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The Semantics of Partial Model Transformations

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The Semantics of Partial Model Transformations

  1. 1. TheSemantics ofPartial ModelTransforma- tions M.Famelis, R.Salay, M.Chechik, The Semantics of Partial ModelIntroductionPartial Models TransformationsTransformingPartial ModelsLifted Michalis Famelis, Rick Salay, and Marsha ChechikTransformSemantics University of TorontoCheckingLifted RulesConclusion June 3rd, 2012, Models in Software Engineering Workshop at ICSE 1 / 27
  2. 2. TheSemantics ofPartial ModelTransforma- Introduction: Uncertainty tions M.Famelis, R.Salay, M.Chechik, Uncertainty: pervasive in SEIntroductionPartial Models Models with uncertainty:TransformingPartial Models – Represent choice among many possibilitiesLifted – Can be refined to many different classical modelsTransformSemanticsCheckingLifted Rules Our goal:Conclusion Handle models with uncertainty in MDE without having to remove uncertainty. In this talk: Transformations of models with uncertainty 2 / 27
  3. 3. TheSemantics ofPartial ModelTransforma- Introduction: Transformations tions M.Famelis, R.Salay, M.Chechik, Existing model (graph) transformations:IntroductionPartial Models – Unambiguous model is assumed as input.TransformingPartial ModelsLifted – When model contains uncertainty:TransformSemantics • either first remove uncertaintyCheckingLifted Rules – Premature commitment.Conclusion – Reduced quality. • or transform all alternatives. – Hard to maintain. 3 / 27
  4. 4. TheSemantics ofPartial ModelTransforma- Motivating Example tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 4 / 27
  5. 5. TheSemantics ofPartial ModelTransforma- Motivating Example tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 4 / 27
  6. 6. TheSemantics ofPartial ModelTransforma- Motivating Example tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 4 / 27
  7. 7. TheSemantics ofPartial ModelTransforma- Motivating Example tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 4 / 27
  8. 8. TheSemantics ofPartial ModelTransforma- Motivating Example tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 4 / 27
  9. 9. 1 Introduction2 Partial Models3 Transforming Partial Models4 “Lifted” Transformation Semantics5 Checking Lifted Rules6 Conclusion
  10. 10. TheSemantics ofPartial ModelTransforma- Partial Models tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 6 / 27
  11. 11. TheSemantics ofPartial ModelTransforma- Partial Models tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 6 / 27
  12. 12. TheSemantics ofPartial ModelTransforma- Partial Models tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 6 / 27
  13. 13. TheSemantics ofPartial ModelTransforma- Partial Models tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 6 / 27
  14. 14. TheSemantics ofPartial ModelTransforma- Semantics of Partial Models tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 7 / 27
  15. 15. TheSemantics ofPartial ModelTransforma- Semantics of Partial Models tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 7 / 27
  16. 16. TheSemantics ofPartial ModelTransforma- Semantics of Partial Models tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 7 / 27
  17. 17. TheSemantics ofPartial ModelTransforma- Semantics of Partial Models tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 7 / 27
