SOTIRIS BATSAKISEURIPIDES G.M. PETRAKIS

TECHNICAL UNIVERSITY OF CRETEINTELLIGENT SYSTEMS LABORATORY

Imposing Restrictions Over Temporal Properties in OWL: A

Rule Based Approach

Introduction

Temporal Properties are not binaryRepresentation in OWL involves additional

objectsCardinality restrictions over temporal

properties cannot apply directlyA rule based approach is proposedTwo different interpretations of restrictions

over temporal properties

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Motivation

OWL property semantics Domains, Ranges, Subproperty, Equivalence,

Symmetric, Assymetric, Functional, Inverse Functional, Reflexive, Irreflexive, Disjoint, Transitive

OWL property restrictions All values from, Some Values From, Intersection ,

Union, Min Cardinallity, Max Cardinality, Exact Cardinality

Representation of temporal properties affects their semantics and restrictions

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Temporal Representation (N-ary)

Professor Course

Professor Teaching Course

Interval

teaches

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Temporal Representation (4D-fluents)

Professor Course

Professor

ProfessorTimeSlice

Course

CourseTimeslice

Interval

teaches

teachestimesliceOf timesliceOf

interval interval

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Property Restrictions & Semantics

Domains-Ranges are adjusted Domain timesliceOf Professor Range timesliceOf Course

Property Semantics Retained Symmetric, Equivalent, Reflexive, Subproperty

CourseTimeSlice

ProfessorTimeslice

CourseProfessor

Interval

teaches

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Property Restrictions Problems

Cardinality Restrictions (min, max, exact) Imposing cardinality on “new” property affects

meaning (many timeslices, perhaps for overlapping intervals exist)

Imposing restriction on property chains is not supported because it leads to undecidability (Horrocks et.al. “Practical Reasoning for Expressive Description Logics” , 1999).

CourseTimeSlice

ProfessorTimeSLice

CourseProfessor

Interval

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Imposing Cardinality Restrictions

SWRL DL safe rules are applied Decidability is retained, supported by reasoners (e.g.

Pellet) Rules apply only on named individuals (ABox) and not

class descriptions (TBox) into the ontology Open world assumption is adopted, thus min

cardinality restrictions cannot be directly applied. Restrictions have two different interpretations

On the entire existence of the object On every specific temporal interval

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First Interpretation-entire existence

A professor can’t teach more than n different courses in his career: Professor(x) ⋀ (timesliceOf(x1, x) ⋀ … ⋀

timesliceOf(xn+1,x) ⋀ teaches(x1, y1) ⋀ teaches(xn+1, yn+1) ⋀ timesliceOf(y1 ,z1)… ⋀ timesliceOf(yn+1, zn+1) ⋀ Alldifferent(z1, z2,…, zn+1) ⋀ Course(z1)… error(x, z1)

Rule directly detects inconsistencies for max cardinality For min cardinality a similar rule asserts which

individuals are related with more than n objects, and a SPARQL query detects individuals without the assertion.

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Second Interpretation-every interval

A professor can’t teach more than n different courses simultaneously : Professor(x) ⋀ (timesliceOf(x1, x) ⋀ … ⋀ timesliceOf(xn+1,x) ⋀ teaches(x1, y1) ⋀ teaches(xn+1, yn+1) ⋀ timesliceOf(y1 ,z1)… ⋀ hasinterval(x1,w1)… ⋀ hasinterval(xn+1,wn+1) ⋀

timesliceOf(yn+1, zn+1) ⋀ Alldifferent(z1, z2,…, zn+1) ⋀ pairwiseoverlapping(w1, …wn+1) ⋀ Course(z1)… error(x, z1)

Rule directly detects inconsistencies for max cardinality Detecting overlapping intervals is achieved using temporal

reasoning rules (S. Batsakis and E.G.M. Petrakis. “SOWL: A Framework for Handling Spatio-Temporal Information in OWL 2.0”, RuleML 2011)

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Temporal Reasoning

Implemented in SWRLApplies on interval Allen’s relations (e.g., before,

after, overlaps) Based on Path Consistency

Intersects and composes existing relations until no rules apply or inconsistency is detected Example Composition

During(x,y) ⋀ Meets(y,z) Before(x,z) Example Intersection

(Before(x,y) OR Meets(x,y)) ⋀ Meets(x,y)Meets(x,y)Tractable Sound and Complete for specific sets of

temporal relations

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Additional Property Semantics

Functional and Inverse functional are handled as at most one cardinality restrictions

Asymmetric: This is handled as a cardinality restriction, where the same property cannot hold for interchanged subjects and objects for timeslices with overlapping intervals.

Irreflexive: This is handled as a cardinality restriction; two timeslices of an object cannot be related with the property.

Transitive: Fluent properties are declared transitive since related timeslices must have equal intervals (by the definition of the 4D-fluent model) and for these intervals transitivity is applied.

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Contributions and limitations

Contributions Offer support for property restrictions and semantics

over temporal representations in OWL Rule based approach that retains decidability Compliance with existing standards and tools (OWL,

SWRL, Pellet)Limitations

Applies only on named individuals Exponential to the number of the cardinality

restriction at hand (e.g. at most n rule is exponential to n)

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Future Work

Detecting the maximal decidable description logic that supports temporal cardinality restrictions

Optimize SWRL implementations of OWL reasoners

Optimize the rules

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Thank You

QUESTIONS?