These are excerpts and elaborations from my book "The Nature of Consciousness"
Qualitative Reasoning "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. Back to the beginning of the chapter "Common Sense" | Back to the index of all chapters |