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3.3. QUALITATIVE MODELS

Qualitative reasoning in AI covers a wide range of approaches that use qualitative models of physical systems to perform various reasoning tasks (Weld and de Kleer, 1990). Common to all approaches is a set of basic notions:

  • Quantity space: The state of a physical system may be characterized by a number of variables. The range of symbols that are legal values of these variables, and an ordering between the values, constitute the quantity space. Since we deal with quantitative models, the space contains values like "high," "low," etc., or "decreasing," "stable," or "increasing" for change (differential) variables.
  • Qualitative state: The qualitative state of a system (at a given instant in time) is the combination of states of all qualitative variables describing the system, each with assigned value from the quantity space. Simulating the qualitative behavior of the system means describing how the qualitative state changes over time.

There are three dominant approaches to building qualitative reasoning models.

Constraint-based approach. This approach was developed by Benjamin Kuipers (Kuipers, 1986) and is embodied in a family of programs called QSIM. A physical system is modeled by a set of qualitative constraints between the variables that comprise the model. The constraints can be seen as qualitative abstraction of the quantitative differential equations that would be used in ordinary mathematical models of the system. Kuipers introduces six constraints:

ADD -- Qualitative addition
MULT -- Qualitative multiplication
MINUS -- Change of sign
DERIV -- A variable is the derivative of another
M+ -- A variable increases as another variable increases
M- -- A variable decreases as another variable increases

Using these constraints, QSIM is able to model a physical system and to predict its qualitative behavior (see next subsection).

Component-based approach. In QSIM, the system is defined by a set of mathematical constraints, where the physical properties of the system is abstracted away. In the component approach, pioneered by de Kleer and Brown (de Kleer and Brown, 1984), the topological structure of the target system is preserved in the model. A model consists of components, connections, and material that flow through connections. "Material" may be physical material, or more abstract entities like electrical current, or even information. The behavior of each component is described by a set of local confluences, i.e., relationships between inputs, internal states, and outputs. A component model is independent of how it is hooked up to the rest of the model (the "no function in structure" principle). In the ENVISION program that embodies this approach, all variables and their derivatives have the same simple quantity space: {-, 0, +}.

Process-based approach. Similar to the previous approach, this one (Forbus, 1984) is also based on component models and system topology. But unlike the component-based approach, the process-based approach allows conceptualizations of physical interactions, called processes. This concept is used to define the dynamic characteristics of the system. The approach is embodied in a system called QPT (Qualitative Process Theory). More details can be found in Forbus (1984).

After this brief foray into the "pure AI"-based approaches to qualitative modeling, we return to the general overview of MBR. Unfortunately, there is no unifying "theory" for models used in MBR, nor any agreed-upon set of guidelines for when to apply a certain type of model. There is a true plethora of model formalisms available, but selecting and modifying a technique for a given task or application is still an art, more than an engineering discipline. We will return briefly to this issue in a later section, but first we will survey some available MBR reasoning techniques.


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