Introduction to Introduction to Qualitative ReasoningQualitative Reasoning

In the Building of Intelligent In the Building of Intelligent Tutoring SystemsTutoring Systems

QP theory and Qualitative QP theory and Qualitative reasoningreasoning

I have included an I have included an application of application of QP theoryQP theory in the modeling of the in the modeling of the equilibrium phenomenaequilibrium phenomena in in inorganic chemistry to inorganic chemistry to demonstrate how the demonstrate how the construction construction of a model using the theoryof a model using the theory can can help the learner to help the learner to acquire good acquire good conceptconcept about the subject and the about the subject and the articulation of ideasarticulation of ideas. .

Motivation Motivation

Tight couplingTight coupling between between concepts concepts and and their embodimenttheir embodiment in software is crucial in software is crucial in building in building smart educational softwaresmart educational software that that can explain its reasoning. can explain its reasoning.

This This is desirableis desirable since conceptual since conceptual understanding and the ability to provide understanding and the ability to provide explanation are important requirements explanation are important requirements for for effective learningeffective learning and it serves as and it serves as an important means to an important means to induce learninginduce learning..

However, However, this spirit is not found in this spirit is not found in traditional software development. traditional software development.

Qualitative reasoning (I)Qualitative reasoning (I)

The term Qualitative Reasoning (QR) The term Qualitative Reasoning (QR) pertains to the pertains to the distinction betweendistinction between reasoning with reasoning with actual numerical valuesactual numerical values and and equations and reasoning with equations and reasoning with less precise less precise representationsrepresentations. .

Such qualitative description of physical Such qualitative description of physical processes provides grounds for generating processes provides grounds for generating causal explanationcausal explanation and and cognitive diagnosiscognitive diagnosis. .

With these With these dynamic mechanismsdynamic mechanisms, , educational software can incorporate educational software can incorporate instructional goalsinstructional goals rather than merely a rather than merely a static content-driven tool. static content-driven tool.

Qualitative reasoning (II)Qualitative reasoning (II)

One of the goals of QR research is to One of the goals of QR research is to understand human-like commonsenseunderstand human-like commonsense reasoning and reasoning and education is one of the education is one of the most important areasmost important areas of practical of practical application of qualitative reasoning. application of qualitative reasoning.

One such system is One such system is CyclePadCyclePad developed by developed by Kenneth ForbusKenneth Forbus of of Northwestern University that teaches Northwestern University that teaches analysis and design of thermal cycles.analysis and design of thermal cycles.

Other popular application domains are Other popular application domains are electronics, chemical engineering and electronics, chemical engineering and teaching computer programming. teaching computer programming.

A qualitative description..A qualitative description..

A qualitative description of the tub-A qualitative description of the tub-filling process will read as: ‘filling process will read as: ‘The level The level of water will keep increasing and will of water will keep increasing and will eventually reach the top, which will eventually reach the top, which will causecause overflow and the floor will get overflow and the floor will get wet’. wet’.

The statement gives a useful The statement gives a useful summary of a possibly summary of a possibly large amount large amount of quantitative informationof quantitative information (such as (such as exact amount and level of the water exact amount and level of the water in the tub) which is in the tub) which is not needednot needed to to comprehend the situation. comprehend the situation.

How to describe this in computer

language? Ontology needed!!

How to derive natural

description from a

software

OntologyOntology

In AI, one can regard ontology as a In AI, one can regard ontology as a specification of a conceptualization specification of a conceptualization and the embodiment of agreement and the embodiment of agreement about that conceptualizationabout that conceptualization. .

It has the It has the knowledge and deduction knowledge and deduction in one frameworkin one framework. .

Several ontology for qualitative Several ontology for qualitative reasoning have been introduced. reasoning have been introduced. Among the well-known are component-Among the well-known are component-

centered, constraint-based and process-centered, constraint-based and process-centered (the QPT). The following centered (the QPT). The following section introduces QP theory.section introduces QP theory.

QP theoryQP theory

The QP theory serves as The QP theory serves as a languagea language to write dynamical to write dynamical theories. This ontology theories. This ontology defines notion of physical defines notion of physical processprocess, hence it is called a process-based approach. , hence it is called a process-based approach.

