Editing Symbolic artificial intelligence (section)

==== Uncertain reasoning ====

Both statistical approaches and extensions to logic were tried.

One statistical approach, [[hidden Markov model]]s, had already been popularized in the 1980s for speech recognition work.{{sfn|Russell|Norvig|2021|p=25}} Subsequently, in 1988, [[Judea Pearl]] popularized the use of [[Bayesian Networks]] as a sound but efficient way of handling uncertain reasoning with his publication of the book Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference.{{sfn|Pearl|1988}} and Bayesian approaches were applied successfully in expert systems.{{sfn|Spiegelhalter |Dawid|Lauritzen|Cowell|1993}} Even later, in the 1990s, statistical relational learning, an approach that combines probability with logical formulas, allowed probability to be combined with first-order logic, e.g., with either [[Markov logic network|Markov Logic Networks]] or [[Probabilistic Soft Logic]].

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 It allowed inferences to be withdrawn when assumptions were found out to be incorrect or a contradiction was derived.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}} [[Lotfi 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}}