The construction of computational cognitive models integrating the connectionist and symbolic paradigms of artificial intelligence is a standing research issue in the field. The combination of logic-based inference and connectionist learning systems may lead to the construction of semantically sound computational cognitive models in artificial intelligence, computer and cognitive sciences. Over the last decades, results regarding the computation and learning of classical reasoning within neural networks have been promising. Nonetheless, there still remains much do be done. Artificial intelligence, cognitive and computer science are strongly based on several non-classical reasoning formalisms, methodologies and logics. In knowledge representation, distributed systems, hardware design, theorem proving, systems specification and verification classical and non-classical logics have had a great impact on theory and real-world applications. Several challenges for neural-symbolic computation are pointed out, in particular for classical and non-classical computation in connectionist systems. We also analyse myths about neural-symbolic computation and shed new light on them considering recent research advances
