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These are excerpts and elaborations from my book "The Nature of Consciousness"
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Possibility Theory Possibility theory
(formulated by Zadehin 1977, and later expanded by French mathematicians Didier Duboisand Henri Prade) developed as a branch of the theory of fuzzy sets in order to deal
with the lexical elasticity of ordinary language (i.e., the fuzziness of words
such as "small" and "many"), and other forms of uncertainty
which are not probabilistic in nature. The subject of possibility theory is the possible (not probable) values
of a variable. Possibility theory is both a
theory of imprecision (represented by fuzzy sets) and a theory of
uncertainty. The uncertainty of an
event is described by a pair of degrees: the degree of possibility of the event
and the degree of possibility of the contrary event. The definition can be
dually stated in terms of necessity, necessity being the complement to one of
possibility. Its basic axioms are that:
1. the degree of possibility is one for a proposition that is true in any
interpretation and is zero for a proposition that is false in any
interpretation; 2. the degree of possibility of a disjunction of propositions
is the maximum degree of the two. When the degree of necessity of a proposition is one, the proposition is
true. When the degree of possibility of a proposition is zero, the proposition
is false. When the degree of necessity is zero, or the degree of possibility is
one, nothing is known about the truth of the proposition. Possibility Logic has a
graded notion of possibility and necessity. Back to the beginning of the chapter "Common Sense" | Back to the index of all chapters |
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