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system (TMS) (Doyle, 1979). In 1980, John McCarthy formalized the theory of
Circumscription (McCarthy, 1980). Circumscription of a predict P means to
exclude most models based on P, and select only a minimum set of models in
which P is assigned to true. Different circumscription criteria will produce
different minimizations of predicates.
Quantitative simulation with computers is commonly applied for scientific
computing. Yet people often predict or explain system behaviors without detailed
calculation data. Such problem solving can not be achieved simply through
deduction, thus qualitative reasoning is proposed in AI for representation and
reasoning without precise quantitative information. In qualitative reasoning,
physical systems or procedures can be decomposed into subsystems or model
fragments, each with structuralized specifications of the subsystem itself and its
interrelationships with other subsystems. Through approaches such as causal
ordering and compositional modeling, functionalities and behaviors of the real
physical systems can be qualitatively represented. Typical qualitative reasoning
techniques include: QDE (qualitative differential equation) based modeling and
reasoning by Johan de Kleer, process-centered modeling and reasoning by
Kenneth Forbus, and constraint-centered qualitative simulation by Benjamin
Kuipers. Combined approaches of quantitative and qualitative reasoning will
make great impact to scientific decision making of expert systems.
Uncertainty is ubiquitous to real world problems, which results from the
deviation of people's subjective cognition from the objective realities. Various
causes may reflect such deviation and bring about uncertainty, such as
randomicity of things, incompleteness, unreliability, imprecision and
inconsistency of human knowledge, and vagueness and ambiguousness of natural
language. With respect to different causes of uncertainty, different theories and
reasoning methodologies have been proposed. In AI and knowledge engineering,
representative approaches of uncertainty theories and reasoning methodologies
are introduced in the following.
Probability theory is widely used to process randomicity and uncertainty of
human knowledge. Bayesian theory has been successfully applied in the
PROSPECTOR expert system, yet it relies on assigned prior probabilities. The
MYCIN model based certainty factors, adopting some assumptions and
principles for conjunction of hypothesis, is a simple and effective method, though
it lacks well established theoretical foundations.
Dempster-Shafer theory of evidence introduces the concept of belief function
to extend classical probabilities, and defines that belief function satisfies a set of
