A Review of Qualitative Reasoning: Modeling and Simulation with Incomplete Knowledge

Qualitative Reasoning: Modeling and Simulation with Incomplete Knowledge describes 15 years of research in the qualitative physics field of AI by the author and his collaborators. Qualitative physics seeks to automate human reasoning about the physical world. The original focus was on the commonsense reasoning that underlies everyday life, such as cooking with stoves, pouring coffee, parking cars, crossing streets, and playing ball. Recent work focuses on expert reasoning about scientific and engineering domains, including circuits, thermodynamics, power plants, chemical plants, and botany. Qualitative physics hypothesizes that commonsense reasoning and expert reasoning are similar enough to justify a unified treatment. The common challenge is to answer qualitative questions about complex systems based on partial knowledge. The cook has only a rough idea of how the stove works; the coffee drinker knows even less about how liquid flows from the pot to the cup; and the engineer must make do with approximate models of machines, plants, and processes. Kuipers addresses qualitative reasoning about continuous, finite-dimensional dynamic systems (hereafter dynamic systems): pieces of the world that are modeled by a finite number of state variables whose time derivatives are continuous functions of their values. Scientists and engineers model many aspects of the world as dynamic systems. They use Newton’s laws to model flying balls as systems whose variables are positions and velocities. They use Kirchoff’s laws to model circuits as systems whose variables are currents and voltages. They answer questions about dynamic systems by formulating and analyzing the ordinary differential equations that govern their evolution. Kuipers sees qualitative reasoning as the task of formulating and analyzing dynamic systems that model commonsense or expert domains. Like most qualitative physics researchers, he believes that ordinary differential equations are inappropriate for qualitative reasoning because they presuppose complete, precise models of dynamic systems, which are often unrealistic and unnecessary. People cross streets without knowing exactly how fast the traffic is moving or how quickly it can screech to a halt. Engineers design and repair artifacts whose physics are unmanageably complex or incompletely understood. Kuipers extends the language of ordinary differential equations with constructs that encode partial knowledge about variable values and the structure of the equations. The task of qualitative reasoning is to formulate and analyze generalized equations. The organization of the book roughly follows the progress of Kuipers’s research: Chapters 1 through 6 present the basic modeling language and analysis algorithm and illustrate them on a range of case studies. Chapters 7 through 12 present extensions that increase the expressive power of the language and the predictive power of the algorithm. Chapters 13 and 14 describe tools for model building. The modeling language consists of qualitative differential equations that define the time derivatives of variables as functions of their values. The functions can contain arithmetic operators, symbolic parameters, and functional parameters. For example, one equation for a falling ball is x .. = gx, with g < 0, which states that the acceleration of x (the second time derivative) equals a negative constant times x, but a more abstract equation is x .. = f(x), with f ∈ M–, which states that the derivative is a monotonedecreasing function of x. The variables and the symbolic parameters take on interval and point values, called qualitative values, drawn from a finite partition of the real line. The most common partition is {(– ∞,0), 0, (0,∞)}, abbreviated as [−], 0, and [+]. The analysis algorithm computes the sequence of qualitative values of the state variables starting from a given initial state. Given an initial state of x = [+] and x . = 0, it computes a final state of x = [–] and x . = [–] from either ball equation. The basic analysis algorithm is a two-stage constraint propagation. The first stage propagates variable values using interval arithmetic. For example, x = [+] and k = [2] imply x .. =