Qualitative process theory

TL;DR: This paper describes the basic concepts of qualitative process theory, several different kinds of reasoning that can be performed with them, and discusses its implications for causal reasoning.

About: This article is published in Artificial Intelligence.The article was published on 1984-12-01 and is currently open access. It has received 2087 citations till now. The article focuses on the topics: Qualitative reasoning & Commonsense reasoning.

Summary

1 . Introduction

• Objects move, collide, flow, bend, heat up, cool down, stretch, compress, and boil .
• These and the other things that cause changes in objects over time are intuitively characterized by processes .
• To understand commonsense physical reasoning the authors must understand how to reason qualitatively about processes, when they will occur, their effects, and when they will stop .
• The water inside might boil, and if the container is sealed it might blow up, also known as A.

Q : What if it gets pumped?

• If there is friction and the pumping energy is constant then there will be a stable oscillation.
• Processes usually start and stop when orderings between quantities change (such as unequal temperatures causing a heat flow).
• The quantity-space representation appears both useful and natural in modeling a wide range of physical phenomena.

1.1. Motivation

• The goal of naive physics [21] is to represent the commonsense knowledge people have about the physical world .
• Here the authors examine why a theory of processes is needed, what representational burden it carries in naive physics, and the properties such a theory must have.

1 ... Change, histories, and processes

• Reasoning about the physical world requires reasoning about the kinds of changes that occur and their effects .
• Using the situational calculus to represent the changing states of the world requires writing explicit axioms that describe what things change and what things remain the same .
• Histories are divided into pieces called episodes, corresponding to a particular kind of thing happening to the object (episodes will be defined more precisely later on).
• Suppose the authors are building a clock in their basement.

K .D . FORBUS

• The assumption that things interact only when they touch in some way also permeates `non-naive' physics-action at a distance is banished, with fields and particle exchanges introduced to prevent its return .
• In particular, the qualitative representations of space and time developed in artificial intelligence have precisely the desired properties for reasoning with histories-they often allow ruling out interactions even with very little information .
• Processes are the analog of the differential equations used to describe the dynamics of the system.
• The description of possible motions it computed was used to assimilate assumptions about the character of the motion (such as assuming a ball would never reach a particular place) and to rule out potential collisions between objects.
• 'Unless the physical situation is simulated by some incremental time scheme, the reasoning involved in extending histories is inherently `non-monotonic' in the sense of [31] .

1 ..2. Reasoning tasks involving qualitative dynamics

• Aside from the role of dynamics in representing change, there are a number of reasoning tasks involving naive physics in which dynamics is central .
• Examples of inferences from several of these categories are being presented later.
• Postdiction is harder than prediction because of the potential necessity of postulating individuals .
• Looking at it the authors may deduce that a coke bottle was dropped, but they do not know much about its history before that, or about anything else that might have been in the room before they looked .
• Computing a description of behavior that attributes changes to particular parts of the situation and particular other changes, also known as Causal reasoning.

1 ..3 . Desiderata for qualitative dynamics theories

• First, a dynamics theory must explicitly specify direct effects and specify the means by which effects are propagated.
• Second, it 'Simmons [42] explores the related problem of reconstructing a sequence of events from a static final state, an interesting combination of measurement interpretation and postdiction.
• Should be possible to resolve the ambiguities that arise from weak data with more precise information.
• It is important to notice that, while qualitative descriptions are approximations, not all approximations are good qualitative descriptions .
• Such as an engineer uses when estimating circuit parameters or stresses on a bridge.the authors.

1.2. Perspective

• The present theory has evolved from several strands of work in artificial intelligence.
• One exception is the notion of quantity introduced by De Kleer as part of incremental qualitative (IQ) analysis [7] , which represented quantities according to how they changed when a system imput was perturbed-increasing, decreasing, constant, or indeterminate .
• IQ analysis does not represent rates, so the authors could not deduce that if the fire on the stove were turned down the water would take longer to boil (Section 5 .4 describes how this conclusion might be drawn).
• The final strand relevant to the theory is, of course, the naive physics enterprise initiated by Pat Hayes [21] .
• In Hayes' axioms for liquids [22] information about processes is encoded in a form very much like the qualitative state idea (see for example axioms 52 through 62) .

