Perspectives of Neuro--Symbolic Integration – Extended Abstract --

Abstract

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 first-order 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 neuro-symbolic integration, in general.