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Information in databases can be imperfect and this imperfec- tion has several forms and causes. In some cases, a single value should be stored, but it is (partially) unknown. The uncertainty about which value to store leads to the aforementioned imperfection. In temporal databases, uncertainty can arise, concerning which temporal notion needs to be stored. Because in temporal databases, temporal notions influence the consistency with which the database models the reality, this uncertainty has a direct impact on the consistency of the model. To represent this temporal uncertainty, previous works have adapted fuzzy sets with con- junctive interpretation, an approach that might prove misleading. This work presents a model that represents the uncertainty using possibility and necessity measures, which are fuzzy sets with disjunctive interpre- tations.
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A POSSIBILISTIC VALID-TIME MODEL
José Enrique Pons, Christophe Billiet,
Olga Pons Capote andGuy de Tré
Department of Computer Science and Artificial IntelligenceUniversity of Granada, Spain
Department of Telecommunications and Information Processing,Ghent University, Belgium
PRESENTATION’S STRUCTURE
Conclusions
Proposal
Background concepts
Motivation
MOTIVATION
• The storage of time-dependent objects in a database has an impact on the consistency in the database.• Humans manage time with vagueness and imprecision. There are the following types of information:
• Uncertainty: The temporal specification for an event is uncertain. Typically in temporal specification for historical databases.• Vagueness: Very often in changes of granularity.• Subjectivity or Ambiguity: The interpretation for the temporal specification relies on the hearer.
• Time Intervals as the basic unit for the representation of time in Artificial Intelligence and language understanding applications.
MotivationUncertainty, VaguenessVery often, the time period in which an object is valid is not known precisely.
Sometimes, the starting, the ending or both points are not known exactly.
Also, the granularity in which a time point is specified, is a source of imprecision.
People work with time in a flexible way. The user wants to specify a query to the temporal database with imprecision.
Days granularity
Months granularity
My Birthday is by May
Jan Feb Mar Apr May Jun Jul Aug Sep
Temporal specifications become vague when we
change to a finer granularity
MotivationImperfection in databaseWe will consider two types of imperfections:• Imperfection in database: “The car was in the garage around April”.• Imprecision in the query specification: “The user wants a car which was in the garage around April”.Sometimes, the starting, the ending or both points are not known exactly.
Days granularity
Months granularity
“Around April”
Jan Feb Mar Apr May Jun Jul Aug Sep
The temporal specification “Around April” is a time
interval that includes some days of March, April and
some days of May.
[ ]
BACKGROUND CONCEPTS
• Temporal databases•Possibilistic variables
Background ConceptsA temporal database is a database which stores the time-dependent objects in its schema.
A relational database provides user-defined time which is an non-interpreted value.
There are three types of time despite of used-defined time:•Transaction Time, TT.•Valid Time, VT.•Decision Time, DT.
Time interval [S,E]
S E
#ID Name Age Works for
Start year
End year
1 Peter 24 John 2010 -
2 Maria 34 John 2001 -
3 John 52 - 1999 -
4 Sarah 29 Maria 2005 2009
Background ConceptsTransaction Time TTIt is the time when the fact is stored in the database.
Usually stored as a timestamp value.
#ID Name Age Works for Stored
1 Peter 24 John 15/10/2010
2 Maria 34 John 13/09/2001
3 John 52 - 10/10/1999
4 Sarah 29 Maria 05/08/2005
#ID Name Age Works for Decided
1 Peter 24 John 15/10/2010
2 Maria 34 John 13/09/2001
3 John 52 - 10/10/1999
4 Sarah 29 Maria 05/08/2005
Background ConceptsDecision Time DT
It is the time when the fact was decided to happen.
It is usually stored as a timestamp value.
Background ConceptsValid TimeIt is the time period when the fact or object is valid in the modeled reality.
It is usually stored as an interval.
Imprecision may arise in the starting, ending or both points for the valid time intervals.
Several proposals for dealing with imprecision in a valid time database.
#ID Name Age Works for
Start year
End year
1 Peter 24 John 2010 -
2 Maria 34 John 2001 -
3 John 52 - 1999 -
4 Sarah 29 Maria 2005 2009
Background Concepts
Consistency
#ID Name Age Works for
Start year
End year
1 Peter 24 John 2010 -
2 Maria 34 John 2001 -
3 John 52 - 1999 -
4 Sarah 29 Maria 2005 2009
Modeling time-dependent objects have an impact on the consistency in a relational database.
Consider a database with employee’s data for a company.
Usually, the Data Manipulation Language DML as well as the Data Definition Language should be re-defined.
