13.1 Sources and Semantics of Uncertainty 323
perception of the world. To address these issues, one must not only ac-
cept that our knowledge about the world is uncertain, it is also necessary
to quantify and formalize the notion of uncertainty so that statements about
the world will have more than just a vague, informal meaning.
Many mathematical theories have been introduced to give a formal seman-
tics to uncertainty. On can classify these approaches into two main classes
(Perez and Jirousek 1985):
- Extensional. An approach of this kind treats uncertainty as a generalized
truth-value attached to formulas. Uncertainty is computed by applying
rules or procedures. When rules are used, the computation of uncertainty
is analogous to the determination of facts by a rule-based system, as in
chapter 3. When procedures are used, uncertainty is computed in a man-
ner that is more closely related to programming with traditional program-
ming languages such as Perl. - Intensional. This approach attaches uncertainty to “states” or “possible
worlds.” These approaches are also described as beingdeclarativeormodel-
based. Intensional approaches have been implemented using computer
systems, as, for example, data mining and stochastic control systems.
Note that uncertainty is represented using probabilities regardless of whether
a system is extensional or intensional. In this chapter we discuss some of
the major theories of uncertainty, classifying them according to the exten-
sional/intensional dichotomy. For an excellent discussion and comparison
of these two approaches to uncertainty, see (Pearl 1988). Much of the mate-
rial in this chapter is based on the treatment in Pearl’s book.
Summary
- There are many sources of uncertainty, such as measurements, unmodeled
variables, and subjectivity. - Formalizations of uncertainty can be classified as either extensional or in-
tensional. - Extensional uncertainty is a generalized truth-value.
- Intensional uncertainty assigns probabilities to possible worlds.