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Learning and Reasoning with Qualitative Models of Physical Behavior

Learning and Reasoning with Qualitative Models of Physical Behavior. Scott Friedman, Ken Forbus, Jason Taylor Qualitative Reasoning Group Northwestern University. Novices & Qualitative Physics. Students have misconceptions about force and motion (McCloskey, 1983; diSessa, 1993)

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Learning and Reasoning with Qualitative Models of Physical Behavior

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  1. Learning and Reasoning with Qualitative Models of Physical Behavior Scott Friedman, Ken Forbus, Jason Taylor Qualitative Reasoning Group Northwestern University

  2. Novices & Qualitative Physics • Students have misconceptions about force and motion (McCloskey, 1983; diSessa, 1993) • Often similar to: impetus theory, Aristotelian models… • Systematicity and cohesiveness of intuitive models are heavily debated in the literature • Intuitive physics models (including misconceptions) are qualitative & tenacious • Good performance in mathematics is not indicative of good performance in qualitative physics (Halloun & Hestenes, 1985) • Qualitative physics misconceptions exist after physics instruction (Clement, 1982)

  3. Novices & Qualitative Physics • Intuitive models are learned from experience • Misconceptions may occur from improperly generalizing or contextualizing (Smith, diSessa, & Roschelle, 1994) • How are naïve qualitative models learned from experience? • Our idea: temporal encoding of exemplars, analogical generalization, and parameterization

  4. Our System • Given: • Multimodal input stimuli • Set of target concepts • Learn intuitive models of the target concepts • Perform similar to naïve students on two reasoning tasks: • Brown (1994) • Hestenes et al (1992) Comic-strip stimuli New Scenarios Reasoning NL NL List of target concepts {pushing, moving, blocking}

  5. Multimodal Stimuli Encapsulated Histories Comic-strip stimuli SEQL Generalizations Temporally encoded CycL exemplars Reasoning List of target concepts {pushing, moving, blocking} New Scenarios def-EH: participants: … conditions: … consequences: … def-EH: participants: … conditions: … consequences: … NL NL

  6. Multimodal Stimuli • Stimuli are multi-state comic strips • States divided by qualitative behaviors • Temporal relations between states • Stimuli contain 1+ example of target concepts • English blurbs • CogSketch(Forbus et al, 2008) processes sketched input • EA NLU (Tomai & Forbus, 2009) processes simplified English • Both use extended OpenCyc KB • 17 stimuli used for experiments “The child child-13 is playing with the truck truck-13.”

  7. Encoding Exemplars Encapsulated Histories Comic-strip stimuli SEQL Generalizations Temporally encoded CycL exemplars Reasoning List of target concepts {pushing, moving, blocking} New Scenarios def-EH: participants: … conditions: … consequences: … def-EH: participants: … conditions: … consequences: … NL NL

  8. Temporally Encoded Exemplars “The child child-13 is playing with the truck truck-13.” Target Concepts {pushing, moving, blocking}

  9. Temporally Encoded Exemplars temporallyCoterminal temporallySubsumes Temporal relations add structure holdsIn startsAfterEndingOf

  10. SEQL Generalization Encapsulated Histories Comic-strip stimuli SEQL Generalizations Temporally encoded CycL exemplars Reasoning List of target concepts {pushing, moving, blocking} New Scenarios def-EH: participants: … conditions: … consequences: … def-EH: participants: … conditions: … consequences: … NL NL

  11. Contextualized Generalizations Pushing All exemplars describing the associated concept are automatically generalized within the context via SEQL • Target Concepts • Pushing • Moving • Blocking Moving Blocking

  12. Generalizing with SEQL Pushing Exemplar enew • Identify destination context(s) Moving Blocking

  13. Generalizing with SEQL Pushing • Structure Mapping Engine (SME) • Input • Base and Target representations • Computes mappings • Entity & relation correspondences • Structural evaluation (similarity) score • Candidate inferences • Used for merging representations Exemplar enew 2. Compare enew to each generalization g via SME (Falkenhainer et al, 1989) …merge enew with the first generalization where: SME-Similarity-Score(enew, g) > assimilation-threshold Base Target Mapping

  14. Generalizing with SEQL Pushing Exemplar enew 3. If unmerged, compare enew to each unassimilated exemplar e via SME …create a new generalization from enew and the first exemplar e where: SME-Similarity-Score(enew, e) > assimilation-threshold

  15. Generalizing with SEQL Pushing Exemplar enew 4. If structurally dissimilar to all exemplars and generalizations: Add enew to the list of unassimilated exemplars.

