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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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