In what ways can connectionist artificial intelligence (neural networks) be integrated with Good Old-Fashioned A.I. (GOFAI)? For instance, how could deep neural networks be integrated with knowledge bases or logical inference? One such example seems to be the OpenCog + Destin integration.
A neural net with even a single hidden layer is capable of Universal function approximation - it can approximate any continuous function 'as closely as you like'.
Hence, one option would be to look for GOFAI applications that would benefit from this property - for example, in state-space search approaches where the utility of a state is not readily defined in advance, and could instead be learned.