Algorithms that extract knowledge from fuzzy big data: Conserving traditional science.

Big data have revealed unexpected and statistically significant correlations along with intractable propositions. In order to address this development, an algorithm is introduced that is consistent with Ramsey's theorem for pairs and G¨odel's incompleteness theorem. The algorithm assigns one of three truth values to a fuzzy proposition in order to update automatic theorem proving. A unique feature of the algorithm is an AI module that selects the multiple axiom sets needed for a proof. A metric for the AI module is the probability that the database of axiom sets is inadequate for the context. The importance of context is illustrated by a simple analog electrical circuit applied to Fermat's last theorem as contrasted with a similar exponential equation having positive real numbers for bases. Another algorithm or decision tree is introduced to differentiate risk factors from necessary conditions. A failure to recognize this distinction has impaired the public health sector for centuries and continues to do so. The second algorithm introduced here represents an effort to conserve science in general. The risk that big data pose for science is the misuse of positive, statistically significant correlations to infer causality when the correlations actually reflect risk factors or even rare coincidences. [ABSTRACT FROM AUTHOR]