1. Approximate Inference Techniques and Their Applications to the Semantic Web Perry Groot IPA Fall days, 26 November 2004

2. IPA 20042 Perry Groot Motivation behind Approximation Reducing complexity  Reasoning under time pressure  Reasoning with other limited resources Reduce/increase number of solutions Reasoning that is not “perfect” but “good enough”

3. IPA 20043 Perry Groot Anytime Reasoning Computation time Quality output

4. IPA 20044 Perry Groot Types of Approximation Numerical Logical  Soundness  Completeness

5. IPA 20045 Perry Groot The purpose of this review is to remind operators of the existence of the Operations Manual Bulletin 80-1, which provides information regarding flight operations with low fuel quantities, and to provide supplementary information regarding main tank boost pump low pressure indications.747 FUEL PUMP LOW PRESSURE INDICATIONS When operating 747 airplanes with low fuel quantities for short Shared Hydraulics Repository (SHR) (pump has (superclasses (mechanical-device)) (text-def (“A device for …”)) (thesaurus-term (|Pumps|))) (every pump has (physical-parts (piston, valve, cylinder)) (device-purpose (Pumping-A-Fluid))) Hey, I know this ontology, so now I know something about Fuel Pump. What the heck is a Fuel Pump? Semantic Markup has (superclasses SHR: pump)) ( fuel-pump FUEL PUMP Machine Processible Semantics © Mike Ushold

6. IPA 20046 Perry Groot KB Architecture TBox ABox Reasoning Description Language Query

7. IPA 20047 Perry Groot C A A C D R.C R. C A A C D R.C R.C C A A C C D C D R.C R.C Description Logics

8. IPA 20048 Perry Groot WomanPerson Female ManPerson Woman MotherWoman hasChild.Person Mother(MARY), hasChild(MARY, PETER) TBox + ABox

9. IPA 20049 Perry Groot Reasoning Satisfiability Subsumption Classification Concept/Instance retrieval Instance realization

10. IPA 200410 Perry Groot Application: Individual Retrieval (I) Retrieval Process 1. Classify Query Q 2. 3.   Q

11. IPA 200411 Perry Groot Application: Individual Retrieval (II) Retrieval Process 1. Classify Query Q 2. Select Instances from subsumed classes 3. Q

12. IPA 200412 Perry Groot Application: Individual Retrieval (III) Retrieval Process 1. Classify Query Q 2. Select Instances from subsumed classes 3. Realize instances from direct parents, if they belong to Q Q

13. IPA 200413 Perry Groot KB Architecture TBox ABox Reasoning Description Language Query Language Weakening Approximate Deduction Knowledge Compilation

14. IPA 200414 Perry Groot Approximate Entailment Two approximate entailment operators [Schaerf & Cadoli, 1995]  S-1-Entailment: Complete but unsound  S-3-Entailment: Sound but incomplete Propositional Theory  Underlying finite language L  Subset S of L used as parameter

15. IPA 200415 Perry Groot Approximate Entailment S-1-entailment: interpret everything outside of S as false S-3-entailment: interpret everything outside of S as true (or normal) S L x¬x¬x S1 S3 0/01/1 1/0 0/1

16. IPA 200416 Perry Groot Approximate Entailment S1S1 L S2S2 L S3S3 L S n = L Anytime behaviour when S i is increased Previous steps can be reused

17. IPA 200417 Perry Groot Approximate Entailment Semantically well-founded Computationally attractive Improvable Dual Flexible

18. IPA 200418 Perry Groot Approximate Entailment Unclear effect Parameter S is crucial for approximate behaviour Almost no quantitative analysis

19. IPA 200419 Perry Groot Approximation for DLs Elements: Concept expressions Task: Satisfiability checking Approximation: “Simpler” concept expr.  Stronger (more specific)  Weaker (less specific) - Unsatisfiability of D implies unsatisfiability of C - Satisfiability of C implies satisfiability of D

20. IPA 200420 Perry Groot Approximation for DLs Depth of subconcept D: number of universal quantifiers that have D in its scope. Depth: 0Depth: 1Depth: 2

21. IPA 200421 Perry Groot Approximation for DLs C i : Replace every existentially quantified subconcept D of depth greater or equal than i by. C = C 0 = C 1 =

22. IPA 200422 Perry Groot Approximating Subsumption Level := 0 Compute Level := Level+1 Unsatisfiable? Max Level? t f ft TRUE FALSE

23. Thank you for your attention