A language to write dynamical theories

1. A language to write dynamical theories Qualitative Process (QP) Theory Part I

2. QP Theory • A number of modeling constructs to define notion of processes was provided. • A QP theory model structural description is given by a set of individualviews and processes. • The former is used to model the behavior of individuals (objects), while the latter are the only mechanisms that support changes in system behavior.

3. QP theory processes • Those things that cause changes in objects over time are characterized by ‘processes’ (e.g. objects roll, move, collide, fly, stretch). • QP theory provides ontology primitives to define objects and to describe processes of such kind.

4. A Five-Slot Process (I) • Individuals, Preconditions, Quantity conditions, Relations and Direct influences. • Preconditions contain statements referring to external conditions. • Quantity-conditions contain inequalities involving quantities (object’s characteristics), which is crucial in determining the statusof a process (active/inactive).

5. A Five-Slot Process (II) • Relations are statements about functional dependencies among quantities. • It is represented by either P+ or P- implements relations that caused the influenced quantity to change in the same direction as the influencing quantity, or in the opposite direction respectively. • Direct influences, describe how state variables change at a certain rate due to processes. • Direct influences are represented by I+ and I-, and implement operation for adding and subtracting the value of the rate from the derivative of the state variable.

6. Other modeling constructs • Qualitative proportionalities are monotonic functions that propagate the effects of processes. • Correspondences are used to map values from the quantity space (values of numbers) of one variable to values in the quantity space of another variable. • A quantity consists of two parts: amount (magnitude) and derivative (sign). Quantity space is a collection of numbers which form a partial order.

7. Qualitative reasoning • The understanding of commonsense reasoning would entail the study of how to reason qualitatively about processes, namely, the kinds of changes that occur and their effects. • Qualitative Reasoning (QR) attempts to give distinction between reasoning with actual numerical values and equations and reasoning withless precise representations (qualitatively).

8. A qualitative description • A qualitative description of the tub-filling process will read as: ‘The level of water will keep increasing and will eventually reach the top, which will cause overflow and the floor will get wet’. • The statement gives a useful summary of a possibly large amount of quantitative information (such as exact amount and level of the water in the tub) which is not needed to comprehend the situation.

9. Problem Description • From the equation F = k.x we can easily see that increasing values of x are followed by increasing value of F. • However, the mathematical equation itself captures nothing about this simple notion.

10. Question 1 • Write using QP theory, some kind of monotonic relationship to represent the notion in F = m.a Note: m = mass & a = acceleration Answers Refer to page 9

11. You need to consider the following: F = m.a • We cannot directly apply an acceleration, we can only cause acceleration by imposing a force (mass remains no change) • Its mass will affect how much acceleration we get (if the force is unchanged) • Its mass will also affect how much force we get (if acceleration remains) acc Q+ force acc Q - mass force Q + mass

12. Question 2 • Will mass be seen on the left-side? Why or why not? Acceleration is not appearing on the left hand side We cannot by accelerating something cause the mass of a solid object to change

13. Conclusion Critical thinking, basic analysis skill, etc. are required, & not merely memorizing the formula! … modeling is the central skill for science teaching… If you “reason”, you can truly “understand”

14. Example: Refer to Figure 1.. • Notice that commonsense conclusions can be drawn without having to engender any mathematical expression such as • F = k.x or F=m.a

15. Figure 1 shows a physical situation that portrays a brick and an elastic string tied up at one end. Figure 1: A sliding block

16. Some conclusions QP theory can be used to conclude are: • Question 1: “What happens if we release the block?” A possible conclusion would be“Assuming the spring does not collapse, the block will oscillate back and forth and if there is friction it will eventually stop”. • Question 2: “What if it gets pumped?” A possible answer will read something like this “If there is no friction the spring will eventually break. If there is friction and the pumping energy is constant then there will be a stable oscillation”.

17. Causality • The notion of causality is an essential aspect of human understanding of phenomena in the world. • Knowledge of causal mechanisms not only lets us predict behavior but also provides justification for predicted (simulated) results.

18. Causality • can be used to impose order upon the world. For instance, when given ‘X causes Y’, we believe that if we want to obtain Y we would bring about X. As such, when we observe Y we will think that X might be the reason for it.

19. A qualitative model for the “stretching” process

21. The process: Stretching

22. Questions Compressing Relaxing-Plus Relaxing-Minus • Name three other processes associated with the phenomena in Figure 1. • Describe ‘Velocity & Position’ relationship in QP theory term. 3. What factor will likely to affect the system behavior? The derivative of ‘position’ is the amount of ‘velocity’. Friction

23. Conclusions • QP theory offers two useful means of representations. • First, it represents the right kinds of knowledge. • Right kinds refer to the implicit causal theories of physical phenomena that the model has. • Second, it represents the right level of knowledge. • This refers to the qualitative principles that govern a subject, including the processes and the causal relationships.

24. The main objective of using QP theory in our work • To build science educational software that incorporates instructional goals and intentions, rather than merely authenticity as in traditional media. • It is believed that students should deeply understand the qualitative principles that govern a subject, including the physical processes and the causal relationships before they are immersed in qualitative problem solving.

25. Computers to act as intelligent agents • should be equipped with models that could capture the behavioral aspects of a system and these models should be explicit with respect to phenomena that must be learned. • should have means to communicate the details captured in those models to learners (i.e. the so-called software articulation).

26. Part II Process modeling Causal explanation