Temporal Primitives - PowerPoint Presentation

Slide1

Temporal Primitives

Institute of Computer Science Foundation for Research and Technology - Hellas

Manos Papadakis & Martin Doerr

Workshop: Extending, Mapping and Focusing the CRM19th International Conference on Theory and Practice of Digital Libraries (TPDL2015)

September 17, 2015,

Poznań

, PolandSlide2

Past phenomena (1/2)

Past is a collection of phenomena manifested in space and timeMinoan Period: cultural phenomena related to the Minoan civilizationHuman lifetime: birth, aging, activities related to a specific personCIDOC CRM refers to constituents of the past as Temporal EntitiesGroups of coherent and related

phenomenaPeriods, Events, Activities etc.They form finite and continuous time framesTemporal Entities main information componentsContext: interactions of things, people and placesTemporal confinement: time extent of comprising phenomena on timeline2Slide3

Past phenomena (2/2)

Description of the past includesDefinition of Temporal EntitiesIntroduction of semantic associations between themConclusion of relevant temporal topology => a possible scenario of the pastSemantic association between Temporal EntitiesInclusion and exclusion relations: is part of, cannot co-exist with etc.Special cases: influence, initiation/termination, follows, survived, etc.

Temporal information and topologyTemporal knowledge representation: Allen Interval TheoryTopology expressed as sets of temporal relations: Allen operators3Slide4

Allen Interval Algebra (1/2)

Time intervalan ordered set of time pointsrepresents a time frame on the timelineit is denoted by its endpoints e.g. (As, Ae)Temporal constraint

Describe endpoint associationsValid interval constraint: As < AeEvery interval has a non zero durationAllen operatorsSets of endpoint constraintsDescribe 7 basic (plus 6 inverse) temporal relations4

Time

A

B

meets

As

Ae

Ae =

BsSlide5

Allen Interval Algebra (2/2)

5X before YX meets Y

X overlaps YX during YX starts YX finishes YX equals Y

X

Y

X

Y

Y

X

Y

X

Y

X

Y

X

Y

X

Allen operatorsSlide6

Motivation (1/3)

Temporal topology between Temporal Entities concludedDirectly: Endpoint association between related intervalsIndirectly: Semantic association implies possible temporal scenariosExample of indirect topology: Influence  ContinuationActivities: Recitation and

Stenography of Homer’s epic poemsIn order to preserve knowledge about pieces of artStenography is a logical continuation of RecitationExtracted temporal topology: logical continuationAn activity cannot continue another instance if it occurs after the formerRecitation must start before the end of Stenography6Slide7

Motivation (2/3)

Temporal constraint of continuation in timeLet A and B be activities Recitation and Stenography, respectivelyMinimum knowledge that implies continuation: As < Bethe starting point of Recitation must be before the end of StenographyCorresponding set of Allen operators

operators that express the continuation endpoint constraint{before OR meets OR overlaps OR starts OR during OR finishes}7

Time

Stenography

Bs

Recitation

A

s

A

e

B

e

b

efore

meets

overlaps

starts

during

finishes

o

verlapped-bySlide8

Motivation (3/3)

Disjunctive Temporal Information: set of possible Allen operatorsAgainst the monotonic knowledge generation sequenceTheoretical and Practical issues:Deductive method that leads to a blurry image of possible interpretationsExpensive queries that include UNIONS of selection clausesStudy of the past is intertwined with temporal

imprecision and incompleteness!Need for a more flexible representation of temporal knowledgeAlternative to Allen operatorsSimple and yet plausible knowledgeConjunctive information8Slide9

Temporal Primitives: Imprecision (1/10)

Fuzzy Temporal Algebrafuzzy intervals are confined by inner and outer boundariesInterior: definite set of time points (inner boundaries)the entity is considered as on-goingBoundary: indefinite set of time points (outer boundaries)fuzzy layer – the entity is marked as possibly activeClosure: Interior and Boundary points

9Point-wise Time

Boundary

X

B

Interior X

I

Closure X

C

Fuzzy Interval XSlide10

Temporal Primitives: Imprecision (2/10)

Fuzzy interpretation of basic temporal constraintsendpoint equality – boundary overlapendpoint inequality – total temporal ordering

10A

B

A

BSlide11

Temporal Primitives: Incompleteness (3/10)

