Temporal Reasoning for Supporting Temporal Queries in

OWL 2.0

Sotiris Batsakis, Kostas Stravoskoufos Euripides G.M. Petrakis

Technical University Of CreteIntelligent Systems Laboratory

Representing evolution of information in time using OWL

Temporal relations involve at least three arguments◦ OWL represents binary relations

Existing approaches: Temporal RDF, Named Graphs, Reification, Versioning, N-ary, 4D-fluents◦ No qualitative information◦ Limited OWL reasoning support

Querying of temporal information is also a problem

We propose a solution to all these problems based on 4D-fluents and N-ary relations.

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Problem Definition

4D Fluents [Welty & Fikes 2006] Classes TimeSlice, TimeInterval are introduced

Dynamic objects become instances of TimeSlice

Temporal properties of dynamic classes become instances of TimeInterval

A time slice object is created each time a (fluent) property changes

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4-D fluents example

N-ary approach [Noy & Rector 2006] Dynamic Properties are attached to reified objects representing events

Dynamic properties are represented as properties and not as objects of properties as in reification

Event objects ◦Attached to specific static objects◦Connect to Time Intervals

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N-ary and Reification example

Advantages◦Changes affect only related dynamic

objects, not the entire ontology◦Reasoning mechanisms and semantics of

OWL fully supported◦OWL 2.0 compatible

Disadvantages ◦Proliferation of objects

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4-D fluents/N-ary: Comments

Information: Points, intervals Quantitative and Qualitative information Qualitative Allen Relations (e.g., Before,

After) are supported ◦ Qualitative relations connect temporal intervals◦ Intervals with unknown endpoints◦ Interval relations are translated into point

relations (Before, After, Equals)

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Extending 4-D fluents/N-ary

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Allen Temporal Relations

Reasoning Infer new relations from existing ones

◦ Before(x,y) AND Before(y,z) Before(x,z) Problem 1: Reasoning over a mix of qualitative and

quantitative information is a problem◦ Extract qualitative relations from quantitative ones ◦ Reasoning over qualitative information

Problem 2: Assertions may be inconsistent or new assertions may take exponential time to compute

Solution: Restrict to tractable sets decided by polynomial algorithms such as Path Consistency [van Beek & Cohen 1990]

Path Consistency suggests composing and intersecting relations until:◦ A fixed point is reached (no additional inferences

can be made)◦ An empty relation is yielded implying

inconsistent assertions Path Consistency is tractable, sound and

complete for specific sets of temporal relations

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Temporal Reasoning(1/2)

Compositions and intersections of relations are defined and implemented in SWRL:

Before(x,y) AND Equals(y,z) Before(x,z) (Before(x,y) OR Equals(x,y)) AND (After(x,y)

OR Equals(x,y))Equals(x,y)

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Temporal Reasoning (2/2)

SOWL Query Language SPARQL-like query language supporting

temporal operators SELECT ?x, ?y… Where { ?x property ?y… At(date)…} Additional operators are introduced to

SPARQL◦ AT, ALWAYS_AT, SOMETIMES_AT◦ Allen operators

Temporal Operators AT specifies time instants for which fluent

properties hold true ALWAYS_AT, SOMETIMES_AT: Return

intervals that fluent always or sometime holds.

Allen’s operators: BEFORE, AFTER, MEETS, METBY, OVERLAPS, OVERLAPPEDBY, DURING, CONTAINS, STARTS, STARTEDBY, ENDS, ENDEDBY and EQUALS

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SELECT ?x,?y WHERE {?x has-employee ?y AT “3-5-2007” }

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AT Temporal Operator Example

SELECT ?x,?y WHERE {?x has-employee ?y BEFORE company1 has-employee ?y }

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Allen Operator Example

We extended 4D-fluents and N-ary relations for representing evolution of qualitative (in adition to quantitative) temporal information in OWL ontologies

Offers temporal reasoning support over qualitative and quantitative relations

Querying support by extending SPARQL with additional temporal operators

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Conclusion

Extending representation-query language for spatial information [Batsakis & Petrakis, RuleML 2011]

Optimizations for large scale applications

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Future Work

Thank you

Questions ?