  18. 18. TheSemantics ofPartial ModelTransforma- Goal of This Work tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 8 / 27
  19. 19. 1 Introduction2 Partial Models3 Transforming Partial Models4 “Lifted” Transformation Semantics5 Checking Lifted Rules6 Conclusion
  20. 20. TheSemantics ofPartial ModelTransforma- Intuition tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 10 / 27
  21. 21. TheSemantics ofPartial ModelTransforma- Intuition tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 10 / 27
  22. 22. TheSemantics ofPartial ModelTransforma- Intuition tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 10 / 27
  23. 23. TheSemantics ofPartial ModelTransforma- Intuition tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 10 / 27
  24. 24. TheSemantics ofPartial ModelTransforma- Intuition tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 10 / 27
  25. 25. TheSemantics ofPartial ModelTransforma- Our approach tions Summarizing the intuition: M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion Applying a transformation to a partial model M 11 / 27
  26. 26. TheSemantics ofPartial ModelTransforma- Our approach tions Summarizing the intuition: M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion Applying a transformation to a partial model M should be the same as if we had created all its concretizations, 11 / 27
  27. 27. TheSemantics ofPartial ModelTransforma- Our approach tions Summarizing the intuition: M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion Applying a transformation to a partial model M should be the same as if we had created all its concretizations, applied the transformation to each separately, 11 / 27
  28. 28. TheSemantics ofPartial ModelTransforma- Our approach tions Summarizing the intuition: M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion Applying a transformation to a partial model M should be the same as if we had created all its concretizations, applied the transformation to each separately, and encoded the result as a partial model. 11 / 27
  29. 29. TheSemantics ofPartial ModelTransforma- Our approach tions Summarizing the intuition: M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsChecking Correctness CriterionLifted RulesConclusion Applying a transformation to a partial model M should be the same as if we had created all its concretizations, applied the transformation to each separately, and encoded the result as a partial model. 11 / 27
  30. 30. TheSemantics ofPartial ModelTransforma- Lifting Transformations tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion Q1: How do we transform M directly to N? Q2: Are the concretizations of N exactly the models n1 . . . nk ? 12 / 27
  31. 31. 1 Introduction2 Partial Models3 Transforming Partial Models4 “Lifted” Transformation Semantics5 Checking Lifted Rules6 Conclusion
  32. 32. TheSemantics ofPartial ModelTransforma- Applying Rules to Partial Models tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion Q1: How do we transform M directly to N? – Lifted semantics of transformations, using logic. Q2: Are the concretizations of N exactly the models n1 . . . nk ? 14 / 27
  33. 33. TheSemantics ofPartial ModelTransforma- Transfer Predicates tions M.Famelis, R.Salay, M.Chechik, R ∗ Represent M =⇒ N as:IntroductionPartial Models ΦN = R(R, M, N) ∧ ΦMTransformingPartial ModelsLiftedTransformSemantics R is a conjunction φ1 ∧ φ2 ∧ ...Checking - One subformula at each application point:Lifted RulesConclusion 15 / 27
