Euripides GM Petrakis Technical university of crete Intelligent systems laboratory Imposing Restrictions Over Temporal Properties in OWL A Rule Based Approach Introduction Temporal Properties are not binary ID: 313729
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Slide1
Sotiris BatsakisEuripides G.M. PetrakisTechnical university of creteIntelligent systems laboratory
Imposing Restrictions Over Temporal Properties in OWL: A Rule Based ApproachSlide2
IntroductionTemporal 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
Technical University of Crete Slide3
MotivationOWL 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
Technical University of Crete Slide4
Temporal Representation (N-ary)
Professor
Course
Professor
Teaching
Course
Interval
t
eaches
Technical University of Crete Slide5
Temporal Representation (4D-fluents)
Professor
Course
Professor
Professor
TimeSlice
Course
Course
Timeslice
Interval
teaches
teaches
timesliceOf
timesliceOf
interval
interval
Technical University of Crete Slide6
Property Restrictions & SemanticsDomains-Ranges are adjustedDomain timesliceOf ProfessorRange timesliceOf CourseProperty Semantics RetainedSymmetric, Equivalent, Reflexive,
Subproperty
Course
TimeSlice
Professor
Timeslice
Course
Professor
Interval
teaches
Technical University of Crete Slide7
Property Restrictions ProblemsCardinality 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).
Course
TimeSlice
Professor
TimeSLice
Course
Professor
Interval
Technical University of Crete Slide8
Imposing Cardinality Restrictions SWRL DL safe rules are appliedDecidability 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
Technical University of Crete Slide9
First Interpretation-entire existence A professor can’t teach more than n different courses in his career: Professor(x) ⋀ (timesliceOf(x1, x) ⋀
…
⋀
timesliceOf
(x
n+1,x)
⋀
teaches(x
1
, y1)
⋀
teaches(xn+1, yn+1) ⋀ timesliceOf
(y1 ,z1)… ⋀ timesliceOf
(yn+1, zn+1) ⋀ Alldifferent(z
1, z2,…, zn+1) ⋀ Course(z1
)… error(x, z1) Rule directly detects inconsistencies for max cardinalityFor min cardinality a similar rule asserts which individuals are related with more than n objects, and a SPARQL query detects individuals without the assertion.
Technical University of Crete Slide10
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(x
1
, y1)
⋀
teaches(xn+1, yn+1) ⋀
timesliceOf(y1 ,z1)… ⋀
hasinterval(x1,w1)… ⋀ hasinterval(x
n+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)
Technical University of Crete Slide11
Temporal ReasoningImplemented in SWRLApplies on interval Allen’s relations (e.g., before, after, overlaps) Based on Path ConsistencyIntersects and composes existing relations until no rules apply or inconsistency is detectedExample CompositionDuring(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 Technical University of Crete Slide12
Additional Property SemanticsFunctional and Inverse functional are handled as at most one cardinality restrictionsAsymmetric: 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.
Technical University of Crete Slide13
Contributions and limitationsContributionsOffer support for property restrictions and semantics over temporal representations in OWLRule based approach that retains decidabilityCompliance with existing standards and tools (OWL, SWRL, Pellet)LimitationsApplies only on named individualsExponential to the number of the cardinality restriction at hand (e.g. at most n rule is exponential to n)
Technical University of Crete Slide14
Future WorkDetecting the maximal decidable description logic that supports temporal cardinality restrictionsOptimize SWRL implementations of OWL reasonersOptimize the rules
Technical University of Crete Slide15
Thank YouQuestions?