1. Graph Grammars: An ITS Technology for Diagram Representations
Niels Pinkwart, Kevin Ashley,
Vincent Aleven, and Collin Lynch
Clausthal University of Technology
University of Pittsburgh
Carnegie Mellon University

2. Graph Grammars: An ITS Technology for Diagram Representations
Argumentation Skills
Argumentation skills essential for humans
Resolve personal issues
Leisure
Professional contexts …
Teaching argumentation skills is central goal of education
General aim: social skills, reasoning skills
Specific aims – e.g., law, science education
Argumentation is Learning (Andriessen 2006)
Typical teaching mode: face-to-face dialog and classroom discussions
Does not scale up
Some students do not participate
Intelligent Tutoring Systems could help
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

3. Diagrams for Teaching Argumentation
Educational technologies for argumentation usually employ diagram representations (e.g. claim / counterclaim)
Cognitive Perspective: Reduce cognitive load, reify important relationships
Technology Perspective: Diagrams provide partial structure
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

4. Examples: Argunaut, LARGO, Araucaria, Belvedere, Reason!Able
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

5. Graph Grammars: An ITS Technology for Diagram Representations
Feedback on Diagrams
Either domain-specific or based on relatively straightforward approaches
Comparison to ideal graph
Search for elements in graphs
No general, re-usable ITS technology for (argument) diagrams has emerged yet
Reason 1: Computational complexity
Diagram creation creative process – semantics of elements less clear than in a UI with text input fields
Logical formalisms: propositional logic insufficient, predicate logic difficult to apply in practice and not specifically suited for graphs
Reason 2: Ill-definedness of many argumentation domains
Often “correctness” notion hard to define
Full formal domain model for ITS sometimes impossible (but would be prerequisite for many ITS paradigms)
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

6. Requirements for ITS approach
Represent diagrams in adequate form system-internally
Handle changes in diagrams – including the specification of (dis)allowed changes to prevent “syntax errors”
Analyze diagrams to give feedback
… specifically geared toward the requirements of graphs
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

7. Graph Grammars: An ITS Technology for Diagram Representations
The LARGO ITS
LARGO (Legal ARgument Graph Observer): ITS to engage students in analyzing & reflecting about examples of expert Socratic reasoning
US Supreme Court Oral Arguments as learning resources
Diagrams to visualize argument as hypothesis testing
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

8. Graph Grammars: An ITS Technology for Diagram Representations
Example: US Supreme Court Oral Argument
MR. HANOIAN: If the vehicle has wheels on it, I think that that makes it mobile and it would be subject to the exception….If it still has its wheels and it still has its engine, it is capable of movement and it is capable of movement very quickly.
JUSTICE: Even though the people are living in it as a home and are paying rent for the trailer space, and so forth?
JUSTICE: Well, there are places where people can plug into water, and electricity, and do. There are many places, for example, in the state I came from where people go and spend the winter in a mobile home. And you think there would be no expectation of privacy in such circumstances?
MR. HANOIAN: Well, I am not suggesting that there is no expectation of privacy in those circumstances, Your Honor.
Test
Hypotheticals
Response: Modify Test
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

9. Example of LARGO diagram
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

10. A LARGO Argument Diagram
Palette
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

11. Intelligent Support in LARGO
Problem 1: legal argumentation is an ill-defined domain
Different views possible
Difficult to define “correctness” in this interpretive field
Problem 2: arguments consist of natural language texts – NLP based approaches are error-prone here
LARGO approach: Attempt to find characteristics in argument diagram
Weaknesses (areas of potential problems) or
Opportunities for reflection
Different types of characteristics (e.g., links between graph elements and important passages in the transcript, or graph portions that correspond to pre-defined “argument patterns”)
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

12. Graph Grammars in LARGO
Formal Definition: Grammar consists of
Set S of Symbols, symbols can have attributes
Start Axiom
Set of production rules
S = Sn  Se  Sc
Sn = {test, hypothetical, fact}
Se = {distinction, analogy, modification, causality, relatedness}
Sc : Characteristics
Words in grammar represent diagrams
Rules are used to handle diagram changes and to analyze diagrams (=detect characteristics)
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