  34. 34. TheSemantics ofPartial ModelTransforma- Transfer Predicates tions M.Famelis, R.Salay, M.Chechik, R ∗ Represent M =⇒ N as:IntroductionPartial Models ΦN = R(R, M, N) ∧ ΦMTransformingPartial ModelsLiftedTransformSemantics R is a conjunction φ1 ∧ φ2 ∧ ...Checking - One subformula at each application point:Lifted RulesConclusion 15 / 27
  35. 35. TheSemantics ofPartial ModelTransforma- Transfer Predicates tions M.Famelis, R.Salay, M.Chechik, R ∗ Represent M =⇒ N as:IntroductionPartial Models ΦN = R(R, M, N) ∧ ΦMTransformingPartial ModelsLiftedTransformSemantics R is a conjunction φ1 ∧ φ2 ∧ ...Checking - One subformula at each application point:Lifted RulesConclusion 15 / 27
  36. 36. TheSemantics ofPartial ModelTransforma- Transfer Predicates tions M.Famelis, R.Salay, M.Chechik, R ∗ Represent M =⇒ N as:IntroductionPartial Models ΦN = R(R, M, N) ∧ ΦMTransformingPartial ModelsLiftedTransformSemantics R is a conjunction φ1 ∧ φ2 ∧ ...Checking - One subformula at each application point:Lifted RulesConclusion 15 / 27
  37. 37. TheSemantics ofPartial ModelTransforma- Transfer Predicates tions M.Famelis, R.Salay, M.Chechik, R ∗ Represent M =⇒ N as:IntroductionPartial Models ΦN = R(R, M, N) ∧ ΦMTransformingPartial ModelsLiftedTransformSemantics R is a conjunction φ1 ∧ φ2 ∧ ...Checking - One subformula at each application point:Lifted RulesConclusion 15 / 27
  38. 38. TheSemantics ofPartial ModelTransforma- Transfer Predicates tions M.Famelis, R.Salay, M.Chechik, R ∗ Represent M =⇒ N as:IntroductionPartial Models ΦN = R(R, M, N) ∧ ΦMTransformingPartial ModelsLiftedTransformSemantics R is a conjunction φ1 ∧ φ2 ∧ ...Checking - One subformula at each application point:Lifted RulesConclusion 15 / 27
  39. 39. TheSemantics ofPartial ModelTransforma- Transfer Predicates tions M.Famelis, R.Salay, M.Chechik, R ∗ Represent M =⇒ N as:IntroductionPartial Models ΦN = R(R, M, N) ∧ ΦMTransformingPartial ModelsLiftedTransformSemantics R is a conjunction φ1 ∧ φ2 ∧ ...Checking - One subformula at each application point:Lifted RulesConclusion 15 / 27
  40. 40. TheSemantics ofPartial ModelTransforma- Example 1/2 tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemantics (ΦLHS → ΦRHS ) ∧ (¬ΦLHS → ΦNE )CheckingLifted RulesConclusion • ΦLHS = c ∧ a ∧ ¬g ∧ ¬s • ΦRHS = (c ↔ c) ∧ (a ↔ a) ∧ (g ↔ a) ∧ (s ↔ a) • ΦNE = (x ↔ x) 16 / 27
  41. 41. TheSemantics ofPartial ModelTransforma- Example 2/2 tions M.Famelis, R.Salay, After matching, grounding and simplifying: M.Chechik, R(R, M, N) = (Product ↔ Product) ∧ (Milk ↔ Milk)∧Introduction (A ↔ A) ∧ (B ↔ B) ∧ (C ↔ C )∧Partial Models (D ↔ D) ∧ (E ↔ A) ∧ (F ↔ A)∧Transforming (G ↔ B) ∧ (H ↔ B) ∧ (I ↔ C )∧Partial Models (J ↔ C ) ∧ (K ↔ D) ∧ (L ↔ D)∧Lifted (gen Milk Product ↔ gen Milk Product)TransformSemanticsCheckingLifted RulesConclusion 17 / 27
  42. 42. TheSemantics ofPartial ModelTransforma- Example 2/2 tions M.Famelis, R.Salay, After matching, grounding and simplifying: M.Chechik, R(R, M, N) = (Product ↔ Product) ∧ (Milk ↔ Milk)∧Introduction (A ↔ A) ∧ (B ↔ B) ∧ (C ↔ C )∧Partial Models (D ↔ D) ∧ (E ↔ A) ∧ (F ↔ A)∧Transforming (G ↔ B) ∧ (H ↔ B) ∧ (I ↔ C )∧Partial Models (J ↔ C ) ∧ (K ↔ D) ∧ (L ↔ D)∧Lifted (gen Milk Product ↔ gen Milk Product)TransformSemanticsCheckingLifted RulesConclusion 17 / 27
