There is an obvious tension between symbolic and subsymbolic theories, because both show complementary strengths and weak nesses 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 ap proaches by the introduction of a Toposbased semisymbolic level used for coding logical firstorder expressions in a homogeneous framework. This semisymbolic level can be used for neural learning of logical first order theories. Besides a presentation of the general idea of the frame work, we sketch some challenges and important open problems for future research with respect to the presented approach and the field of neuro symbolic integration, in general.
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Perspectives of NeuroSymbolic IntegrationExtended Abstract