In In numerical simulationnumerical simulation, much of the processes are , much of the processes are characterized by characterized by differential equationsdifferential equations that describe how that describe how the parameters of objects are changed over time.the parameters of objects are changed over time.

However, the notion of ‘process’ is believed to be richer However, the notion of ‘process’ is believed to be richer and more structured than this. and more structured than this.

The understanding of The understanding of commonsense reasoningcommonsense reasoning would would entail the study of how entail the study of how to reason qualitativelyto reason qualitatively about about processes, namely, processes, namely, the kinds of changesthe kinds of changes that occur and that occur and their effectstheir effects. .

The QP theory serves as The QP theory serves as a languagea language to write dynamical to write dynamical theories. This ontology theories. This ontology defines notion of physical defines notion of physical processprocess, hence it is called a process-based approach. , hence it is called a process-based approach.

In In numerical simulationnumerical simulation, much of the processes are , much of the processes are characterized by characterized by differential equationsdifferential equations that describe how that describe how the parameters of objects are changed over time.the parameters of objects are changed over time.

However, the notion of ‘process’ is believed to be richer However, the notion of ‘process’ is believed to be richer and more structured than this. and more structured than this.

The understanding of The understanding of commonsense reasoningcommonsense reasoning would would entail the study of how entail the study of how to reason qualitativelyto reason qualitatively about about processes, namely, processes, namely, the kinds of changesthe kinds of changes that occur and that occur and their effectstheir effects. .

The primitives used in QP The primitives used in QP theorytheory (I)(I)

Main primitives of this process-based ontology are Main primitives of this process-based ontology are ViewsViews and and ProcessesProcesses. An . An individual viewindividual view is to is to describe both the contingent existence of objects describe both the contingent existence of objects and and object propertiesobject properties that change drastically with that change drastically with time. While a time. While a process process is described by five partsis described by five parts: : individualsindividuals, , preconditionspreconditions, , quantity conditionsquantity conditions, , relationsrelations and and influencesinfluences. .

The slot The slot individual individual contains lists of objects or contains lists of objects or entities upon which the process is applicable (such entities upon which the process is applicable (such as Sas S2-2- and and HH++ in our later example). in our later example). Preconditions Preconditions contain statements referring to external conditions. contain statements referring to external conditions.

Main primitives of this process-based ontology are Main primitives of this process-based ontology are ViewsViews and and ProcessesProcesses. An . An individual viewindividual view is to is to describe both the contingent existence of objects describe both the contingent existence of objects and and object propertiesobject properties that change drastically with that change drastically with time. While a time. While a process process is described by five partsis described by five parts: : individualsindividuals, , preconditionspreconditions, , quantity conditionsquantity conditions, , relationsrelations and and influencesinfluences. .

The slot The slot individual individual contains lists of objects or contains lists of objects or entities upon which the process is applicable (such entities upon which the process is applicable (such as Sas S2-2- and and HH++ in our later example). in our later example). Preconditions Preconditions contain statements referring to external conditions. contain statements referring to external conditions.

The primitives used in QP The primitives used in QP theorytheory (II)(II)

Quantity conditionsQuantity conditions are statements about are statements about inequalities inequalities involving quantities of the objectsinvolving quantities of the objects, which can be used to , which can be used to determine whether or not a process is active. determine whether or not a process is active.

RelationsRelations are statements about relationships between are statements about relationships between variables. Two primitives that are very important in variables. Two primitives that are very important in describing the relationships between quantities are the describing the relationships between quantities are the correspondencescorrespondences and and qualitative proportionalitiesqualitative proportionalities..

CorrespondencesCorrespondences can be used in can be used in mapping values from the mapping values from the quantity space of one variable to values in the quantity space quantity space of one variable to values in the quantity space of another variableof another variable. .

In this ontology dynamic aspects are expressed by the In this ontology dynamic aspects are expressed by the notion of direct influence. Direct influences can only appear notion of direct influence. Direct influences can only appear in processes and are presented in the slot in processes and are presented in the slot InfluencesInfluences..

