Discovering logical knowledge in non-symbolic domains

Deep learning and symbolic artificial intelligence remain the two main paradigms in Artificial Intelligence (AI), each presenting their own strengths and weaknesses. Artificial agents should integrate both of these aspects of AI in order to show general intelligence and solve complex problems in real-world scenarios; similarly to how humans use both the analytical left side and the intuitive right side of their brain in their lives. However, one of the main obstacles hindering this integration is the Symbol Grounding Problem [144], which is the capacity to map physical world observations to a set of symbols. In this thesis, we combine symbolic reasoning and deep learning in order to better represent and reason with abstract knowledge. In particular, we focus on solving non-symbolic-state Reinforcement Learning environments using a symbolic logical domain. We consider different configurations: (i) unknown knowledge of both the symbol grounding function and the symbolic logical domain, (ii) unknown knowledge of the symbol grounding function and prior knowledge of the domain, (iii) imperfect knowledge of the symbols grounding function and unknown knowledge of the domain. We develop algorithms and neural network architectures that are general enough to be applied to different kinds of environments, which we test on both continuous-state control problems and image-based environments. Specifically, we develop two kinds of architectures: one for Markovian RL tasks and one for non-Markovian RL domains. The first is based on model-based RL and representation learning, and is inspired by the substantial prior work in state abstraction for RL [115]. The second is mainly based on recurrent neural networks and continuous relaxations of temporal logic domains. In particular, the first approach extracts a symbolic STRIPS-like abstraction for control problems. For the second approach, we explore connections between recurrent neural networks and finite state machines, and we define Visual Reward Machines, an extension to non-symbolic domains of Reward Machines [27], which are a popular approach to non-Markovian RL tasks.