1.3. Overview of the paper

• This paper is an expanded treatment of the central ideas of qualitative process theory [15, 16] .
• The basic deductions sanctioned by the theory are discussed as well, including analyzing the net effects of processes and the limits of their activity.
• Axioms are used only when they help the reader interested in the fine details .
• The following notational conventions are used for axioms : Predicates and relations are capitalized (e .g., Fluid-Connection), and functions are in lower case (e .g., amount-of, made-of) .
• At this writing, major parts of the theory have been tested via implementation .

2. Objects and Quantities

• To talk about change the authors first establish some conventions for describing objects and their properties at various times .
• In this section the authors describe the temporal notation used and develop the representation of quantity and the quantityspace representation for numerical values .
• Individual views are then introduced to describe both the contingent existence of objects and object properties that change drastically with time .
• Finally histories are introduced to represent what happens to objects over time .

2.1 . Time

• A novel feature of this representation is that two intervals can meet ; that is, the start of one interval can be directly after the end of another interval such that no interval lies between them (i.e., time is not dense).
• Instants are represented as `very short' intervals which have zero duration but still have distinct beginnings and ends.
• The authors will assume the functions start and end which map from an interval to the instants that serve as its start or end points .
• The function during maps from an interval to the set of intervals and instants contained within it .
• The authors will assume a function time which maps from instants to some global ordering, and a function duration which maps from an interval to a number equal to the difference between the times for the start and the end of the interval.

2.2. Quantities

• Processes affect objects in various ways .
• Many of these effects can be modeled by changing parameters of the object, properties whose values are drawn from a continuous range .
• Examples of parameters that can be represented by quantities include the pressure of a gas inside a container, one-dimensional position, the temperature of some fluid, and the magnitude of the net force on an object.

2.3. Parts of quantities

• The derivative of a quantity can in turn be the amount of another quantity (for example, the derivative of (one-dimensional) position is the amount of (one-dimensional) velocity).
• Amounts and derivatives are numbers, and the functions A and D map from quantities to amounts and derivatives respectively .
• Every number has distinguished parts sign and magnitude.
• The functions s and m map from numbers to signs and magnitudes respectively .
• For conciseness, the combinations of these functions that select parts of quantities are noted as: Am -magnitude of the amount, AS -sign of the amount, Dm -magnitude of the derivative, or rate, D. -sign of the derivative.

2 .4 . The quantity space

• The orderings and even the elements of a quantity space are not fixed over time .
• The elements in a particular quantity space are determined by the comparisons needed to establish certain kinds of facts, such as whether or not processes are acting .
• This means there are only a finite number of elements in any reasonable quantity space, hence there are only a finite number of distinguishable values .
• Thus the quantity space is a good symbolic description, because it supports case analyses and reasoning by exclusion.
• Two elements that are ordered and with no elements in the ordering known to be between them are called neighbors.

Ievel(WD) has height(bottom(D)), height(top(D)), and level(WC) as neighbors, but not height(top(C))

• Determining neighbors will be important in determining when processes start and stop acting .
• The arrow indicates that the quantity at the head is greater than the quantity at the tail.
• For simplicity, the authors ignore temporal references here.
• The authors shall now be a bit more formal about defining quantity spaces and the relationships between parts of quantities .
• 0) (Taxonomy is drawn from [22] and means that exactly one of its arguments is true .) 5 illustrates the algebra used.

2.5. Individual views

• Objects can be created and destroyed, and their properties can change dramatically .
• Water can be poured into a cup and then drunk, for example, and a spring can be stretched so far that it breaks .
• For every collection of objects that satisfies the description of the individuals for a particular type of individual view, there is a view instance, or VI, that relates them .
• The distinction between preconditions and quantity conditions is important.
• The intuition is to separate changes that can be predicted solely within dynamics (quantity conditions) from those'which cannot .

