Probability logic as a fuzzy logic

The basic principles of fuzzy logic have been formulated by Zadeh (1975) and successively examined by several other authors (as an example, see Pavelka, 1979). Now, in spite of the fact that fuzzy logic is usually considered rather far from probability logic, the purpose of some recent researches of mine is to show that fuzzy logic is a useful tool to manage information that is probabilistic in nature. Namely, we propose a fuzzy logic in which the complete theories (that is, the models) are finitely additive probabilities defined on the set F of formulas of a given language. In such a logic, given a fuzzy subset v of axioms, the fuzzy subset C(υ) of logical consequences of υ is defined as the intersection (in fuzzy set theory sense) of the class of complete theories containing υ, i.e. the lower envelope generated by υ.