Scalable Semantic Annotation using Lattice-based Ontologies

Transcription

1 Scalable Semantic Annotation using Lattice-based Ontologies Ben Lickly 1 Man-Kit Leung 1 Thomas Mandl 2 Edward A. Lee 1 Elizabeth Latronico 2 Charles Shelton 2 Stavros Tripakis 1 1 University of California, Berkeley 2 Bosch Research, LLC October 7, 2009 Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 1/15

2 Outline 1 Introduction Actor-oriented Models Motivation 2 Example Car-tracking Demo 3 Problem Formulation Theory Design 4 Conclusion Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 2/15

3 Introduction Actor-oriented Models Actor-oriented Models Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 3/15

4 Introduction Motivation What Questions Do We Want to Ask? Types Units Dimensions Constant / Non-constant Product configuration Code ownership Code Maturity Level... Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 4/15

5 Introduction Motivation What Questions Do We Want to Ask? Types Units Dimensions Constant / Non-constant Product configuration Code ownership Code Maturity Level... Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 4/15

6 Introduction Motivation Approach Ptolemy II: Our modeling and simulation environment Pthomas: A framework on top of Ptolemy II, allowing analysis of these semantic properties Types of analysis: Inference Validity Checking Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 5/15

7 a Example Calculus Review time acceleration(t) dt = speed(t) speed time Position vs. Time speed(t) dt = position(t) position time Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 6/15

8 Example Car-tracking Demo Demo Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 7/15

9 Example Car-tracking Demo Demo Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 7/15

10 Example Car-tracking Demo Demo Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 7/15

11 Example Car-tracking Demo Demo Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 7/15

12 Example Car-tracking Demo Demo Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 7/15

13 Example Car-tracking Demo Demo Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 7/15

14 Example Car-tracking Demo Demo Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 7/15

15 Example Car-tracking Demo Demo Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 7/15

16 Problem Formulation Theory Background Lattice A partially ordered set in which every pair of elements has both a least upper bound and a greatest lower bound. Monotonic Function A function f for which x 1 x 2 = f ( x 1 ) f ( x 2 ) Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 8/15

17 Problem Formulation Theory Problem Statement Given: Lattice: P (1) Constants & Variables: p 1, p 2, P (2) Constraints of the form: f (p 1, p 2, ) p n (f monotonic) (3) is there a satisfying assignment to variables? Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 9/15

18 Problem Formulation Theory Problem Statement Given: Lattice: P Constants & Variables: p 1, p 2, P (2) Constraints of the form: f (p 1, p 2, ) p n (f monotonic) (3) is there a satisfying assignment to variables? This problem has a linear time algorithm! (Rehof and Mogensen, 1996) (1) Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 9/15

19 Problem Formulation Design Writing Actor Constraints Undef. Speed f I (p y ) = Accel. Unitless Error Component Elements Constraints Integrator input x, output y if p y = Undef. if p y = Pos. if p y = Speed if p y = Time otherwise f I (p y ) p x f O (p x ) p y Undef. Pos. f O (p x ) = Speed Time Error if p x = Undef. if p x = Speed if p x = Accel. if p x = Unitless otherwise Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 10/15

20 Problem Formulation Design User interface Problem: C M 1 Default Constraints Set globally by the property solver (actors, connections, etc.) 2 Actor-specific Constraints Uses an adapter pattern for actors 3 Instance-specific Constraints Specified through model annotations Generality Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 11/15

21 Conclusion Related work Constraint Satisfiability (Rehof and Mogensen) Linear time algorithm for monotone function problem Hindley-Milner Type Theory Sound, incomplete static check of programs before run time. Web Ontology Language (OWL), Eclipse Modeling Framework (EMF), Object Constraint Language (OCL) Similarities: Ontology frameworks (concepts and relationships) Differences: Expressiveness vs. Efficiency Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 12/15

22 Conclusion Future work Handling of conflicts Is there a minimal set of relaxations to the constraints that makes them satisfiable? Extension to infinite lattices Unit system Unit conversion, Default units, Aliasing Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 13/15

23 Conclusion Summary Our framework (Pthomas) for analyzing model properties: 1 Requires minimal user specification (lattice and constraints) 2 Infers unspecified properties 3 Catches and reports design errors 4 Scales up efficiently to large models Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 14/15

24 Conclusion Conclusion Use this approach in your own tool! Pthomas, as well as our Ptolemy II modeling environment, can be downloaded from Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 15/15

25 Conclusion Conclusion Use this approach in your own tool! Pthomas, as well as our Ptolemy II modeling environment, can be downloaded from Questions? Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 15/15

26 Theory Relational Constraint Problem (RCP) RCP : (P, C) P is a partially ordered set, C is a set constraints of the form: r(p x, P y,...) where r is a relation (e.g. =, +,, ). A solution is a satisfying assignment to property variables. Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 16/15

27 Theory Definite Monotone Function Problem (DMFP) Special case of RCP DMFP : (P, C F ) P is a lattice, C F is a set of definite inequalities: F (P y, P z,...) P x where F is a monotonic function. Here, there is a unique least fixed point (LFP) solution. Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 17/15

28 Theory Algorithm Algorithm D (Rehof and Mogensen, 1996) Pseudocode C var {τ A C : A a variable} ; C const {τ A C : A a constant} ; p(β) = Undef. for all variables β ; while there are unsatisfied constraints in C var do Let τ β be one such constraint ; β β τ ; end if there are unsatisfied constraints in C const then Fail: There is no solution ; end For a finite lattice, this algorithm takes O(height(L) C ). Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 18/15

29 Theory Algorithm Conflicts What is a conflict? Unsatisfiable constraints How is it detected? C const {τ A C : A a constant} ;... if there are unsatisfied constraints in C const then Fail: There is no solution ; end Ben Lickly, et al. (UC Berkeley, Bosch) Scalable Semantic Annotation using Ontologies 19/15