Kevin M. Clermont (Cornell University – School of Law) has posted Conjunction of Evidence and Fuzzy Logic on SSRN. Here is the abstract:
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Classical logic and probability theory produce in law the troublesome conjunction paradox. They tell us the conjoined likelihood of independent elements equals the product of each element’s likelihood. Meanwhile, the law requires each element of a cause of action to meet the standard of proof, but it does not apply the standard of proof to the conjunction. Hence, if the cause entails more than one element, no assurance exists that the product of likelihoods will meet the standard of proof.
Fuzzy logic, however, explodes the conjunction paradox. It does so by saying that the elements’ conjoined likelihood equals the least likely element’s likelihood. This is exactly equivalent to the law’s approach. That consistency constitutes a powerful piece of proof that the law employs fuzzy logic in preference to classical logic and probability theory.