2.6. Functional relationships

• A key notion of qualitative process theory is that the physical processes and individual views in a situation induce functional dependencies between the parameters of a situation .
• From this statement alone the authors do not know _what other parameters might affect level, nor do they know the exact way level varies with amount-of .
• When it is necessary to name the function, the authors write Function-Spec((id), ) where (id) is the name of the function being described and (spec) is a set of «a statements and correspondences (see below) that further specify that function.
• Suppose for example that level is expressed in a global coordinate system, so that whenever two open containers whose bottoms are at the same height have fluid at the same level the pressure the fluid exerts (on the bottom, say) is the same .
• If the length of the band described above is greater than its rest length the internal force is greater than zero.

2.7. Histories

• To represent how things change through time the authors use Hayes' notion of a history.
• Episodes and events differ in their temporal aspects .
• The particular class of histories Hayes introduced are called parameter histories, since they are concerned with how a particular parameter of a specific individual changes .'.
• Since processes will often act between several objects, the authors need a way of talking about several objects at a particular time .
• The question of what constitutes a useful situation brings us back to the local evolution problem described in the introduction .

3 . Processes

• So far their description of the world has been static-the authors can say that things are different from one time to another, but have not provided the means by which changes actually occur.
• The ways in which things change are intuitively characterized as processes .
• A physical process is something that acts through time to change the parameters 10In current AI systems this problem usually does not arise because the situations under consideration are composed solely of relevant objects .
• As the authors attempt to make programs that can deal with more realistic problems this issue will become very important . of objects in a situation .
• Examples of .processes include fluid and heat flow, boiling, motion, stretching and compressing.

3.1. Specifying processes

• Fig . 10 illustrates process specifications for heat flow and boiling .
• To recapitulate, for every collection of objects that satisfy the individuals specification for a particular type of process, there is a process instance (PI) that relates them .
• The relations component usually describes, but is not limited to, indirect effects via functional relationships between quantities, such as the flow rate in fluid flow being qualitatively proportional to the difference in the pressures of the contained fluids involved .
• Heat flow happens between two objects that have heats and are connected via some path through which heat can flow .
• Boiling happens to a contained liquid being heated, and creates a gas made of the same stuff as the liquid .

3 .2 . Influences and integration

• There are two kinds of influences, direct and indirect .
• The influences component of a process specifies the direct influences imposed by that process .
• Importantly, processes are the only source of direct influences .

3.3. Limit points

• Recall that a quantity space consists of a collection of elements and ordering relations between them .
• The major source of elements for the quantity space of some quantity Q are the numbers and constants that are compared to Q via quantity conditions .
• Because they correspond to discontinuous changes in the processes that are occurring (or individual views that hold), they are called limit points.
• Limit points serve as boundary conditions .
• These different modes of behavior are modeled by individual views.

Sole mechanism assumption. All changes in physical systems are caused directly or indirectly by processes.

• This process vocabulary can be viewed as specifying the dynamics theory for the domain .
• A physical situation, then, is described by a collection of objects, their properties, the relations between them (including individual views), and the processes that are occurring .
• If the authors make the additional assumption that their process vocabulary for a domain is complete, then they know what types of quantities can be directly influenced .
• Thus the authors know all the potential ways any physical situation will change .
• Without these closed-world assumptions (see [5, 35, 38] ), it is hard to see how a reasoning entity could use, much less debug or extend, its physical knowledge.

3.5. Reprise

• It may be tempting to think that processes are mere abbreviations for `deeper' representations, such as constraint laws .
• The aims of naive physics are not the ysame as the aims of physics or engineering analysis.
• In physics the authors are trying to construct the simplest models that can make detailed predictions about physical phenomena .
• Qualitative process theory concerns the form of dynamical theories, not their specific content .
• The language provided by the theory also allows one to write a heat flow process that violates energy conservation and transfers `caloric fluid' between the source and destination .

3.6.1 . Finding possible processes

• A process vocabulary specifies the types of processes that can occur .
• Given a collection of individuals and a process vocabulary, the individual specifications from the elements in the process vocabulary must be used to find collections of individuals that can participate in each kind of process .
• These process instances (PIs) represent the potential processes that can occur between a set of individuals.
• A similar deduction is used for finding view instances.