  43. 43. TheSemantics ofPartial ModelTransforma- Example 2/2 tions M.Famelis, R.Salay, After matching, grounding and simplifying: M.Chechik, R(R, M, N) = (Product ↔ Product) ∧ (Milk ↔ Milk)∧Introduction (A ↔ A) ∧ (B ↔ B) ∧ (C ↔ C )∧Partial Models (D ↔ D) ∧ (E ↔ A) ∧ (F ↔ A)∧Transforming (G ↔ B) ∧ (H ↔ B) ∧ (I ↔ C )∧Partial Models (J ↔ C ) ∧ (K ↔ D) ∧ (L ↔ D)∧Lifted (gen Milk Product ↔ gen Milk Product)TransformSemanticsCheckingLifted RulesConclusion 17 / 27
  44. 44. TheSemantics ofPartial ModelTransforma- Example 2/2 tions M.Famelis, R.Salay, After matching, grounding and simplifying: M.Chechik, R(R, M, N) = (Product ↔ Product) ∧ (Milk ↔ Milk)∧Introduction (A ↔ A) ∧ (B ↔ B) ∧ (C ↔ C )∧Partial Models (D ↔ D) ∧ (E ↔ A) ∧ (F ↔ A)∧Transforming (G ↔ B) ∧ (H ↔ B) ∧ (I ↔ C )∧Partial Models (J ↔ C ) ∧ (K ↔ D) ∧ (L ↔ D)∧Lifted (gen Milk Product ↔ gen Milk Product)TransformSemanticsCheckingLifted RulesConclusion 17 / 27
  45. 45. TheSemantics ofPartial ModelTransforma- Example 2/2 tions M.Famelis, R.Salay, After matching, grounding and simplifying: M.Chechik, R(R, M, N) = (Product ↔ Product) ∧ (Milk ↔ Milk)∧Introduction (A ↔ A) ∧ (B ↔ B) ∧ (C ↔ C )∧Partial Models (D ↔ D) ∧ (E ↔ A) ∧ (F ↔ A)∧Transforming (G ↔ B) ∧ (H ↔ B) ∧ (I ↔ C )∧Partial Models (J ↔ C ) ∧ (K ↔ D) ∧ (L ↔ D)∧Lifted (gen Milk Product ↔ gen Milk Product)TransformSemanticsCheckingLifted RulesConclusion 17 / 27
  46. 46. TheSemantics ofPartial ModelTransforma- Example 2/2 tions M.Famelis, R.Salay, After matching, grounding and simplifying: M.Chechik, R(R, M, N) = (Product ↔ Product) ∧ (Milk ↔ Milk)∧Introduction (A ↔ A) ∧ (B ↔ B) ∧ (C ↔ C )∧Partial Models (D ↔ D) ∧ (E ↔ A) ∧ (F ↔ A)∧Transforming (G ↔ B) ∧ (H ↔ B) ∧ (I ↔ C )∧Partial Models (J ↔ C ) ∧ (K ↔ D) ∧ (L ↔ D)∧Lifted (gen Milk Product ↔ gen Milk Product)TransformSemanticsCheckingLifted RulesConclusion 17 / 27
  47. 47. TheSemantics ofPartial ModelTransforma- Example 2/2 tions M.Famelis, R.Salay, After matching, grounding and simplifying: M.Chechik, R(R, M, N) = (Product ↔ Product) ∧ (Milk ↔ Milk)∧Introduction (A ↔ A) ∧ (B ↔ B) ∧ (C ↔ C )∧Partial Models (D ↔ D) ∧ (E ↔ A) ∧ (F ↔ A)∧Transforming (G ↔ B) ∧ (H ↔ B) ∧ (I ↔ C )∧Partial Models (J ↔ C ) ∧ (K ↔ D) ∧ (L ↔ D)∧Lifted (gen Milk Product ↔ gen Milk Product)TransformSemanticsCheckingLifted RulesConclusion 17 / 27
  48. 48. 1 Introduction2 Partial Models3 Transforming Partial Models4 “Lifted” Transformation Semantics5 Checking Lifted Rules6 Conclusion
  49. 49. TheSemantics ofPartial ModelTransforma- Testing Rule Application tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion Q1: How do we transform M directly to N? Q2: Are the concretizations of N exactly the models n1 . . . nk ? – Check equivalence of encodings using SAT. 19 / 27
  50. 50. TheSemantics ofPartial ModelTransforma- Checking Using a SAT Solver tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 20 / 27
  51. 51. TheSemantics ofPartial ModelTransforma- Checking Using a SAT Solver tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 20 / 27
  52. 52. TheSemantics ofPartial ModelTransforma- Checking Using a SAT Solver tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 20 / 27
  53. 53. TheSemantics ofPartial ModelTransforma- Checking Using a SAT Solver tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 20 / 27
  54. 54. TheSemantics ofPartial ModelTransforma- Checking Using a SAT Solver tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 20 / 27
  55. 55. TheSemantics ofPartial ModelTransforma- Checking Using a SAT Solver tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 20 / 27
