Perspectives of Neuro–Symbolic Integration

There is an obvious tension between symbolic and subsymbolic theories, because both show complementary strengths and weaknesses in corresponding applications and underlying methodologies. The resulting gap in the foundations and the applicability of these approaches is theoretically unsatisfactory and practically undesirable. We sketch a theory that bridges this gap between symbolic and subsymbolic approaches by the introduction of a Topos-based semi-symbolic level used for coding logical first-order expressions in a homogeneous framework. This semi-symbolic level can be used for neural learning of logical firstorder theories. Besides a presentation of the general idea of the framework, we sketch some challenges and important open problems for future research with respect to the presented approach and the field of neurosymbolic integration, in general.