# Theories Of Probability: An Examination Of Logical And Qualitative Foundations (advanced Series On Mathematical Psychology)

by Louis Narens /
2007 / English / PDF

2 MB Download

Standard probability theory has been an enormously successful
contribution to modern science. However, from many perspectives it
is too narrow as a general theory of uncertainty, particularly for
issues involving subjective uncertainty. This first-of-its-kind
book is primarily based on qualitative approaches to
probabilistic-like uncertainty, and includes qualitative theories
for the standard theory as well as several of its generalizations.
One of these generalizations produces a belief function composed of
two functions: a probability function that measures the
probabilistic strength of an uncertain event, and another function
that measures the amount of ambiguity or vagueness of the event.
Another unique approach of the book is to change the event space
from a boolean algebra, which is closely linked to classical
propositional logic, to a different event algebra that is closely
linked to a well-studied generalization of classical propositional
logic known as intuitionistic logic. Together, these new
qualitative theories succeed where the standard probability theory
fails by accounting for a number of puzzling empirical findings in
the psychology of human probability judgments and decision making.

Standard probability theory has been an enormously successful
contribution to modern science. However, from many perspectives it
is too narrow as a general theory of uncertainty, particularly for
issues involving subjective uncertainty. This first-of-its-kind
book is primarily based on qualitative approaches to
probabilistic-like uncertainty, and includes qualitative theories
for the standard theory as well as several of its generalizations.
One of these generalizations produces a belief function composed of
two functions: a probability function that measures the
probabilistic strength of an uncertain event, and another function
that measures the amount of ambiguity or vagueness of the event.
Another unique approach of the book is to change the event space
from a boolean algebra, which is closely linked to classical
propositional logic, to a different event algebra that is closely
linked to a well-studied generalization of classical propositional
logic known as intuitionistic logic. Together, these new
qualitative theories succeed where the standard probability theory
fails by accounting for a number of puzzling empirical findings in
the psychology of human probability judgments and decision making.