Common sense question & Common sense question & answeranswer Figure 1 illustrates some Figure 1 illustrates some

conclusions about a conclusions about a physical physical situationsituation that portrays a that portrays a brickbrick and an and an elastic stringelastic string tied up at tied up at one end. Noticed that one end. Noticed that commonsense conclusions can commonsense conclusions can be drawn without having to be drawn without having to engender any mathematical engender any mathematical expression such as expression such as F = kxF = kx or or F=maF=ma..

Fig. 1 Some conclusions QP theory can be used to conclude [5]

Q: What happens if we release the block? A: Assuming the spring does not collapse, the block will oscillate back and forth. If there is friction it will eventually stop. Q: What if it gets pumped? A: 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.

Chemical analysis and Chemical analysis and chemical equilibrium chemical equilibrium Chemical analysis deals with the Chemical analysis deals with the

resolution of a chemical compound resolution of a chemical compound into its proximate or ultimate parts into its proximate or ultimate parts and the determination of its elements and the determination of its elements or the foreign substances it may or the foreign substances it may contain. contain.

Every testing method in qualitative Every testing method in qualitative analysis involves a reaction between analysis involves a reaction between the the reagent reagent and an and an unknown sampleunknown sample (the cation). (the cation).

Consider the example iron (II) sulphide above. Given an Consider the example iron (II) sulphide above. Given an unknown sample which contains unknown sample which contains ferrous ionsferrous ions, reaction , reaction of ferrous ions and sulphide ions (reagent) will result in of ferrous ions and sulphide ions (reagent) will result in the formation of a the formation of a black precipitateblack precipitate of iron (II) sulphide of iron (II) sulphide (Eq.1). (Eq.1).

Equation 2 shows an equilibrium state between Equation 2 shows an equilibrium state between HH22SS and and both ionsboth ions. .

In a reaction, equilibrium is achieved at the point where In a reaction, equilibrium is achieved at the point where the rates of the forward reactionthe rates of the forward reaction and the and the backward backward reaction are equal. reaction are equal.

A test scheme is devised to allow the user to choose A test scheme is devised to allow the user to choose one reagent at a time to determine the unknown sample. one reagent at a time to determine the unknown sample.

For the above example, only HFor the above example, only H2S gives positive result S gives positive result which is the black precipitation (FeS). which is the black precipitation (FeS).

Fe2+ + H2S (reagent) FeS + 2H+ (Eq. 1) H2S (reagent) 2H+ + S2- (Eq. 2)

Unknown sample

Next section shows that Next section shows that reasoning about chemical reasoning about chemical equilibrium equilibrium would require would require

only common sense only common sense knowledgeknowledge rather than rather than

complex formula or complex formula or quantitative data. quantitative data.

Modeling chemical reactions using Modeling chemical reactions using QP theory QP theory

In this section, In this section, chemical reactionschemical reactions are qualitatively expressed as are qualitatively expressed as two two QP theory processesQP theory processes, namely the , namely the dissociationdissociation (Fig. 2) and the (Fig. 2) and the precipitation precipitation (Fig. 3). (Fig. 3).

In In equation 2equation 2, when , when either of the ions either of the ions reaches saturation pointreaches saturation point, there will , there will be be no more dissociation of Hno more dissociation of H22SS to to

form ions H+ and Sform ions H+ and S2- 2- (see quantity (see quantity conditions and relations in fig. 2). conditions and relations in fig. 2).

Process Dissociation of H2S Individuals H dissolved ion S dissolved ion liq fluid that dissolve ion Preconditions Ds[amount-of(liq)] = 0 Quantity Conditions Am[amount-of(H2S)] > ZERO ~ saturated(H) ;process will stop when this becomes false ~ saturated(S) ;process will stop when this becomes false Relations dissociation-rate Q-concentration-of(H) ;it says that dissociation will decrease dissociation-rate Q-concentration-of(S) ;when H and S are high in their concentration Correspondence((dissociation-rate(H2S), ZERO), ;not to dissociate when H gets saturated

concentration-of(H), saturated(H))) Correspondence((dissociation-rate(H2S), ZERO),;not to dissociate when S gets saturated

concentration-of(S), saturated(S))) Influences I+(concentration-of(H), Am[dissociation-rate]) ;the higher the dissociation rate