If Sarah is hired in 2012 we can’t add the tuple.The solution for this is to define a new primary key.But also a consistence mechanism must be defined.
#ID Name Age Works for
Start year
End year
1 Peter 24 John 2010 -
2 Maria 34 John 2001 -
3 John 52 - 1999 -
4 Sarah 29 Maria 2005 2009
4 Sarah 29 Maria 2012 -
4 Sarah 29 Maria 2001 2007Spurious row!
PROPOSAL
•Representation of imperfect time intervals.• Relational representation of imperfect time intervals.• Querying.
ProposalPossibilistic VariablesA possibilistic variable X over a universe U is a variable taking exactly one value in U, but for some reason, that value is partially unknown.
The possibility distribution πx on U models the available knowledge about the value that X takes.
We will use triangular distributions that are represented by three values: [D,a,b]. In the example [25,3,3].
25
Possibility1
0
“I bought my car at the end of June 2012”
The car was bought one specific day
June 201222 28
Representation of imperfect time intervalsIll-known interval: An ill-known time interval is represented by two ill-known time points: X and Y.
Possibilistic valid-time period(PVP): is an ill-known interval of time specifying when the data regarding an object are valid.
At the end of April
At the beginning Of June
Possibility1
0
The car entered the garage at the end of April and left the garageat the beginning of June.
The car was in the garage a specific time interval, but for some reason, the upper and lower boundaries are partially known.
Relational representation of imperfect time pointsThe domain for a time point is given by the domain of all the possibility distributions over the temporal domain plus three special constants:• UNKNOWN = Any value in the time domain is equally possible.• UNDEFINED = The value is not defined.• NULL = Nothing is known about the value.
Value Relational representation
µ(x)
FT F1 F2 F3UNKNOWN 0 N N N 1
UNDEFINED 1 N N N 0
NULL 2 N N N Not defined.
M = [D,a,b] 3 D a b µM
D
Possibility1
0D-a D+b
Querying valid-time intervalsQuery specification:~Q = (Qtime, Q)Where:• Q denotes a collection of possibly fuzzy non-temporal preferences.• Qtime = (I, AR) with
• I = (a,b) a crisp time interval.• AR is one of the Allen’s relations.
ID IID Seg Man. Name PVP
001 1 B Peug. 205 [1985,2,3],[1997,2,1]
002 1 C Peug. 305 [1977,2,2],[1989,2,3]
003 1 B Citro. C2 [2002,1,1],[2006,1,1]
001 2 B Peug. 206 [2000,1,2],[2011,2,1]
001 3 B Peug. 207 [2006,1,1],[2011,1,1]
“The user wants to obtain a list of models from segment B, made by the manufacturer Peugeot before the time interval 2001-2005”
Qtime= ([2001,2005],before),Q = (Segment = B) ^ (Manufacturer = Peugeot)
Query evaluationThe evaluation of the query requirements for a record results in a degree in the unit interval.
In order to evaluate the query, two things happen independently:• The preferences in Q are evaluated, resulting in a satisfaction degree, noted eQ here.• The crisp interval given by the user is evaluated with respect to the allen’s relation.
ID IID PossQTime
NecQTime
Q
001 1 1 1 1
002 1 1 1 0.5
003 1 1 0.5 0
001 2 1 0 1
001 3 0 0 1
“The user wants to obtain a list of models from segment B, made by the manufacturer Peugeot before the time interval 2001-2005”
Qtime= ([2001,2005],before),Q = (Segment = B) ^ (Manufacturer = Peugeot)
Ranking and aggregationTo present the results to the user, a ranking method is used: The sum of the possibility and necessity measures gives an evaluation score in [0,2].Then, the score is rescaled to the unit interval.
The final ranking is now given as a convex combination:
Efinal (r )= ω * eQ (r ) + (1- ω) e Qtime
With ω in [0,1]
The value ω allows to give more weight to the temporal constraint or mor weight to the non-temporal constraints.
ID IID PossQTime
NecQTime
eQTime Q Efinal(ω = 0.5)
001 1 1 1 1 1 1
002 1 1 1 1 0.5 0.75
003 1 1 0.5 0.75 0 0.375
001 2 1 0 0.5 1 0.75
001 3 0 0 0 1 0.5
CONCLUSIONS AND FURTHER WORK
Conclusions
• We presented a model to represent and query ill-known temporal intervals.
• It is possible to model Allen’s relations and also more complex relations.
• Some interesting implementations, but not a truly standard.
• Further work in a flexible implementation in fuzzy temporal databases.
Further research work
• Definition of a data manipulation language and a data definition language for relational databases.
• Extend the querying capabilities: Both ill-known time intervals in query specification and in the database.