3.6.2 . Determining activity

• By determining whether or not the preconditions and quantity conditions are true, a status can be assigned to each process instance for a situation .'.
• The collection of active PIs is called the process structure of the situation .
• The process structure represents "what's happening" to the individuals in a particular situation .
• Similarly, the view structure is the collection of active VIs in the situation .
• Whenever the authors discuss the process structure, they usually include the view structure as well.

3.6.3. Determining changes

• Most of the changes in an individual are represented by the Ds-values for its quantities.
• If all the signs of the influences are the same then the D 3-value is simply that sign.
• Since the authors do not have numerical information, ambiguities can arise .
• This is not the case; the key observation is that, in physical systems, such loops always contain a derivative relationship-which is modeled by a direct influence, not a qualitative proportionality .
• Suppose for instance that their model of fluid flow included influences to model the changes in heat and temperature that result from mass transfer .

3.6.4. Limit analysis

• Changes in quantities can result in the process and view structures themselves changing.
• The ordering between each neighbor and the current amount of the quantity can be combined with the Ds-values of each to determine if the relationship will change (see Fig . 12 ).
• The set of changes between single inequalities plus consistent conjunctions of changes (corresponding to the occurrence of simultaneous changes) forms the set of quantity hypotheses for the current situation .
• This assumption rules out a simple form of Zeno's paradox .
• Note, however, that relaxing this assumption would result in only one additional state in the possibilities returned by the limit analysis-that the current set of active processes never changes .

114 K .D . FORBUS

• This table summarizes how the ordering relationship between two quantities may change according to the sign of their derivatives over some interval.
• If the bottoms of two open containers are at the same height and the only thing happening is a fluid flow from one to the other, then it is impossible for the source of the flow to run out of liquid.
• Second, a process can influence more than one quantity .
• There are some special situations, due to the nature of quantities, where sometimes the authors can rule out classes of hypotheses without detailed domainspecific information .
• If all of the quantities are changing (Ds value of -1 or 1) in ways that insure the relationships between them will change, then the finite difference between C and D implies that the change in the equality between A and B occurs first .

Equality change law. With two exceptions, a process structure lasts over an interval of time . It lasts for an instant only when either

• (1) a change from equality occurs, or (2) a change to equality occurs between quantities that were influenced away from equality for only an instant.
• The first case assumes that the values of numbers are not `fuzzy', and the second case assumes that the changes wrought by processes are finite (i .e., no impulses).
• Remember that the set of quantity hypotheses consists of single changes and conjunctions of single changes .
• Consider the set of conjunctive hypotheses which contain only changes that occur in an instant, and in particular, the maximal element (in terms of inclusion) of the set .
• Depending on the domain and the style of reasoning to be performed there are several choices ; among them simulation [2] , algebraic manipulation [6] , teleology [7] , or possibly default assumptions or observations [17] .

3.7. Processes and histories

• Adding processes to the ontology of naive physics requires extending the history representation of change .
• Process and view episodes are included in the histories of the objects that participate in the process, and the union of the object's parameter histories and the histories of the processes and views it participates in comprise its total history .
• Fig. 13 illustrates the full history over a small interval for the ball being dropped through a flame discussed previously.
• As mentioned previously, the two key problems in reasoning with histories are the local evolution problem (extending the known portion of an object's history, preferably by carving up the situation into pieces that can be reasoned about semi-independently) and the intersection/interaction problem .
• The authors usually don't worry about getting their feet wet in a basement despite ; the proximity of flowing water and steam in their plumbing .

3.8. A language for behavior

• The first kind consists of processes that form a p-component, a shared-parameter combination .
• Consider for example a resistor in a circuit that never exceeds its electrical capacity .
• When writing encapsulated histories, the authors will use most of the syntactic structure of processes and individual views, in that the combination will have individuals, preconditions, quantity conditions, and relations .
• In performing an energy analysis, for example, the quantity conditions are rewritten in terms of energy .

