Introduction to Qualitative Reasoning

1. Introduction to Qualitative Reasoning In the Building of Intelligent Tutoring Systems

2. QP theory and Qualitative reasoning • I have included an application of QP theory in the modeling of the equilibrium phenomena in inorganic chemistry to demonstrate how the construction of a model using the theory can help the learner to acquire good concept about the subject and the articulation of ideas.

3. Motivation • Tight coupling between concepts and their embodiment in software is crucial in building smart educational software that can explain its reasoning. • This is desirable since conceptual understanding and the ability to provide explanation are important requirements for effective learning and it serves as an important means to induce learning. • However, this spirit is not found in traditional software development.

4. Qualitative reasoning (I) • The term Qualitative Reasoning (QR) pertains to the distinction between reasoning with actual numerical values and equations and reasoning with less precise representations. • Such qualitative description of physical processes provides grounds for generating causal explanation and cognitive diagnosis. • With these dynamic mechanisms, educational software can incorporate instructional goals rather than merely a static content-driven tool.

5. Qualitative reasoning (II) • One of the goals of QR research is to understand human-like commonsense reasoning and education is one of the most important areas of practical application of qualitative reasoning. • One such system is CyclePad developed by Kenneth Forbus of Northwestern University that teaches analysis and design of thermal cycles. • Other popular application domains are electronics, chemical engineering and teaching computer programming.

6. A qualitative description.. How to describe this in computer language? Ontology needed!! • 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. How to derive natural description from a software

7. Ontology • In AI, one can regard ontology as a specification of a conceptualization and the embodiment of agreement about that conceptualization. • It has the knowledge and deduction in one framework. • Several ontology for qualitative reasoning have been introduced. • Among the well-known are component-centered, constraint-based and process-centered (the QPT). The following section introduces QP theory.

8. QP theory • The QP theory serves as a language to write dynamical theories. This ontology defines notion of physical process, hence it is called a process-based approach. • In numerical simulation, much of the processes are characterized by differential equations that describe how the parameters of objects are changed over time. • However, the notion of ‘process’ is believed to be richer and more structured than this. • 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.

9. The primitives used in QP theory (I) • Main primitives of this process-based ontology are Viewsand Processes. An individual view is to describe both the contingent existence of objects and object properties that change drastically with time. While a process is described by five parts: individuals, preconditions, quantity conditions, relations and influences. • The slot individual contains lists of objects or entities upon which the process is applicable (such as S2- and H+in our later example). Preconditions contain statements referring to external conditions.

10. The primitives used in QP theory (II) • Quantity conditions are statements about inequalities involving quantities of the objects, which can be used to determine whether or not a process is active. • Relationsare statements about relationships between variables. Two primitives that are very important in describing the relationships between quantities are the correspondences and qualitative proportionalities. • Correspondences can be used in mapping values from the quantity space of one variable to values in the quantity space of another variable. • In this ontology dynamic aspects are expressed by the notion of direct influence. Direct influences can only appear in processes and are presented in the slot Influences.

11. Common sense question & answer • Figure 1 illustrates some conclusions about a physical situation that portrays a brick and an elastic string tied up at one end. Noticed that commonsense conclusions can be drawn without having to engender any mathematical expression such as F = kx or F=ma.

13. Chemical analysis and chemical equilibrium • Chemical analysis deals with the resolution of a chemical compound into its proximate or ultimate parts and the determination of its elements or the foreign substances it may contain. • Every testing method in qualitative analysis involves a reaction between the reagent and an unknown sample (the cation).

14. Unknown sample • Consider the example iron (II) sulphide above. Given an unknown sample which contains ferrous ions, reaction of ferrous ions and sulphide ions (reagent) will result in the formation of a black precipitate of iron (II) sulphide (Eq.1). • Equation 2 shows an equilibrium state between H2S and both ions. • In a reaction, equilibrium is achieved at the point where the rates of the forward reaction and the backward reaction are equal. • A test scheme is devised to allow the user to choose one reagent at a time to determine the unknown sample. • For the above example, only H2S gives positive result which is the black precipitation (FeS).

15. Next section shows that reasoning about chemical equilibrium would require only common sense knowledge rather than complex formula or quantitative data.

16. Modeling chemical reactions using QP theory • In this section, chemical reactions are qualitatively expressed as two QP theory processes, namely the dissociation (Fig. 2) and the precipitation (Fig. 3). • In equation 2, when either of the ions reaches saturation point, there will be no more dissociation of H2S to form ions H+ and S2- (see quantity conditions and relations in fig. 2).

17. Fig. 2 Process dissociation of H2S

19. Instead, the separated ions will combine to form the initial reagent, hence lack of S2- to yield black precipitation. • Saturation is caused by an increase in the concentration of the H+ and S2-. • To express this phenomenon, we could write the relationships as shown in figure 2. Even though ion Fe present Look at the ‘Corr’ parts

20. H combines with S • If we look at equation 1 once more, Fe2+ + H2S (reagent)  FeS + 2H+ says that FeS might not be formed if H+ is in excess. • When H+ is saturated it will tend to combine with S2- to revert the reagent. There is a situation where H+ could get saturated very fast, i.e., the solution used is acidic (e.g. HCl is added) rather than neutral (e.g. water). • When this happen a chemical equilibrium is said to be reached. Substances such as H2S that exhibit reverse reaction are stored as chemical facts (domain knowledge) to allow the system knows that H2S will cause reverse reaction. • According to the Le Châtelier’s principle, whenever a stress is imposed at the right-hand side of the equation, reaction will move to the left-hand sideto release the stress. • In our case, the reverse reaction will occur to reduce the H+. When reasoning works on the two processes, equilibrium phenomena can be explained.

21. Discussion • Qualitative reasoning ontology, take for example the QP theory offers two useful means of representations. • First, it represents the right kinds of knowledge. • Second, it represents the right level of knowledge. • It is conjectured that students should deeply understand the qualitative principles that govern a subject, including the processes and the causal relationships before they are immersed in qualitative problem solving.