Temporal Primitives: an alternative to Allen operatorsEach primitive represents a simple-plausible endpoint constraintTwo operands that refer to interval endpointsOne operator that describes “less than” and “equals” (in time)Based on the included constraint, primitives may describeGeneralized state of temporal topology

Disjunction of possible Allen operatorsSpecific temporal associationParticular Allen operatorLet A and B be two fuzzy intervals we propose seven basic primitives based on equality (=) and proper inequality (<)11Slide12

Temporal Primitives: Basic Primitives (4/10)

A starts before the start of B (As < Bs){before OR meets OR overlaps OR includes OR finished-by}A starts before the end of

B (As < Be){before OR meets OR overlaps OR starts OR started-by OR includes OR during OR finishes OR finished-by OR overlapped-by OR equals}A ends before the start of B (Ae < Bs){before}A ends before the end of

B (Ae < Be){before OR meets OR overlaps OR starts OR during}A starts at the start of B (As = Bs){starts OR started-by OR equals}A ends at

the start of

B (

Ae

=

Bs

)

{meets}

A

ends at

the

end of

B (

Ae

=

Be){finishes OR finished-by OR equals}

12Slide13

Temporal Primitives: Negative Evidence

(5/10)Cases of negative evidence lead to generalized relationsExample: exclusion  inability of coexistenceAn activity cannot start after another instance The former must start before

or at the end of the latter activitySuch cases cannot be described by single basic primitivesNeed for generalized operators – improper inequalityLess or equal to (≤) We introduce four generalized primitives based on improper inequalityForm combinations of basic primitivesGroup expressiveness of comprising temporal constraints

13Slide14

Temporal Primitives: Generalized Primitives (6/10)

A starts before or at the start of B (As ≤ Bs){before OR meets OR overlaps OR starts OR started-by OR includes OR

finished-by OR equals}A starts before or at the end of B (As ≤ Be){before OR meets OR met-by OR overlaps OR overlapped-by OR starts OR started-by OR includes OR during OR finishes OR finished-by OR equals}A ends before or at the start B (Ae ≤

Bs){before OR meets}A ends before or at the end of B (Ae ≤ Be){before OR meets OR overlaps OR starts OR during OR finishes OR finished-by OR equals}

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Temporal Primitives: Visualization (7/10)

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Temporal Primitives: Expressiveness (8/10)

Temporal Primitives conform to principlesCompleteness & minimalityEvery temporal association can be described by exactly one Temporal PrimitiveISA Hierarchical SubsumptionPrimitives with stronger interpretations subsume weaker ones

Upper levels refer to generalized temporal topologiesLower levels describe more strict temporal scenarioAllen Alternative RepresentationAllen operators can be expressed using primitivesEither single or conjunctive sets of temporal information16Slide17

Temporal Primitives: ISA Hierarchy (9/10)

17Slide18

Temporal Primitives: Allen Operators (10/10)

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Allen operatorTemporal PrimitivesA before B

A “ends before the start of” BA meets B

A “ends at the start of” B

A overlaps B

A “starts before the start of” B &

B “starts before the end of” A &

A “ends before the end of” B

A starts B

A “starts at the start of” B &

A “ends before the end of” B

A during B

B “starts before the start of” A &

A “ends before the end of” B

A finishes B

B “starts before the start of” A &

A “ends at the end of” B

A equals B

A “starts at the start of” B &

A “ends at the end of” BSlide19

Conclusion

We propose an alternative to Allen operators: Temporal PrimitivesBased on simple Temporal ConstraintDescribe every possible scenario of Temporal AssociationGeneralizedSpecificConforms to the monotonic knowledge gain Generalized scenarios expressed as conjunctive set of primitivesImproves query execution time, excluding UNION of selections

Deal with temporal imprecisionadapts the fuzzy interval model interpretationIntroduce an ISA Hierarchy between the comprising primitivesSubsume expressive power – useful on knowledge refinement 19Slide20

Contact info

Manos Papadakis, Martin DoerrFORTH - Institute of Computer Science, Greece{mpapad, martin}@ics.forth.gr

20Slide21

Questions

21“It is free,

but it's priceless.You can't own it, but you can use it. You can't keep it,

but you can spend it. Once you've lost it you can never get it back.”

Thank you