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An inference program for RDF Master thesis by G.Naudts Open University of the Netherlands Agfa Standards Case study 3 Research questions 1) Haskell spec of RDF inference program 2) Soundness and completeness 3) What logics? 4)

  1. An inference program for RDF Master thesis by G.Naudts Open University of the Netherlands Agfa

  2. Standards

  3. Case study 3

  4. Research questions 1) Haskell spec of RDF inference program 2) Soundness and completeness 3) What logics? 4) optimization 5) inconsistency

  5. RDF / DEMO • Database: Regels: child(X, Y), child(Y, Z) :> grandparent(Z, X). grandparent(Z, X), gender(Z, female) :> grandmother(Z, X). Feiten: child(christine, elza). child(wim, christine). gender(elza, female). • Query: grandmother(Z, X).

  6. WWW aspects • subqueries • closed / open world • verifiability / trust -> origin • inconsistencies

  7. Implementation

  8. Inference engine for RDF • Two versions: 1) Classic structure, well tested 2) Better adapted to the semantic web

  9. Search Tree / DEMO

  10. Finite State Machine

  11. Open World Consequences • An open set has no borders • An (open?) set has no complement • An element belongs to set A or set B or not known (no law of excluded middle) • There is no universal quantifier for open sets

  12. Research questions 1) Haskell spec of RDF inference program 2) Soundness and completeness 3) What logics? 4) optimization 5) inconsistency

  13. Graph syntax of RDF

  14. Graph theory

  15. Research questions 1) Haskell spec of RDF inference program 2) Soundness and completeness 3) What logics? 4) optimization 5) inconsistency

  16. Logic • Constructive logic cfr. Escher - architect • Each triple in a proof must exist • Verifiability

  20. RDF Graph • URI:http://www.daml.org/2001/01/gedcom/ gedcom# • gd:sun(def:Frank,def:Christine).

  21. Research questions 1) Haskell spec of RDF inference program 2) Soundness and completeness 3) What logics? 4) optimization 5) inconsistency

  22. Optimization / DEMO • Question: grandmother(Z, X) • Solution: fact -> rule -> …. -> rule -> solution = grandmother(elza,wim) • Specific rule: t1, t2, t3, .., tn --> grandmother(Z,X) • child(X,Y), child(Y,Z), gender(Z, female):> grandmother(Z,X). • Other

  23. Research questions 1) Haskell spec of RDF inference program 2) Soundness and completeness 3) What logics? 4) optimization 5) inconsistency

  24. Inconsistencies • Importance of selected logic • No Ex Contradictione Quodlibet • Trust system • Wait and see

  25. Research questions 1) Haskell spec of RDF inference program 2) Soundness and completeness 3) What logics? 4) optimization 5) inconsistency

  26. Case study 26

  28. Questions?

  29. DEMO 1 start Enter command (? for help): ? h : help ? : help q : exit s : perform a single inference step g : go; stop working interactively m : menu e : execute menu item qe : enter a query p : print the graphs

  30. DEMO 2 m&&&& You entered:m&&&&& Please, try again. m Type the command e.g. "e pro11." pro11 authentication example pro21 flight simulation pro31 subClassOf example pro41 demo example pro51 gedcom Enter "e item".

  31. DEMO 3 Enter "e item". e pro41 RDFProlog version 2.0 Reading files ... Enter command (? for help): s step: goal: grandmother(_1?Z,_1?X)./10 goallist: grandmother(_1?Z,_1?X)./10 substitution: [] history:

  32. DEMO 4 s step: goal: grandparent(1$_$_2?Z,1$_$_2?X)./2 goallist: grandparent(1$_$_2?Z,1$_$_2?X)./2 gender(1$_$_2?Z,female)./2 substitution: [(_1?Z,1$_$_2?Z)(_1?X,1$_$_2?X)] history: (grandparent(1$_$_2?Z,1$_$_2?X),gender(1$_$_2?Z,female) :> grandmother(1$_$_2?Z,1$_$_2?X)./2,grandmother(_1?Z,_1?X)./10)

  33. DEMO 5 s step: goal: child(2$_$_1?X,2$_$_1?Y)./2 goallist: child(2$_$_1?X,2$_$_1?Y)./2 child(2$_$_1?Y,2$_$_1?Z)./2 gender(1$_$_2?Z,female)./2 substitution: [(_1?Z,1$_$_2?Z)(_1?X,1$_$_2?X)(1$_$_2?Z,2$_$_1?Z)(1$_$_2?X,2$_$_1?X)] history: (child(2$_$_1?X,2$_$_1?Y),child(2$_$_1?Y,2$_$_1?Z) :> grandparent(2$_$_1?Z,2$_$_1?X)./2,grandparent(1$_$_2?Z,1$_$_2?X)./2) (grandparent(1$_$_2?Z,1$_$_2?X),gender(1$_$_2?Z,female) :> grandmother(1$_$_2?Z,1$_$_2?X)./2,grandmother(_1?Z,_1?X)./10)