  16. Result of Generalizing with SEQL Pushing 17 stimuli (50 concept exemplars) 10 generalizations + 12 unassimilated exemplars Moving Blocking

  17. Generalization Anatomy • Generalizations are probabilistic abstractions of exemplars • Entities that correspond analogically become generalized entities (GenEntFn) in the generalization • Facts have probabilities reflecting their frequency • We want to capture the central behavior in a formal model

  18. Building Models Encapsulated Histories Comic-strip stimuli SEQL Generalizations Temporally encoded CycL exemplars Reasoning List of target concepts {pushing, moving, blocking} New Scenarios def-EH: participants: … conditions: … consequences: … def-EH: participants: … conditions: … consequences: … NL NL

  19. Encapsulated Histories • Represent categories of behavior over a span of time • Refer to multiple qualitative states or events • Can describe causal or temporal relationships between concepts • Used here as descriptive models of typical behavior • Agent is agnostic to the underlying mechanisms of change • If the participants (entities) and conditions of an EH hold, it is activated by the agent, and its consequences are assumed to hold • Automatically generated by parameterizing SEQL generalizations

  20. Filtering Generalizations • Some generalizations are poor for causal reasoning • They don’t capture the relationship between concepts • We can filter these out • Find highly-correlated concepts within a context: • For probability threshold t, find concepts C where P(cC) > t in at least one generalization in the context • Filter generalizations that are indecisive w/r/t cC • Using binary entropy function H, exclude generalizations where: H(P(cC)) > H(t)

  21. Models from Generalizations • Filter facts below a probability threshold t • Use temporal relations to hypothesize causal role of each fact f to the concept c • If f starts with or before c, f might cause c • If f starts with or after c, c might cause f • If f temporally subsumes c, f might be a condition for c

  22. Generating Encapsulated Histories define-encapsulated-history Push05 Participants: Entity(?P1) Entity(?P2) PushingAnObject(?P3) Direction(?dir1) Direction(?dir2) Conditions: providerOfMotiveForce(?P3, ?P1) objectActedOn(?P3, ?P2) dir-Pointing(?P3, ?dir1) touches(?P1, ?P2) dirBetween(?P1, ?P2, ?dir1) dirBetween(?P2, ?P1, ?dir2) Consequences: Normal-Usual(and(PushingAnObject(?P3) providerOfMotiveForce(?P3, ?P1) objectActedOn(?P3, ?P2))) causes-SitProp(Push05, exists(?M1, and(MovementEvent(?M1) objectMoving(?M1, ?P1) motionPathway(?M1, ?dir1))) • Resulting EHs are more general than the initial stimuli • Low probability attributes and relations have been generalized and filtered • Only high probability facts remain • Used for reasoning about scenarios with same ontology as learning stimuli • EH activation identifies modeled behaviors as “Normal” or typical • PushingAnObject, at left • Failure to activate any EH on a concept instance means the instance is anomalous • Effective for simple counterfactual reasoning & indirect proofs

  23. Resulting Encapsulated Histories • 10 generalizations total • 4/10 automatically filtered out for being causally irrelevant • 6/10 automatically parameterized into encapsulated histories • Blocking: • E1 touches & pushes E2 in dir d, which is blocked by E3 to dir d • Pushing: • E1 touches & pushes E2 in direction d, causing E2 to move in dir d • E1 touches & pushes E2 in dir d, caused by E1 moving in dir d, which results in E2 moving in d • Movement • E1 moves in dir d, caused by E2 moving toward E1 and pushing it in dir d • …same as above, but on a surface above the ground • E1 moves in dir d along a surface, caused by E2 pushing it in dir d