The following restrictions hold on cases:

• The preconditions and quantity conditions for P1 imply the preconditions and quantity conditions for P2 respectively.
• All statements in the relations and influences fields of P2 hold for P1 unless explicitly excluded, also known as Inheritance.
• The abstract motion process already includes the individuals B, a movable object, and dir, a direction .
• The abstract motion process will be explained in more detail later .
• In sliding and rolling there is contact with a surface, but different constraints on the kind of contact.

4 . Examples

• The examples are fairly informal for two reasons.
• Second, while QP theory provides the means to represent an important part of a domain's theory, a complete model usually has to address several considerations besides dynamics, such as spatial reasoning (qualitative kinematics, as it were) .
• Still, these examples are complex enough to provide an indication of the theory's utility .
• The assumptions about other kinds of required knowledge are noted as they occur.

4 .1 . Modeling fluids and fluid flow

• This example illustrates some of the basic deductions sanctioned by qualitative process theory and introduces the representations of fluids that are used in other examples.
• Consider the two containers illustrated in Fig .
• This model is very simple, because it ignores the possibility of different kinds of fluids and the details of how fluids move through the fluid paths ( [22] illustrates some of the distinctions that should be drawn in a more detailed model).
• Usually the authors will just represent the interconnections between possible process structures as they have done here .
• With only a single process and simple relationships between quantities, resolving influences and limit analysis are simple.

4.2. Modeling a boiler

• The situation consists of a container partially filled with water .
• Initially the lid of the container is open ; the authors stipulate that if boiling ever occurs, the lid will be closed and sealed .
• The authors will ignore the rest of the details, such as the nature of heat and fluid paths and the detailed geometry of containers.
• (Note that, as usual, the authors are making a closed-world assumption both in assuming their process vocabulary is complete and that they know all of the relevant individuals .).
• This in turn causes a heat flow to the air surrounding the container and to the air and the water inside the container .

A[t-melt(WATER)] -> A[temperature(WATER)] -> A[temperature(SOURCE)]

• Suppose the preconditions for the heat flow continue to be met and boiling occurs .
• Then by their initial assumptions the lid will be sealed, closing all fluid flow paths and thus preventing any flows .
• The amount-of quantity spaces that result are illustrated in Fig .
• To find out, the authors must go back to the boiling episode and check the indirect consequences of the changes in amount-of.

ZERO -~ A[amount-of(WATER)] ZERO --> A[amount-of(STEAM)]

• In particular, Assume the function that determines pressure is continuous in amount-of, heat, and volume .
• Then for any particular D[amount-of] and D[heat], the authors can find a corresponding D[volume] such that (M D8 [pressure].
• Let Since the water and steam are in contact their pressures will be equal, and since pressure indirectly affects the boiling temperature, the boiling temperature will also rise .
• The possible relative rates introduce three cases .

(Dm[t-boil(WATER)] > Dm[temperature(STEAM)])

• Then the boiling will stop, the heat flow will increase heat again, the temperature will rise, and the boiling will begin again .
• 18The astute reader will notice that this situation gives rise to a cycle of states that corresponds to a rising equilibrium rather than an oscillation .
• In all three cases, the increasing pressure makes 132 K.D. FORBUS.

4.3. Modeling motion

• Since QP theory describes the form of qualitative dynamics theories, it can only carry part of the representational burden imposed by motion .
• After developing a simple motion vocabulary, the authors compare the QP descriptions with the earlier qualitative-state representation in order to illustrate the strengths and weaknesses of the QP model.

4.3 .1. A simple motion vocubulary

• By ignoring the particular kind of motion it exhibits (FLY, SLIDE, SWING, ROLL) which depends on the particular shape and type of contact with other surfaces, the authors can develop an abstract vocubulary for describing motion .
• The symbols 1 and -1 will denote distinct directions along some axis, and for some quantity Q and direction dir Direction-Of(dir, Q) will be true exactly when As[Q] equals dir .
• Here friction occurs when there is surface contact, and produces a force on the object that is qualitatively proportional to the normal force and acts in a direction opposite that of the motion .
• The simplest description of a collision just involves a reversal of velocity, as illustrated in 19McCloskey [28] and Clement [50] argue that naive theories of motion in their culture correspond to impetus theories, rather than Aristotelian theories as previously suggested.
• An object's impetus is an internalized force that keeps on pushing the object, thus causing motion .

