formats for date literals

It is also dependent on the default language and the date format

currently set These formats are shown inFigure 14.14

We used the USA format in parts of the book, so we will assume that the default date format in our sample DBMS is the same

Different DBMSs use different syntax for date arithmetic SQL Server would use something like this:

AND DATEADD(DAY, -1, pol.eff_end_dt) > ‘07/15/2010’

where DAY is the granularity (which can also be abbreviated as

DD or D), while DB2 might use:

AND (pol.eff_end_dt - 1 DAY) > ‘07/15/2010’

with the reserved word DAY indicating the granularity We will use the T-SQL format for our examples, and will assume our clock tick granularity is one month, to keep it in synch with the examples used in the book However, in real-world databases, the granularity would more likely be a day, a second

or a microsecond This fCTD translation could be built into a reusable database function as part of the framework based on metadata

T1[starts] P1

This is a pair of relationships, one the inverse of the other In the non-superscripted relationship, the first time period is the point in time, i.e the single clock-tick time period.Figure 14.15 shows this relationship, and its place in our taxonomy The two dashed lines in the illustration graphically represent T1 and P1, with T1being the upper dashed line

The predicate for this relationship, as it holds between a period of time expressed as a pair of dates using the closed-open convention, and a point in time, is:

(T 1 ¼ eff_beg_dt)

It says that T1starts at P1 Consider the following request for information: which policies begin on the same date as the 2009 Diabetes Manage-ment Wellness Program?

ISO yyyy-mm-dd 2010-09-25

09/25/2010 25.09.2010 2010-09-25

mm/dd/yyyy dd.mm.yyyy yyyy-mm-dd

USA EUR JIS

Figure 14.14 Date Formats for Date Literals

The SQL written to fulfill this request is:

SELECT * FROM V_Allen_Example

WHERE pol_eff_beg_dt ¼ wp_eff_beg_dt

T1[finishes] P1

This is a pair of relationships, one the inverse of the other In

the non-superscripted relationship, the first time period is the

point in time, i.e the single clock-tick time period.Figure 14.16

shows this relationship, and its place in our taxonomy The two

dashed lines in the illustration graphically represent T1 and P1,

with T1being the upper dashed line

The predicate for this relationship, as it holds between a

period of time expressed as a pair of dates using the closed-open

convention, and a point in time, is:

(T 1 ¼ eff_end_dt – fCTD(1))

Since the effective end date of a time period is the next clock

tick after the last clock tick in that time period, this predicate

says that P1ends on the clock tick that is T1

Fills

Occupies

Aligns

Starts

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Intersects

Time Period Relationships Along a Common Timeline

Figure 14.15 T1[starts] P1