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Both statistical approaches and extensions to logic were tried.
One statistical approach, [[
Other, non-probabilistic extensions to first-order logic to support were also tried. For example, [[non-monotonic reasoning]] could be used with [[Reason maintenance|truth maintenance systems]]. A [[truth maintenance system]] tracked assumptions and justifications for all inferences. It allowed inferences to be withdrawn when assumptions were found out to be incorrect or a contradiction was derived. Explanations could be provided for an inference by [[Explainable artificial intelligence|explaining which rules were applied]] to create it and then continuing through underlying inferences and rules all the way back to root assumptions.{{sfn|Russell|Norvig|2021|pp=335-337}} [[Lofti Zadeh]] had introduced a different kind of extension to handle the representation of vagueness. For example, in deciding how "heavy" or "tall" a man is, there is frequently no clear "yes" or "no" answer, and a predicate for heavy or tall would instead return values between 0 and 1. Those values represented to what degree the predicates were true. His [[fuzzy logic]] further provided a means for propagating combinations of these values through logical formulas.{{sfn|Russell|Norvig|2021|p=459}}
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