1. CS240A: Databases and Knowledge Bases Time Ontology and Representations Carlo Zaniolo Department of Computer Science University of California, Los Angeles Revised: January 2003 Notes From Chapter 5 of Advanced Database Systems by Zaniolo, Ceri, Faloutsos, Snodgrass, Subrahmanian and Zicari. Morgan Kaufmann, 1997

2. Time Properties  Structure  Boundedness  Density  Time Data Types  Time and Facts

3. Time Structure  Linear Time  Branching Time  Directed Acyclic Graph  Periodic/Cyclic Time Sunday. E.g., days of the week.  Boundedness of Time From now on, we will assume a linear time structure.  Boundedness  Unbounded  Time origin exists (bounded from the left)  Bounded time (bounds on both ends)

4. Time Density  Discrete:  Time line is isomorphic to the integers  Timeline composed of a sequence of non­decomposable time periods of some fixed, minimal duration, termed chronons.  Between each pair of chronons is a finite number of other chronons.  Dense: (difficult to implement)  Time line is isomorphic to the rational numbers.  Between any two chronons is an infinite number of other instants.  Continuous: (very difficult to implement)  Time line is isomorphic to the real numbers.  Between each pair of instants is a infinite number of other instants.  A bounded discrete representation of time is the simplest option used in SQL-2 and most temporal DBs.

5. Time Datatype in SQL-2  DATE : four digits for the year and two for month and day. Multiple formats allowed:  E.g., 2001-12-08 or 12/08/2001 or 12.08.2001  ISO, USA, EUR, JIS representations supported---DBA selects which one is used in specific system.  Internal representation is the same, independent of external ones. The internal representation of a time is a string of 4 bytes (each packs 2 decimal digits).  TIME : 2 digits for hour, 2 for minutes, and 2 for seconds (plus optional fractional digits---system dependent). E.g., 13:50:00, 13:50, 1:50 PM denote the same time— internally three 2-packed decimal digits.

6. Time Datatype in SQL-2 (cont.)  TIMESTAMP : date+time with six fractional digits for the second field. A timestamp is a seven-part value (year, month, day, hour, minute, second, and microsecond) that designates a date and time as defined above, Time includes a fractional specification of microseconds. E.g. 2001-01-05-13.01.59.000000  The internal representation of a timestamp is a string of 10 bytes, each of which consists of 2 packed decimal digits. The first 4 bytes represent the date, the next 3 bytes the time, and the last 3 bytes the microseconds.  The length of a TIMESTAMP column, as described in the SQLDA, is 26 bytes, which is the appropriate length for the character string representation of the value.

7. Time Data Type in SQL-2 (cont.)  TIME(STAMP) WITH ZONE: offset according to UTC (universel temps coordonné)  INTERVAL: I.e. a time span. In DB2 is called a labeled duration. E.g., 10 DAYS  Time expressions. Using the labeled duration in arithmetic : orderdate + 10 DAYS < CURRENT DATE --- this is valid, but CURRENT DATE - overdate > 10 DAYS --- this is invalid.  CAST expressions: E.g. CAST(2 DAYS AS HOURS) returns 48 HOURS

8. Various Temporal Types used in temporal DBs  A time instant is a time point on the time line.  An event is an instantaneous fact, i.e, something occurring at an instant. The event occurrence time of an event is the instant at which the event occurs in the real world.  An instant set is a set of instants.  A time period is the set of time instants between two instants (start time and end time).  In TSQL2, the basic temporal element is a finite union of periods.

9. Periods versus Time Intervals  Periods are frequently called (time) intervals.  but this conflicts with the SQL data type INTERVAL and we will try to avoid it.  A SQL time interval is a directed duration of time. A duration is an amount of time with a known length, but no specific starting or ending instants.Also called a span.  A positive interval denotes forward motion of time; a negative interval denotes backwards motion of time.

10. Valid Time and Transaction Time  Valid Time of a fact: when the fact is true in the modeled reality  Transaction Time of a fact: when it was recorded in the database.  Thus we have four different kinds of tables: 1. Snapshot 2. Valid-time 3. Transaction-time 4. Bitemporal

11. Example: Tom's Employment History  On January 1, 1984, Tom joined the faculty as an Instructor.  On December 1, 1984, Tom completed his doctorate, and so was promoted to Assistant Professor effective on July 1, 1984 (retroactive update).  On March 1, 1989, Tom was promoted to Associate Professor, effective July 1, 1989 (proactive update).

12. Queries and Updates  A transaction time table is append-only: it keeps the history of the updates made on the database.  Transaction time tables supports rollback queries, such as:  On October 1, what rank was our database showing for Tom?  A valid time table can be updated: e.g., Tom’s past record is changed once his rank is changed retroactively.  Valid time tables support historical queries, such as:  What was Tom’s rank on October 1 (according to our current database)? Transaction time databases also can support historical queries.

13. Bitemporal Tables  Bitemporal Tables are append­only and supports queries of both kinds (rollback&historical) such as:  On October 1, 1984, what did we think Tom's rank was at that date?  TSQL3: SELECT Rank FROM Faculty AS F WHERE Name = 'Tom‘ AND VALID(F) OVERLAPS DATE '1984­10­01‘ AND TRANSACTION(F) OVERLAPS DATE '1984­10­01'