  34. DEMO 6 s step: goal: /0 goallist: /0 child(2$_$_1?Y,2$_$_1?Z)./2 gender(1$_$_2?Z,female)./2 substitution: [(_1?Z,1$_$_2?Z)(_1?X,1$_$_2?X)(1$_$_2?Z,2$_$_1?Z)(1$_$_2?X,2$_$_1?X)(2$_$_1?X,christine)(2 $_$_1?Y,elza)] history: (child(christine,elza)./2,child(2$_$_1?X,2$_$_1?Y)./2) (child(2$_$_1?X,2$_$_1?Y),child(2$_$_1?Y,2$_$_1?Z) :> grandparent(2$_$_1?Z,2$_$_1?X)./2,grandparent(1$_$_2?Z,1$_$_2?X)./2) (grandparent(1$_$_2?Z,1$_$_2?X),gender(1$_$_2?Z,female) :> grandmother(1$_$_2?Z,1$_$_2?X)./2,grandmother(_1?Z,_1?X)./10)

  35. DEMO 7 s step: goal: child(2$_$_1?Y,2$_$_1?Z)./2 goallist: child(2$_$_1?Y,2$_$_1?Z)./2 gender(1$_$_2?Z,female)./2 substitution: [(_1?Z,1$_$_2?Z)(_1?X,1$_$_2?X)(1$_$_2?Z,2$_$_1?Z)(1$_$_2?X,2$_$_1?X)(2$_$_1?X,christine)(2 $_$_1?Y,elza)] history: (child(christine,elza)./2,child(2$_$_1?X,2$_$_1?Y)./2) (child(2$_$_1?X,2$_$_1?Y),child(2$_$_1?Y,2$_$_1?Z) :> grandparent(2$_$_1?Z,2$_$_1?X)./2,grandparent(1$_$_2?Z,1$_$_2?X)./2) (grandparent(1$_$_2?Z,1$_$_2?X),gender(1$_$_2?Z,female) :> grandmother(1$_$_2?Z,1$_$_2?X)./2,grandmother(_1?Z,_1?X)./10)

  36. DEMO 8 s **** No unification; path aborted. **** s **** Backtrack done. **** s

  37. DEMO 9 s step: goal: /0 goallist: /0 child(2$_$_1?Y,2$_$_1?Z)./2 gender(1$_$_2?Z,female)./2 substitution: [(_1?Z,1$_$_2?Z)(_1?X,1$_$_2?X)(1$_$_2?Z,2$_$_1?Z)(1$_$_2?X,2$_$_1?X)(2$_$_1?X,wim)(2$_$_ 1?Y,christine)] history: (child(wim,christine)./2,child(2$_$_1?X,2$_$_1?Y)./2) (child(2$_$_1?X,2$_$_1?Y),child(2$_$_1?Y,2$_$_1?Z) :> grandparent(2$_$_1?Z,2$_$_1?X)./2,grandparent(1$_$_2?Z,1$_$_2?X)./2) (grandparent(1$_$_2?Z,1$_$_2?X),gender(1$_$_2?Z,female) :> grandmother(1$_$_2?Z,1$_$_2?X)./2,grandmother(_1?Z,_1?X)./10)

  38. DEMO 10 s step: goal: child(2$_$_1?Y,2$_$_1?Z)./2 goallist: child(2$_$_1?Y,2$_$_1?Z)./2 gender(1$_$_2?Z,female)./2 substitution: [(_1?Z,1$_$_2?Z)(_1?X,1$_$_2?X)(1$_$_2?Z,2$_$_1?Z)(1$_$_2?X,2$_$_1?X)(2$_$_1?X,wim)(2$_$_ 1?Y,christine)] history: (child(wim,christine)./2,child(2$_$_1?X,2$_$_1?Y)./2) (child(2$_$_1?X,2$_$_1?Y),child(2$_$_1?Y,2$_$_1?Z) :> grandparent(2$_$_1?Z,2$_$_1?X)./2,grandparent(1$_$_2?Z,1$_$_2?X)./2) (grandparent(1$_$_2?Z,1$_$_2?X),gender(1$_$_2?Z,female) :> grandmother(1$_$_2?Z,1$_$_2?X)./2,grandmother(_1?Z,_1?X)./10)