Relations: (M A[velocity(B)] start(E)) = -(M A[velocity(B)] end(E)) (M A[velocity(B)] during(E)) = ZERO duration(E) = ZERO (T contact(B, C, dir) end(E))

• Sometimes all that is known about a situation is the particular kind of behavior that will occur .
• Envisioning using such simulation rules is simple ; given an initial state, use the rules to generate a set of new states.
• And because the authors have specified a direction, they now must also specify the place they are starting from, since that will determine what the neighbors in the position quantity space are .
• The qualitative simulation rules would thus roughly correspond to a compilation of the limit analysis on this new motion vocabulary.
• In particular, the qualitativestate representations for motion are not easily composable to form descriptions of more complex systems .

4.4. Modeling materials

• If it doesn't move, then its internal structure is `taking up' the force (this can happen even if it does move-try hitting an egg with a baseball bat-but the authors will ignore this case).
• The authors can use the notions-of quantity and process provided by QP theory to state these facts .
• Three individual views describe the states of an elastic object, either stretched, relaxed, or compressed .
• If the applied force is very small, objects will often behave rigidly .
• First, consider what pushes and pulls are .

time (T( Push-Transmitter(endl (s), end2(s))

• Now the problem becomes how to define Taut .
• This model assumes that only the ends of the string contact other objects-it would fail for a rope hanging over a pulley, for instance .
• This of course ignores the fact that the non-free segments may not be tight, as say for string lying on the floor .
• A full definition would also require tension along the entire string, but the authors have strayed far enough from dynamics already.

4.5. An oscillator

• Dynamical reasoning involves more than just simulation .
• Here the authors will examine a simple situation involving motion and materials, ascertain that it oscillates, and perturb it to figure out under what conditions it will remain stable.
• Note that the view and process structures must be the same, because in principle the preconditions might have changed.
• The authors can however deduce that the spring won't break under the conditions above.
• For every object there is a total energy, which is the sum of its energy quantities (Fig . 38 describes systems and energy quantities more formally, and Fig . 39 describes sources, sinks, and conservation laws).

VtEtime

• A simple energy theory-energy and systems .
• The energy of a system is the sum of the energy quantities for its parts.
• This means that the block can only go out as far as it was at t1, since if it ever went out farther the authors would contradict the previous statement.

V pi E process-instance V sys E system

• A simple energy theory-sources, sinks, and conservation .
• This means that, unlike the encapsulated histories previously encountered, the authors cannot use this one for simulation .
• Then while the quantity condition above will remain true, the energy will be continually increasing, which means the force on the spring will increase over time (since during part of the cycle the energy is all in the spring, and the spring energy is qualitatively proportional to the internal force of the spring) .
• The authors will call the energy lost to friction over a cycle e-loss and the energy added to the system over a cycle e-pump .
• If the energy of the system is at this point, the influences of friction and pumping will cancel and the system will stay at this energy .

5. Further Consequences

• Qualitative process theory provides a representational framework for a certain class of deductions about the physical world .
• In this section the authors examine the consequences of this framework for several `higher-level' issues in commonsense physical reasoning .
• Several of these issues arise in reasoning about designed systems, while others arise more generally.

5.1. Distinguishing oscillation from stutter

• There are several ways to produce such summaries .
• A real oscillation will therefore include process episodes that last over an interval, whereas stutter-a kind of `mythical oscillation-will only include process episodes that last but an instant.
• First, I propose that causality requires some notion of mechanism .'.
• The graphical notation for constraint networks is similar to logic diagrams, except that `terminals' are given explicit names and the `devices' are multi-functional .
• These are dependent quantities, and should not be the subject of assumptions in building causal arguments.