  24. Reasoning with Learned Models Encapsulated Histories Comic-strip stimuli SEQL Generalizations Temporally encoded CycL exemplars Reasoning List of target concepts {pushing, moving, blocking} New Scenarios def-EH: participants: … conditions: … consequences: … def-EH: participants: … conditions: … consequences: … NL NL

  25. Problem Solving Experiments • Two problem solving tasks • Brown (1994): Does the table pushes up against the book? • Hestenes et al (1992): which direction will this moving puck will go when given an instantaneous “kick?” • Problem scenarios were provided in same modalities as learning stimuli • The simulation reasoned through both scenarios by activating EHs • Contradiction detection • Compare with human results

  26. Results from Brown (1994) • 73 high school students asked whether a table exerts an upward force against a book resting on its surface

  27. Results from the Force Concept Inventory • High school & college students given this scenario: a puck is moving with constant velocity along on a frictionless surface. If given an instantaneous “kick,” which choice best describes its path?

  28. Summary of Learning Results • Given • 17 multistate multimodal stimuli • Target concepts: {pushing, movement, blocking} • SEQL assimilation threshold = 0.5 • Parameterization probability threshold = 0.9 • Learning & reasoning on Companions Cognitive Architecture • Output from learning • After encoding: 50 concept exemplars • After generalization: 10 generalizations • After parameterization: 6 encapsulated histories • System reasoned with these learned models…

  29. Simulation Results: Brown • System found two active instances of an EH in the scenario: Using EH: E1 pushes E2 in dir d, E2 pushes E3 in dir d and E2 is blocked by E3 • E1: gravity; E2: book; E3: table; d: down • E1: gravity; E2: table; E3: ground; d: down • System infers that the book pushes the table and the table pushes the ground, and that both are blocked. • The system could not conclude that the table pushed the book: • Assumed that the table did push against the book, and arrived at an indirect proof: Using EH: E1 touches & pushes E2 in direction d, causing E2 to move in dir d • The consequence of the table (E1) pushing the book (E2) upwards (d) is the book moving upwards, which is not visible in the scenario.

  30. Simulation Results: FCI • System observed a branch after the second state and instantiated EHs to determine which following state(s) are feasible • Activated an EH instance on choice (a): Using EH: E1 touches & pushes E2 in direction d, causing E2 to move in dir d • E1: foot; E2: puck; d: up • Could not activate EHs on other choices, due to direction mismatches

  31. Conclusion • Simulation that learns naïve qualitative models • Temporal encoding of concept exemplars • Analogical generalization • Qualitative model generation from probabilistic abstractions • Resulting explanations are compatible with those of physics-naïve students • Evidence that naïve physics models can be learned via analogical generalization

  32. Future Work • Incorporate other physical concepts to model human reasoning over all of the Force Concept Inventory (Hesteneset al, 1992) • Automatically induce physical process models to develop deeper domain theories • No more batch mode: shift to an anomaly response model of concept learning • Incorporate this into the Companions Cognitive Architecture • Incorporate into a larger model of conceptual change

  33. Related Work • Using sketched & NL input for learning • Lockwood, K. and Forbus, K. (2009). Multimodal Knowledge Capture from Text and Diagrams.  To appear in Proceedings of the Fifth International Conference on Knowledge Capture. • Computational models of conceptual change • Ram, A. (1993). Creative conceptual change. Proceedings of CogSci 1993. • Esposito, F., Semeraro, G., Fanizzi, N., & Ferilli., S. (2000). Conceptual Change in Learning Naive Physics: The Computational Model as a Theory Revision Process. In E. Lamma and P. Mello (Eds.), AI*IA99: Advances in Artificial Intelligence, Lecture Notes in Artificial Intelligence 1792, 214-225, Springer: Berlin. • Concept learning & causal learning • Fisher, D. H. (1987). Knowledge acquisition via incremental concept clustering. Machine Learning, 2,139-172. • Gopnik, A., Glymour, C., Sobel, D., Schulz, L., Kushnir, T., Danks, D. (2004). A Theory of Causal Learning in Children: Causal Maps and Bayes Nets. Psychological Review, 111(1), 3-32.

  34. Acknowledgments This work was funded by the Office of Naval Research under grant N00014-08-1-0040

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