  39. DEMO 11 s step: goal: /0 goallist: /0 gender(1$_$_2?Z,female)./2 substitution: [(_1?Z,1$_$_2?Z)(_1?X,1$_$_2?X)(1$_$_2?Z,2$_$_1?Z)(1$_$_2?X,2$_$_1?X)(2$_$_1?X,wim)(2$_$_ 1?Y,christine)(2$_$_1?Z,elza)] history: (child(christine,elza)./2,child(christine,2$_$_1?Z)./2) (child(wim,christine)./2,child(2$_$_1?X,2$_$_1?Y)./2) (child(2$_$_1?X,2$_$_1?Y),child(2$_$_1?Y,2$_$_1?Z) :> grandparent(2$_$_1?Z,2$_$_1?X)./2,grandparent(1$_$_2?Z,1$_$_2?X)./2) (grandparent(1$_$_2?Z,1$_$_2?X),gender(1$_$_2?Z,female) :> grandmother(1$_$_2?Z,1$_$_2?X)./2,grandmother(_1?Z,_1?X)./10)

  40. DEMO 12 s step: goal: gender(1$_$_2?Z,female)./2 goallist: gender(1$_$_2?Z,female)./2 substitution: [(_1?Z,1$_$_2?Z)(_1?X,1$_$_2?X)(1$_$_2?Z,2$_$_1?Z)(1$_$_2?X,2$_$_1?X)(2$_$_1?X,wim)(2$_$_ 1?Y,christine)(2$_$_1?Z,elza)] history: (child(christine,elza)./2,child(christine,2$_$_1?Z)./2) (child(wim,christine)./2,child(2$_$_1?X,2$_$_1?Y)./2) (child(2$_$_1?X,2$_$_1?Y),child(2$_$_1?Y,2$_$_1?Z) :> grandparent(2$_$_1?Z,2$_$_1?X)./2,grandparent(1$_$_2?Z,1$_$_2?X)./2) (grandparent(1$_$_2?Z,1$_$_2?X),gender(1$_$_2?Z,female) :> grandmother(1$_$_2?Z,1$_$_2?X)./2,grandmother(_1?Z,_1?X)./10)

  41. DEMO 13 s step: goal: /0 goallist: /0 substitution: [(_1?Z,1$_$_2?Z)(_1?X,1$_$_2?X)(1$_$_2?Z,2$_$_1?Z)(1$_$_2?X,2$_$_1?X)(2$_$_1?X,wim)(2$_$_ 1?Y,christine)(2$_$_1?Z,elza)] history: (gender(elza,female)./2,gender(elza,female)./2) (child(christine,elza)./2,child(christine,2$_$_1?Z)./2) (child(wim,christine)./2,child(2$_$_1?X,2$_$_1?Y)./2) (child(2$_$_1?X,2$_$_1?Y),child(2$_$_1?Y,2$_$_1?Z) :> grandparent(2$_$_1?Z,2$_$_1?X)./2,grandparent(1$_$_2?Z,1$_$_2?X)./2) (grandparent(1$_$_2?Z,1$_$_2?X),gender(1$_$_2?Z,female) :> grandmother(1$_$_2?Z,1$_$_2?X)./2,grandmother(_1?Z,_1?X)./10)

  42. DEMO 14 solution: Solution: Substitution: [(_1?Z,1$_$_2?Z)(_1?X,1$_$_2?X)(1$_$_2?Z,2$_$_1?Z)(1$_$_2?X,2$_$_1?X)(2$_$_1?X,wim)(2$_$_ 1?Y,christine)(2$_$_1?Z,elza)] Proof: (gender(elza,female)./2,gender(elza,female)./2) (child(christine,elza)./2,child(christine,elza)./2) (child(wim,christine)./2,child(wim,christine)./2) (child(wim,christine),child(christine,elza) :> grandparent(elza,wim)./2,grandparent(elza,wim)./2) (grandparent(elza,wim),gender(elza,female) :> grandmother(elza,wim)./2,grandmother(elza,wim)./10) General rule: "gender(X2,female),child(X1,X2),child(X3,X1) :> grandmother(X2,X3)."

  43. Variable numbering 1 Enter "e item". e pro41 RDFProlog version 2.0 Reading files ... Enter command (? for help): s step: goal: grandmother(_1?Z,_1?X)./10 goallist: grandmother(_1?Z,_1?X)./10 substitution: [] history:

  44. Variable numbering 2 s step: goal: grandparent(1$_$_2?Z,1$_$_2?X)./2 goallist: grandparent(1$_$_2?Z,1$_$_2?X)./2 gender(1$_$_2?Z,female)./2 substitution: [(_1?Z,1$_$_2?Z)(_1?X,1$_$_2?X)] history: (grandparent(1$_$_2?Z,1$_$_2?X),gender(1$_$_2?Z,female) :> grandmother(1$_$_2?Z,1$_$_2?X)./2,grandmother(_1?Z,_1?X)./10)

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