Fig. 2 Process dissociation of H2S

Process Precipitate formation of FeS Individuals Fe dissolved ion S dissolved ion liq fluid that dissolve ion Preconditions Ds[amount-of(liq)] = 0 Quantity Conditions Am[amount-of(S)] > ZERO ;process will stop if no more S to react with Fe Am[amount-of(Fe)] > ZERO ;to yield product Relations ; Let K be a quantity K Q+concentration-of(Fe) K Q+concentration-of(S) ;increase concentration of S will also increase K Am[formation-rate] Q+concentration-of(S) ;hence the formation rate FeS ;K = [Fe] * [S]

Correspondence((amount-of(FeS), ZERO), ;no formation of FeS if its Ks is 4.0 * 10-19 moll-1 (K(FeS), ZERO)) ;or less, defined as zero here

Influences I+(amount-of(FeS), Am[formation-rate]) ;the higher the formation rate ;the more precipitation we get for FeS

Fig. 3 Precipitation process for FeS (adapted from [18])

Instead, the separated ions will combine to Instead, the separated ions will combine to form the initial reagent, hence lack of Sform the initial reagent, hence lack of S2-2- to to yield black precipitation. yield black precipitation.

Saturation is caused by an increase in the Saturation is caused by an increase in the concentration of the Hconcentration of the H+ + and Sand S2-2-. .

To express this phenomenon, we could write To express this phenomenon, we could write the relationships as shown in figure 2. the relationships as shown in figure 2.

Even though ion Fe present

Look at the ‘Corr’ parts

If we look at equation 1 once more, FeIf we look at equation 1 once more, Fe2+2+ + H + H22S (reagent) S (reagent) FeSFeS + 2H + 2H+ + says that FeS might not be formed if Hsays that FeS might not be formed if H++ is in is in excess. excess.

When HWhen H++ is saturated it will tend to combine with S is saturated it will tend to combine with S2-2- to to revert the reagent. There is a situation where Hrevert the reagent. There is a situation where H++ could get could get saturated very fast, i.e., the saturated very fast, i.e., the solution used is acidicsolution used is acidic (e.g. HCl (e.g. HCl is added) rather than neutral (e.g. water).is added) rather than neutral (e.g. water).

When this happen a chemical equilibrium is said to be When this happen a chemical equilibrium is said to be reached. Substances such as Hreached. Substances such as H22S that exhibit reverse S that exhibit reverse reaction are stored as chemical facts (domain knowledge) reaction are stored as chemical facts (domain knowledge) to allow the system knows that Hto allow the system knows that H22S will cause reverse S will cause reverse reaction. reaction.

According to the According to the Le Châtelier’sLe Châtelier’s principle, whenever principle, whenever a stress a stress is imposedis imposed at the at the right-hand sideright-hand side of the equation, of the equation, reaction reaction will move to the left-hand sidewill move to the left-hand side to release the stressto release the stress. .

In our case, the reverse reaction will occur to reduce the In our case, the reverse reaction will occur to reduce the H+. When reasoning works on the two processes, H+. When reasoning works on the two processes, equilibrium phenomena can be explained.equilibrium phenomena can be explained.

H combines with S

Discussion Discussion Qualitative reasoning ontology, take for example Qualitative reasoning ontology, take for example

the QP theory offers the QP theory offers two useful meanstwo useful means of of representations. representations.

First, it represents the First, it represents the right kinds of knowledgeright kinds of knowledge.. Second, it represents the Second, it represents the right level of right level of

knowledgeknowledge. . It is conjectured that students should deeply It is conjectured that students should deeply

understand the qualitative principles that govern a understand the qualitative principles that govern a subject, including the processes and the causal subject, including the processes and the causal relationships before they are immersed in qualitative relationships before they are immersed in qualitative problem solving. problem solving.

Right kinds refer to the implicit causal theories of physical phenomena that the model has