1. SOTIRIS BATSAKIS EURIPIDES G.M. PETRAKIS TECHNICAL UNIVERSITY OF CRETE INTELLIGENT SYSTEMS LABORATORY Imposing Restrictions Over Temporal Properties in OWL: A Rule Based Approach

2. Introduction Temporal Properties are not binary Representation in OWL involves additional objects Cardinality restrictions over temporal properties cannot apply directly A rule based approach is proposed Two different interpretations of restrictions over temporal properties Technical University of Crete

3. 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 Technical University of Crete

4. Temporal Representation (N-ary) ProfessorCourse ProfessorTeaching Course Interval teaches Technical University of Crete

5. Temporal Representation (4D-fluents) ProfessorCourse Professor TimeSlice Course Timeslice Interval teaches timesliceOf interval Technical University of Crete

6. Property Restrictions & Semantics Domains-Ranges are adjusted Domain timesliceOf Professor Range timesliceOf Course Property Semantics Retained Symmetric, Equivalent, Reflexive, Subproperty Course TimeSlice Professor Timeslice Course Professor Interval teaches Technical University of Crete

7. 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). Course TimeSlice Professor TimeSLice Course Professor Interval Technical University of Crete

8. 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 Technical University of Crete

9. First Interpretation-entire existence A professor cant teach more than n different courses in his career: Professor(x) (timesliceOf(x 1, x) … timesliceOf(x n+1,x) teaches(x 1, y1) teaches(x n+1, y n+1 ) timesliceOf(y 1,z 1 )… timesliceOf(y n+1, z n+1 ) Alldifferent(z 1, z 2,…, z n+1 ) Course(z 1 )… error(x, z 1 ) 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. Technical University of Crete

10. Second Interpretation-every interval A professor cant teach more than n different courses simultaneously : Professor(x) (timesliceOf(x 1, x) … timesliceOf(x n+1,x) teaches(x 1, y1) teaches(x n+1, y n+1 ) timesliceOf(y 1,z 1 )… hasinterval(x 1,w 1 )… hasinterval(x n+1,w n+1 ) timesliceOf(y n+1, z n+1 ) Alldifferent(z 1, z 2,…, z n+1 ) pairwiseoverlapping(w 1, …w n+1 ) Course(z 1 )… error(x, z 1 ) 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

11. Temporal Reasoning Implemented in SWRL Applies on interval Allens 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 Technical University of Crete

12. 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. Technical University of Crete

13. 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) Technical University of Crete

14. Future Work Detecting the maximal decidable description logic that supports temporal cardinality restrictions Optimize SWRL implementations of OWL reasoners Optimize the rules Technical University of Crete

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