Neural-Symbolic Systems for Verification, Run-Time Monitoring and Learning

Neural-symbolic systems combine symbolic reasoning and neural computation. They
have been shown capable of outperforming purely symbolic and purely
connectionist machine learning by using symbolic background knowledge with
data-driven learning in neural networks. A neural-symbolic system translates
symbolic knowledge into the initial structure of a neural network, which can be
trained from examples in the usual way. Learning expands or revises that
knowledge. Knowledge extraction closes the cycle by producing a revised
symbolic description of the network. Neural-symbolic systems exist for logic
programming, answer-set programming, modal and intuitionistic logic,
nonmonotonic logic, temporal logic, first-order logic, etc. In this talk, I
will review briefly the developments in the area and how neural-symbolic
systems can be used with model checking for adapting system descriptions. I
will also exemplify how system properties described in temporal logic can be
encoded in a neural network, which can be used for run-time monitoring of a
system in the presence of deviations from the system specification. I will
conclude with a brief presentation of some recent achievements and discuss the
challenges in knowledge extraction from neural networks, relational learning in
neural networks, and symbolic reasoning in deep networks.