>> At that point it was already clear that logic based inference was only so powerful, and different methods were necessary.

Er, logic inference is "only so powerful"? The first order predicate calculus (first order logic) is Turing-complete and there is plenty of maths that prove the soundess and completeness of various logic inference rules. In other words, if you can compute a function, you can compute it with first order logic.

The switch from symbolic to statistical AI happened partly because of the AI winter that cut the funding to all AI, which at the time was primarily symbolic AI, partly because it became evident that developing and maintaining huge databases of logic rules was inefficient. Some of the early work in machine learning focused on overcoming this inefficiency by inducing rules from data.