13. Graph Grammar Words in LARGO
Word in Grammar: 4-tuple (N, E, M, C)
Nodes in diagram
Edges in diagram
Metadata (e.g., counters, important or irrelevant transcript regions)
Detected characteristics
In the axiom, M and C may contain task-specific information
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

14. Graph Grammars: An ITS Technology for Diagram Representations
Example
N = {testA, testB, hypotheticalA, hypotheticalB, fact}
E = {modification, relatednessA, relatednessB, causality, distinction}
with:
testA.conditionText = “IF vehicle has wheels AND capable of moving”,
testA.conclusionText = “THEN search without warrant permitted”,
testA.linkStart = 1050,
testA.linkEnd = 1150,
hypotheticalA.text = “vehicle in motor home park (with water and electricity connections) OUTCOME: search permitted”,
hypotheticalA.linkStart = 1520,
hypotheticalA.linkEnd = 1550,
relatednessA.text = nil,
relatednessA.from = hypotheticalA,
relatednessA.to = testA, …
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

15. Graph Grammars: An ITS Technology for Diagram Representations
Example (contd.)
M = {counter, irrelevant}
C = {characteristic}
with:
counter.testCount = 2.
counter.hypoCount = 2,
counter.factCount = 1,
counter.relationCount = 5,
irrelevant.linkStart = 100,
irrelevant.linkEnd = 200,
characteristic.linkStart = 2500,
characteristic.linkEnd = 2600,
characteristic.id = missed_hypo,
characteristic.referenceList = 
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

16. Graph Grammars: An ITS Technology for Diagram Representations
Grammar Rules
Technically: Production rule is L = (NL, EL, ML, CL)  (NR, ER, MR, CR) = R
Applying a rule L  R to a graph G is possible if G contains subgraph G’ which matches L.
Matching includes attribute matching
Result: Graph (G  R) \ G’
Two types of rules:
Generation rules (editing diagrams, specification of student‘s design space by constraining graphs that can be created)
Feedback rules (analysis of diagram for characteristics, express pedagogical knowledge of system)
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

17. Example of Generation rule
// Rule 4: Edges can be added anytime
({N,M},,{counter1},)  ({N,M},E,{counter2}, )
with:
N, M  Sn and E  Se
Condition:
N ≠ M
Result:
E.from = N,
E.to = M,
counter2.relationCount =counter1.relationCount+1
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

18. Graph Grammars: An ITS Technology for Diagram Representations
Feedback rules
Upon click on advice button, the system analyzes the diagram for characteristics using the feedback grammar rules.
These rules add entries to the fourth component of the tuple (N,E,M,C) and leave the first two unchanged
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

19. Example: Feedback rule in LARGO
Diagram that contains a hypothetical which is both related to the facts and to a test, and at the same time also contains another test.
Pedagogical opportunity to invite the student to reflect upon how the hypothetical scenario relates to the different tests in the light of the facts of the case (e.g., by comparing the decision rules)
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

20. Graph Grammars: An ITS Technology for Diagram Representations
Example (contd.)
// Rule 59: Reflection on hypothetical
({hypothetical,fact,test},{E,F},{counter},) 
({hypothetical,fact,test},{E,F},{counter},{characteristic})
with
E, F  Se
Condition:
E.from  {hypothetical, fact},
E.to  {hypothetical, fact},
F.from  {hypothetical, test},
F.to  {hypothetical, test},
counter.testCount > 1
Result:
characteristic.id = discuss_hypo_mult_tests,
characteristic.referenceList = {hypothetical, fact, test, E, F}
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

21. Graph Grammars: An ITS Technology for Diagram Representations
Feedback Example
Grammar rules also helpful for selecting which feedback to present
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations

22. Graph Grammars: An ITS Technology for Diagram Representations
Summary & Conclusion
Graph Grammars: An ITS technique for (argument) diagrams,
more powerful than simple pattern matching techniques
specifically designed for graph representations
meets ITS requirements (expression of pedagogical knowledge; syntax constraints)
Approach general enough to be applicable also in other fields that benefit from diagrams – e.g., database design, scientific inquiry, software design, causal reasoning
Adaptation to another domain requires specification of domain concepts (nodes, edges) and pedagogical knowledge. Parsing engine is re-usable.
Use in same domain (but with different task) very easy
Niels Pinkwart
FLAIRS 2008
Graph Grammars: An ITS Technology for Diagram Representations