  56. 56. TheSemantics ofPartial ModelTransforma- Checking Using a SAT Solver tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 20 / 27
  57. 57. TheSemantics ofPartial ModelTransforma- Checking Example tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 21 / 27
  58. 58. TheSemantics ofPartial ModelTransforma- Checking Example tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 21 / 27
  59. 59. TheSemantics ofPartial ModelTransforma- Checking Example tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 21 / 27
  60. 60. TheSemantics ofPartial ModelTransforma- Checking Example tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 21 / 27
  61. 61. TheSemantics ofPartial ModelTransforma- Checking Example tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion 21 / 27
  62. 62. 1 Introduction2 Partial Models3 Transforming Partial Models4 “Lifted” Transformation Semantics5 Checking Lifted Rules6 Conclusion
  63. 63. TheSemantics ofPartial ModelTransforma- Summary tions M.Famelis, R.Salay, M.Chechik,IntroductionPartial ModelsTransformingPartial ModelsLiftedTransformSemanticsCheckingLifted RulesConclusion Q1: How do we transform M directly to N? – Lifted semantics of transformations, using logic. Q2: Are the concretizations of N exactly the models n1 . . . nk ? – Check equivalence of encodings using SAT. 23 / 27
  64. 64. TheSemantics ofPartial ModelTransforma- Conclusion tions M.Famelis, R.Salay, M.Chechik, Transforming models that contain uncertainty.Introduction • Represent uncertainty using Partial Models.Partial Models • Lift transformation rules from classical to Partial Models.TransformingPartial Models • Check Correctness Criterion for the lifted transformation .LiftedTransformSemantics Next steps:CheckingLifted Rules • Compositionally test Correctness Criterion.Conclusion • Systematically create Transfer Predicates using FOL. • Handle expanding/contracting model vocabularies. • Partial Models as an Adhesive HLR Category? 24 / 27
  65. 65. TheSemantics ofPartial ModelTransforma- Overall Picture tions M.Famelis, R.Salay, M.Chechik, Overall research goal [MoDeVVa’11]:IntroductionPartial Models • Handling uncertainty...Transforming • Partial models: sets of possibilities.Partial Models • Syntactic “partiality” annotations.LiftedTransform • Other kinds of partiality (“MAVO”) [FASE’12].SemanticsCheckingLifted Rules • ...throughout the software lifecycle.Conclusion • Partial models as first-class artifacts. (1) Reasoning [ICSE’12] (2) Refinement [VOLT’12] (3) Transformation 25 / 27
  66. 66. Questions?
  67. 67. TheSemantics ofPartial ModelTransforma- Bibliography I tions M.Famelis, R.Salay, M.Chechik,Introduction M. Famelis, Shoham Ben-David, Marsha Chechik, and Rick Salay.Partial Models “Partial Models: A Position Paper”. In Proceedings of MoDeVVa’11, pages 1–6, 2011.TransformingPartial Models Michalis Famelis, Marsha Chechik, and Rick Salay. “Partial Models: Towards Modeling and Reasoning with Uncertainty”.Lifted In Proceedings of ICSE’12, 2012.TransformSemantics R. Salay, M. Chechik, and J. Gorzny.Checking “Towards a Methodology for Verifying Partial Model Refinements”.Lifted Rules In Proceedings of VOLT’12, 2012.Conclusion R. Salay, M. Famelis, and M. Chechik. “Language Independent Refinement using Partial Modeling”. In Proceedings of FASE’12, 2012. 27 / 27

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