5.3. Qualitative proportionalities revisited

• The previous section argued that functional dependence is central to the kind of `incremental' causality that people find useful in reasoning about the physical world.
• Construction a learning theory for physical domains will require ways to learn process descriptions and causal connections.
• The return bar would move the paper up, but before doing so would return the carriage to the right .
• Being able to say there are no intervening parameters is then also a useful ability.
• Out notation will be o-all((quantity), (plus-set), (minus-set)) which means that there is a function which determines the quantity, relies on the quantities in the two sets solely, and is strictly increasing in its dependence on the quantities in the plus-set and strictly decreasing in its dependence on the quantities in the minus-set .

QUALITATIVE PROCESS THEORY 159

• Thus the collection of xo-statements that are true for a system can vary as a function of the values of the quantities, which is why they usually appear within some individual view or process .
• The idea of a mode of a system in 'real' physics roughly corresponds to particular process and view structures which hold during the system's operation.

5.4. Differential qualitative analysis

• IQ analysis concerns the relationship between two situations, one of which is the direct result of things happening in the other.
• The authors often have an idea of the different consequences that would result if something were changing a bit faster-if they put the heat up on the stove the water in the kettle would boil sooner, and if their arm were quicker the serve would have been returned.
• The second number is the duration of the interval associated with the episode .
• Intuitively the authors know that if the rate changes, the duration of time will vary inversely, or the distance the value moves will vary accordingly for the same duration .
• This often is not the case, so the authors must require that either the beginning or the end of the two episodes being compared are the same .

6. Discussion

• This paper has described qualitative process theory, which attempts to model aspects of commonsense reasoning about physical domains .
• Physical processes are the mechanisms by which change occurs .
• (2) Numerical values can be usefully represented by the quantity space, which describes the value of a number in terms of inequalities.
• These basic deductions can be woven together to perform more complex inferential tasks, such as envisioning.
• (6) QP theory provides a structured role for the use of experiential and default knowledge in physical reasoning-for example, in resolving influences and choosing or ruling out alternatives in limit analysis.

6.1 .1 . ICAI and engineering problem solving

• Since many engineered devices are implemented as physical systems, QP theory should be useful in reasoning about them .
• Indeed, QP theory was developed in part to be used in the STEAMER project, whose goal is to provide instruction about steam propulsion plants for Navy trainees .".
• This technique would have several advantages, for example, the qualitative-reasoning system in the compiler itself need not be especially fast, and more sophisticated techniques for generating explanations could be exployed than would otherwise be possible (such as McDonald's MUMBLE [32] .
• A good boiler design will provide operating regions in which the individual views representing these undesired conditions are inactive .
• This would be useful because it seems that a common source of human error in operating complex systems (such as nuclear power plants) is premature commitment to a particular theory about the state of the system (see [371) .

6 .1 .2. Economic modeling and decision support systems

• In economics, for example, physical limitations often prove important.
• Storage capacities, transportation capacities, and rates of manufacture are important examples (see [20, 45] ) .'.
• The features which make qualitative models useful for physical reasoning, such as the ability to characterize the classes of things that can happen even with very little data, should be useful in other domains, especially in domains where numerical data is unreliable or hard to come by.
• Caution seems advisable in attempting such applications .
• In addition, the very structure of the domain can change with time ; for instance, the tax code can change .

6.2. Other work

• The first attempts to formalize processes modeled them as collections of interacting automata [3] or extended sTRIPs-like operators [24] .
• Time was modeled by specifying that automata representing quantities changed instantly while automata representing processes took an interval of time to change .
• While a significant advance over the models of action available at the time, the importance of qualitative descriptions had not yet been understood .
• If you are told that there is dynamite underneath, your estimate will be considerably different .

6.3. Current directions

• Since the original publication of qualitative process theory, several projects have adopted or extended some of its ideas .
• (2) Reid Simmons has developed process representations for geologic inter-pretation by qualitative simulation, including the use of a diagram .
• His system extends the quantity-space representation by using quantitative information, including representing values by intervals and using specific equations to describe functional dependencies [42] .
• (3) Johan De Kleer and John Seely Brown have extended their devicecentered qualitative physics for machines to include inequality information so that state transitions can be more precisely modeled (see this volume) .
• (4) Al Stevens, Dan Weld, and Albert Boulanger are using qualitative process theory in constructing a theory of explanations for machines [47] .