In Bayesian probability theory, probabilities are defined for
propositions which follow the laws of Boolean algebra
[11,132] and can be either true or false, i.e.,
propositions which satisfy the laws of ordinary logic. We shall
denote the propositions by capital letters. Three basic operations
are defined in Boolean algebra: conjunction, disjunction and negation.
We shall denote ``*A* and *B*'' by *AB*, ``*A* or *B*'' by *A*+*B* and
``not *A*'' by .

Natural language involves propositions whose truth value is ambiguous,
``sky is blue'' for example. The definitions of words sky and blue
are more or less ambiguous and therefore it is possible to think that
the truth value of ``sky is blue'' is neither completely true nor
completely false but something in between. Fuzzy logic
[136,133] tries to capture the ambiguity of propositions in
natural language, but we shall consider only unambiguously defined
propositions^{}.