Piero Scaruffi(Copyright © 2013 Piero Scaruffi | Legal restrictions )
These are excerpts and elaborations from my book "The Nature of Consciousness"
"Qualitative" reasoning is the discipline that aims at describing a physical system through something closer to common sense than Physics' dynamic equations.
In “Qualitative” Physics, a physical system is conceived as made of parts that contribute to the overall behavior through local interactions, and its behavior is represented inside some variation of Hayes' measure space.
Ultimately, qualitative reasoning is a set of methods for representing and reasoning with incomplete knowledge about physical systems. A qualitative description of a system allows for common-sense reasoning that overcomes the limitations of classical Logic. Qualitative descriptions capture the essential aspects of structure, function and behavior, at the expense of others. Since most phenomena that matter to ordinary people depend only on those essential aspects, qualitative descriptions are enough for moving about in the world.
Several approaches are possible, depending on the preferred ontology: Benjamin Kuipers adopts qualitative constraints among state variables; Johan DeKleer focuses on the devices (pipes, valves, springs) connected in a network of constraints; Kenneth Forbus deals with processes by extending the notion of history. Ultimately, a system's behavior is almost always described by constraint propagation.
DeKleer describes a phenomenon in a measure space through "qualitative differential equations", or "confluences". His "envisionment" is the set of all possible future behaviors.
Forbus defines a “quantity space” as a partially ordered set of numbers. Common sense is interested in knowing that quantities "increase" and "decrease" rather than in formulas yielding the quantities’ values in time. In other words, the sign of the derivative is more important than the exact value of a quantity.
Kuipers formalizes qualitative analysis as a sequence of formal descriptions. From the structural description the behavioral description (or "envisionment") can be derived, and from this the functional description can be derived. In his quantity space, besides the signs of the derivatives, what matters most are critical or "landmark" values, such as the temperature at which water undergoes a phase transition. Change is handled by discrete state graphs and qualitative differential equations. A qualitative differential equation is a quadruple of variables, quantity spaces (one for each variable), constraints (that apply to the variables) and transitions (rules to define the domain boundaries). Each of these three frameworks prescribes a number of constraint propagation techniques, which can be applied to a discrete model of the physical system.
Physics is a science of laws of nature which are continuous and exact. Things move because they are subject to these laws. Qualitative Physics is a science of laws of common sense that are discrete and approximate. Things move because other things make them move. Qualitative Physics may not be suitable for studying galaxies and electrons, but can work wonders at analyzing a piece of equipment, a machine, and, in general, a physical system made of components. For example, it has been applied to troubleshooting machines: a model of behavior of a system makes it easier to figure out what must be wrong in order for the system to work the way it is working, i.e. which component is not doing its job properly.
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